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Artificial intelligence, distributional fairness, and
pivotality

Victor Klockmann, Alicia von Schenk, Marie Claire Villeval

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Victor Klockmann, Alicia von Schenk, Marie Claire Villeval. Artificial intelligence, distributional fairness, and pivotality. European Economic Review, 2025, 178, pp.105098. 10.1016/j.euroecorev.2025.105098. hal-05165240

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Artificial intelligence, distributional fairness, and pivotality☆

Victor Klockmann<sup>a,b,c</sup><u>D</u>, Alicia von Schenk<sup>a,b,c</sup><u>D</u>, Marie Claire Villeval<sup>d,e</sup><u>D</u>,<sup>*</sup>

ARTICLE INFO

JEL classification:

C91
D10
D63
D90
O33

Keywords:

Artificial intelligence

Big data

Pivotality

Distributional fairness

Experiment

ABSTRACT

In the field of machine learning, the decisions of algorithms depend on extensive training data
contributed by numerous, often human, sources. How does this property affect the social nature
of human decisions that serve to train these algorithms? By experimentally manipulating the
pivotality of individual decisions for a supervised machine learning algorithm, we show that
the diffusion of responsibility weakened revealed social preferences, leading to algorithmic
models favoring selfish decisions. Importantly, this phenomenon cannot be attributed to shifts
in incentive structures or the presence of externalities. Rather, our results suggest that the
expansive nature of Big Data fosters a sense of diminished responsibility and serves as an excuse
for selfish behavior that impacts individuals and the whole society.

# 1. Introduction

The exponential data growth in the 21st century is reshaping industries and societies worldwide. For 2025, Statista estimates that a staggering 147 zettabytes of data will be created, captured, copied, and consumed, demonstrating the unprecedented scale and complexity of the digital age.<fnref n="1" /> This increase in data availability has driven rapid adoption of Artificial Intelligence (AI) in various sectors, with 42% of companies already integrating AI into their operations. However, only a minority of these firms have taken measures to reduce or eliminate unintended biases in AI decisions, raising ethical concerns.<fnref n="2" />

While AI promises enhanced decision-making and personalized experiences, its reliance on vast datasets raises concerns about unintended consequences. The training of AI, particularly in supervised machine learning models, frequently entails many human decisions that influence its behavior, contributing to a possible diffusion of responsibility. For example, when users create, like, or report offensive content on social media, they inadvertently help train AI algorithms, often without realizing their impact or

<footnote><sup>a</sup> Department of Economics, Julius-Maximilians-Universität Würzburg, Sanderring 2, Würzburg 97070, Germany</footnote>

<footnote><sup>b</sup> Faculty of Economics and Business, Goethe University Frankfurt, Theodor-W.-Adorno-Platz 4, Frankfurt 60323, Germany</footnote>

<footnote><sup>c</sup> Center for Humans and Machines, Max Planck Institute for Human Development, Lentzeallee 94, Berlin 14195, Germany</footnote>

<footnote><sup>d</sup> CNRS, Université Lumière Lyon 2, Université Jean-Monnet Saint-Etienne, emlyon business school, GATE, 35 rue Raulin, F-69007, Lyon, France</footnote>

<footnote>☆ We are grateful to Ferdinand von Siemens, Matthias Blonski, Michael Kosfeld and seminar participants at the Goethe University Frankfurt, GATE, and the Max Planck Institute for Human Development Berlin for useful comments. Financial research support from the Leibniz Institute for Financial Research SAFE, the Goethe University Frankfurt, and the LABEX CORTEX (ANR-11-LABX-0042) of Université Claude Bernard Lyon 1, within the program Investissements Avenir (2019-ANR-LABX-02) operated by the French National Research Agency (ANR) is gratefully acknowledged. The research reported in the paper was approved by the joint Ethics Committee of Goethe University Frankfurt and Johannes Gutenberg University Mainz.</footnote>

<footnote>* Corresponding author at: CNRS, Université Lumière Lyon 2, Université Jean-Monnet Saint-Etienne, emlyon business school, GATE, 35 rue Raulin, F-69007, Lyon, France.</footnote>

<footnote>E-mail address: villeval@gate.cnrs.fr (M.C. Villeval).</footnote>

<footnote n="1">1 https://www.statista.com/statistics/871513/worldwide-data-created/; accessed on July 13, 2025.</footnote>

<footnote n="2">2 https://www.multivu.com/players/English/9240059-ibm-2023-global-ai-adoption-index-report/; accessed on July 13, 2025.</footnote>
actively intending to influence the process. Consequently, the responsibility for approving controversial content may be shared between platform operators, the AI system, and their users. In automated recruitment systems, the selection of preferred candidates by recruiters for the training data can lead to biased results, with responsibility distributed throughout the system and not just with those involved in implementing the AI.<fnref n="3" />

This diffusion of responsibility poses ethical challenges, especially in assigning accountability for AI-driven decisions. The concept of “many hands” complicates the attribution of responsibility to someone, since multiple parties contribute to the AI’s decision-making process. This creates a wedge between the decisions made by humans and the consequential effects of machine decisions also on third parties. As AI increasingly becomes integrated into critical decision-making processes, clarifying and addressing accountability becomes imperative to ensure ethical and fair outcomes (Coeckelbergh, 2020).

Our study focuses on how individuals perceive the impact of their training data on their own and others' well-being, and how this perception affects their behavior as contributors to the training dataset of a supervised machine learning model. Previous studies in different contexts have shown that pivotality or diffused responsibility for others' earnings influence prosocial or moral behavior (e.g., Choo et al., 2019; Falk et al., 2020). Drawing from the concept of the “bystander effect” (Darley and Latané, 1968), some people may use diffuse responsibility, in which they view their actions as not critical to certain outcomes, to justify selfish behavior even if such behavior potentially harms others. Bénabou et al. (2018) also explain how individuals build narratives of not being pivotal to maintain a positive self-image while acting immorally. We investigated whether these findings also apply in the context of the training of AI: does the absence of pivotality of individuals' choices for the created training data lead to the emergence of algorithms that follow less prosocial decision-making models?

We conducted an online experiment to study the causal effect of incorporating additional data sources into algorithm training on the prosociality of individuals' decisions. Increasing the number of training sources is expected to affect prosocial behavior through various mechanisms. First, it may impact moral accountability and diffuse responsibility. The increase in training sources can provide individuals with justifications for engaging in selfish behavior when faced with a trade-off between self-interest and social preferences. This is because the widening gap between an individual's decisions and the ultimate impact of machine decisions may weaken the individual's perceived responsibility. Second, there is a change in the structure of incentives. Increasing the number of training sources decreases the weight of an individual's current decisions in determining their future utility by AI decisions. This may lead to more selfish decisions as a compensatory response to the diminished influence of one's current decisions on one's future earnings.

In our experiment, the distributional fairness of AI was addressed through money allocation decisions that could be either selfish or altruistic. Participants were randomly paired to play a series of 30 binary dictator games inspired by Bruhin et al. (2019). Like in Klockmann et al. (2022), the repeated allocation decisions of the dictator in each pair were then used to train a standard machine learning algorithm. This algorithm aimed to predict the dictator's hypothetical allocation choice in a 31st game and determined the earnings for both the dictator and the receiver in this game, making the training data meaningful in terms of incentives. The baseline condition, termed Full Pivotality, in which the algorithm was trained exclusively with the data of the dictator, serves a crucial purpose in our study. While in the real world AI systems often merge data from multiple sources to make recommendations or are pre-trained, there is a new trend towards developing personalized AI systems. An example are Custom GPT agents that can be trained on content and data that reflect the preferences and behaviors of a specific person or audience. Although a full pivotality scenario remains rare outside of controlled experiments, this “what if” condition enabled us to examine the impact of removing pivotality in more typical diversified data settings.

Our treatments varied the number of sources in AI training data, diminishing the degree of participants' responsibility for arising inequality in the algorithm's allocation choices. They also varied who was impacted by the AI prediction. This allowed us to manipulate the pivotality of behavior in training the machine learning model while controlling for changed financial incentives in shaping the algorithm's prediction.

In the *No Pivotality* treatment, the algorithm was trained with the choice data in the first 30 games of the player and of 99 other dictators. It then made a prediction in the 31st game, based on what it learned from these 100 training sources. By incorporating the choices of a larger group, this treatment varied both pivotality (each dictator having now a marginal responsibility for the consequences of the AI prediction) and the structure of incentives (the dictator's current decisions are weighted a hundred times less on the expected utility of their future earnings than in the Full Pivotality baseline).

To disentangle the impact of changed responsibility and financial incentives on dictators' behavior, we conducted two further treatment conditions: Full Pivotality-Others and Full Pivotality-Double. In the *Full Pivotality-Others* treatment, the dictator served as the exclusive source of training data, while the machine learning model's prediction affected exclusively the earnings of another pair of participants not involved in the training. This setup ensured that participants retained full responsibility for determining future earnings through training (as in the Full Pivotality baseline) but eliminated direct influence of the dictator's current decisions on

<footnote n="3">³ Many examples illustrate how human social behavior and preferences interfere with AI training. Companies use algorithms to tailor digital ads and product recommendations based on tracked consumer behavior, with varying levels of intensity. Robo-advice in finance, exemplified by Vanguard's Personal Advisor Services, combines AI and human expertise for investment guidance (see other examples in https://hbr.org/2018/01/artificial-intelligence-for-the-real-world; accessed on July 13, 2025). The advice's content on the composition of portfolios affects surplus distribution between providers of financial products and investors. Further, through training data, chatbots can learn social preferences based on past conversations, potentially influencing the utility experienced by another party. Consider the chatbot Tay, which, as a result of learning from politically incorrect and racist messages on Twitter, also released inflammatory messages, leading to its withdrawal (https://www.theguardian.com/world/2016/mar/29/microsoft-tay-tweets-antisemitic-racism; accessed on July 13, 2025; see also Gebru, 2020).</footnote>
their own future earnings (similar to the No Pivotality treatment). Still, the Full Pivotality-Others treatment also introduced an externality of the decisions on other's earnings. To mitigate the possibility of behavior being influenced by such an externality, we conducted the Full Pivotality-Double treatment. This treatment replicated the Full Pivotality baseline but introduced an externality by implementing the AI's decision also in another pair of participants within the session.

Our main results indicate that pivotality in generating training data for AI decision-making strongly influences individuals' behavior. Dictators who had a minimal contribution to the algorithm's training data and no responsibility for determining others' outcomes (No Pivotality) displayed significantly more selfish behavior compared to those who were fully pivotal (Full Pivotality, Full Pivotality-Double, and Full Pivotality-Others). We further estimated significantly weakened revealed social preferences and fair-mindedness when responsibility diffused (No Pivotality vs. Full Pivotality).

Our analysis revealed that when dictators possessed full pivotality in training a machine learning model that affected the payoffs of a pair of players other than themselves (Full Pivotality-Others), their allocation of payoffs showed no significant difference compared to when dictators solely generated training data impacting their own outcomes (Full Pivotality). There was no discrepancy between the prosocial behavior individuals expected from the AI when they were not personally affected monetarily, and the principles they taught the AI to apply to themselves. Moreover, when an externality was introduced for another group (Full Pivotality-Double), there was no discernible impact on selfishness. This indicates that the observed increase in selfishness when pivotality was diffused was not driven by changes in incentive structure (i.e., decreased impact of current decisions on future payoffs). Instead, the primary factor influencing their allocation decisions was a shift in the responsibility for future earnings.

Our results shed light on how accountability and individual behavior influence the distributional fairness of AI decisions. When multiple agents contribute to AI training, individual responsibility for fair outcomes diminishes. This diffusion of responsibility can lead to more selfish behavior, ultimately biasing algorithmic models in favor of the preferences of those involved in the training process. While existing research has examined the role of pivotality in human decision-making (e.g., Falk et al., 2020), our study extends this concept to AI, addressing a critical concern for policymakers and modern democracies. As AI systems increasingly shape economic and social outcomes, it becomes crucial to involve citizens in algorithmic development without exacerbating moral disengagement or fostering inequitable models in training scenarios where responsibility is diffuse.

The remainder of this paper is as follows. Section 2 reviews the related literature. Section 3 outlines the experimental design and procedures. Section 4 introduces our conjectures. Section 5 reports the results. Section 6 discusses these results and concludes.

## 2. Literature review

Our study contributes to three main strands in the literature. First, it builds on the growing body of work on AI, ethics, and algorithmic biases. Research by Anderson and Anderson (2007) and Bostrom and Yudkowsky (2014) explores foundational questions in machine ethics, emphasizing the philosophical challenges of aligning AI with human values. Bonnefon et al. (2016), Awad et al. (2018, 2020), and Rahwan et al. (2019) focus on public morality and AI decision-making, particularly in the context of moral dilemmas like those faced by autonomous vehicles. Lambrecht and Tucker (2019) and Kordzadeh and Ghasemaghaei (2022) highlight the role of algorithmic biases and the societal implications of data-driven AI systems. This literature has insisted on the importance of involving public morality in designing machine ethics that cannot be derived from the technical rules of robotics. Compared to these investigations that elicit individuals' *stated moral* preferences, the novelty of our study is using *revealed social* preferences through monetary choices that generate training data for an algorithm that makes consequential predictions. Indeed, instead of considering moral dilemmas, our design builds on distributional fairness and social preferences. This approach responds to the call for broad scientific research agendas to better understand machine behavior, including their implications in terms of fairness and accountability (Rahwan et al., 2019).

Second, our focus on training constitutes a novelty relative to the experimental literature on human-machine interactions (see the survey of Chugunova and Sele, 2022). Robots were previously introduced to isolate social preferences in strategic decision making (e.g., Houser and Kurzban, 2002; Ferraro et al., 2003; Yamakawa et al., 2016), to create a social preferences vacuum chamber (Benndorf et al., 2021), to eliminate the opponent's strategic behavior in a competition (Houy et al., 2020), or to isolate the role of social incentives in teams (Corgnet et al., 2019). In these studies, robots made decisions based on predetermined choices. In our experiment, the algorithm learned from the current players' actions and there was no strategic interaction between the players and the AI. Importantly, following the European Union's proposed AI regulation, we informed participants that their behavior created training data that would later be fed into a machine learning algorithm.<fnref n="4" />

<footnote n="4">⁴ The EU AI Act, which came into force on August 1, 2024, introduces gradual requirements aimed at increasing transparency and accountability in AI-driven processes. One such provision, set to apply from August 2, 2026, mandates that “Providers shall ensure that AI systems intended to interact with natural persons are designed and developed in such a way that natural persons are informed that they are interacting with an AI system unless this is obvious from the circumstances and the context of use”. (Chapter IV, Article 50). Although this provision focuses on transparency in AI interactions rather than the specific use of personal data for AI training, it reflects broader regulatory efforts to enhance public awareness of AI systems and their societal impact. Parallel initiatives, such as the European Parliament's 2021 mandate on algorithmic transparency for digital platform workers and Spain's requirements for platforms to disclose algorithmic decision-making to worker representatives, reinforce this trend. Even as individuals may lack full clarity on how their data is used, surveys like one by the Harvard Business Review (covering 900 people across five countries) show that 97% of respondents express concern about data misuse, despite uncertainty over what data is collected (https://hbr.org/2015/05/customer-data-designing-for-transparency-and-trust). The increasing visibility of AI systems in everyday experiences, such as personalized ads influenced by online behavior, highlights the growing awareness of AI's role in shaping personal and societal outcomes.</footnote>
Indeed, we are not investigating the impact of the awareness of training an AI, but that of pivotality when knowing that one's decisions are used to train a supervised machine learning model. Finally, in contrast to a study showing that people cheat more when interacting with a machine because of lower image concerns (Cohn et al., 2022), our AI was not passive, it learned and made impactful decisions.

Third, our study relates to the literature on moral accountability that has shown the importance of pivotality, delegation, and ambiguity in the diffusion of responsibility. Bénabou et al. (2018) showed theoretically how individuals use narratives to downplay the externalities of their actions or to pretend not to be decisive in final outcomes. Falk et al. (2020) provided evidence that individuals rely on the narrative that their actions do not influence an outcome to behave more selfishly. Falk and Szech (2013) showed that a decision maker's perceived pivotality influences the likelihood of immoral actions in a trading setting. They found that lower perceived pivotality increases the likelihood of killing a mouse and that overall, more mice are killed in treatment when pivotality is diffused. Subsequent research, such as the comment by Breyer and Weimann (2015), cautioned against drawing far-reaching policy conclusions from the findings by Falk and Szech (2013), particularly their claim that markets erode moral values. Work by Bartling et al. (2023) suggested that it may not be pivotality per se that explains these findings, but rather the repetition of choices. Their research showed that when many decisions are made, moral values tend to erode, whereas in one-shot decision-making situations, morals play a more significant role. This could provide a complementary perspective, suggesting that perceived pivotality may relate to repeated decisions in a broader sense, where the impact of each individual choice is more diffuse. In a study on collective decision-making processes, Bartling et al. (2015) reported that individuals vote strategically to avoid being pivotal for an unpopular voting result. Indeed, the lower the perceived pivotality, the easier it is for individuals to deal with deviations from their moral self-image (Ploner and Regner, 2013). The past literature has further shown that people behave more selfishly when they can use the uncertainty of the environment as an excuse (e.g., Dana et al., 2007; Grossman, 2015; Exley, 2016; Garcia et al., 2020), or when they can delegate the responsibility of a selfish choice to another player because it diffuses their responsibility (e.g., Bartling and Fischbacher, 2012; Oexl and Grossman, 2013).

We contribute to the literature by examining a new context where we exogenously vary pivotality among individuals training a machine learning algorithm, along with the presence of externalities. By creating a disconnect between human decisions and machine outcomes also affecting other parties, we investigate the interplay of pivotality, incentives, and social preferences. Notably, our non-computer science participants and the use of random forest may have fostered a sense of delegation, potentially reducing perceived accountability for algorithmic choices.

Our research on pivotality complements our companion paper (Klockmann et al., 2022), where we examined how the intergenerational transmission of training data influences individual behavior in relation to AI. In that study, pivotality remained unchanged. Subjects played dictator games, knowing that they were training an algorithm that would make decisions impacting future participants. We focused on how preferences for egalitarian or selfish outcomes shifted when participants realized their decisions affected future players and their own payoffs. We found that the share of egalitarian decisions increased only when dictators faced the risk of being harmed themselves by selfish algorithmic choices rather than merely observing potential future harm to others. In contrast, the current study investigates pivotality in algorithmic training, examining how individual responsibility shapes fair algorithm development. Thus, the two studies emphasize distinct aspects of human decision-making in distributional preferences and algorithmic training.

# 3. Design and procedures

## 3.1. Design

The experiment consisted of three parts. In Part 1, participants performed a series of real-effort tasks. Part 2 had two stages: participants played multiple mini-dictator games in the first stage, and in the second stage, a machine learning algorithm predicted what their choices would be in new games, based on observed behavior from the first stage. We also measured the dictators' beliefs about other dictators' actions. Part 3 involved eliciting socio-demographic and other individual information.

Part 1 In Part 1, each participant completed five tedious real-effort tasks that comprised finding a sequence of binary numbers within a matrix of zeros and ones (see Figure OA2.18 in Online Appendix OA.2). Participants were informed upfront that they would receive 1200 points for completing these tasks which would be used in Part 2. The objective was to generate a feeling of entitlement without introducing earnings inequality in this part. On average, participants spent about 90 s per task.

Part 2 In the first stage of Part 2 (periods 1 to 30), participants played 30 mini-dictator games (see Online Appendix OA.2 for an English translation of the instructions). Each participant was anonymously paired with another participant and was randomly assigned either the role of the dictator (“participant A”) or of the receiver (“participant B”). Matching and roles were kept fixed throughout the experiment. Each participant was informed in advance that the dictator’s choices would be used as training data for a machine-learning algorithm. This algorithm would subsequently generate predictions that would impact their earnings.

In each of the 30 periods, the dictator could choose one of two unique payoff allocations, X or Y. The dictator’s amount was always weakly higher with option X (the “selfish option”) and weakly smaller with option Y (the “altruistic option”). Because both pair members had to complete the same tasks to generate the group endowment, choosing the selfish option X when the receiver would be strictly better off with option Y indicates that the dictator was exploiting his or her exogenously assigned decision-making power.
<figure><img src="image_4.png" /><figcaption>Fig. 1. Dictator games.</figcaption></figure>

Notes: Each circle represents 12 binary dictator games. Each game is represented by a line that connects option X (in blue) and option Y (in red). The dotted lines correspond to games that were not presented to the participants. Rather, one of them was picked at random for the AI's prediction. The slope of each line represents the cost for the dictator to increase the receiver's payoff. In the top-left (bottom-right, resp.) circle, both options in each game represent disadvantageous (advantageous, resp.) inequality for the dictator. In the middle circle, the relative position depends on the chosen option. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Across the 30 games, we varied various factors to identify the participant's distributional preferences. The factors included the inequality between pair members, the sum of payoffs in each option, the dictator's relative position in the pair (advantageous or disadvantageous), and whether one option was Pareto dominant. Bruhin et al. (2019) inspired the calibration of payoffs. Fig. 1 illustrates the games, representing each by a solid line that connects option X and option Y. Table OA1.1 in Online Appendix OA.1 lists all pairs of options. At the end of this stage, one of the 30 decisions was randomly selected to determine the earnings for both the dictator and the receiver in this stage.<fnref n="5" />

In the second stage of Part 2 (period 31), we introduced a 31st pair of options X and Y. For that period, the program randomly selected one of the six games represented by a dashed line in Fig. 1 (see the details of options in Table OA1.2 in Online Appendix OA.1). However, instead of the dictator choosing between the two options, we used a random forest algorithm as the standard supervised classification method to make the decision (for more details, refer to Appendix A).<fnref n="6" /> In the baseline condition (called the *Full Pivotality treatment*, see below) the algorithm used only the 30 decisions of the dictator as training data to make an out-of-sample prediction of how this dictator would have decided in period 31 when facing a new pair of options. This prediction was implemented to determine the pair's earnings in this period. We explained that to the participants before they made their repeated choices in the first stage. Moreover, to ensure transparency, we also provided them with comprehensive information about the concept of machine learning and classification in an information box within the instructions (see Online Appendix OA.2).

Part 3 In the last part we collected sociodemographic information such as gender, age, field and length of study, average weekly spending, and school graduation grade (Abitur). We elicited participants' familiarity with artificial intelligence and machine learning and their confidence in these technologies, and we assessed their understanding of the functionality of the random forest algorithm. We asked dictators about their satisfaction with the AI prediction in period 31, and how accurately the implemented decision reflected their preferences.

<footnote n="5">⁵ Note that previous studies in experimental economics have discussed the choice of paying for one or all rounds in multi-period experiments. Our decision to pay only one choice in stage 1 was essential to make the 31st game salient and ensure that participants paid strong attention to each decision. In a theoretical analysis, Azrieli et al. (2018) prove that in rather general strategic environments with few assumptions on utility functions, paying for only one period is the best and only incentive-compatible mechanism. See also (Cox et al., 2015) when risk is involved. For eliciting social preferences, which inevitably requires multiple decisions per individual, Charness et al. (2016) do not make a strong recommendation for either paying one or several rounds and refer to the variety of methods used in the literature.</footnote>

<footnote n="6">⁶ The exact functionality of the algorithm remained consistent across all conditions and is not the primary focus of this study. Our main interest lies in the training of AI as an a priori neutral technology using behavioral data.</footnote>
<table><caption>**Table 1**
Overview of treatments.</caption><thead><tr><th>Treatment</th><th>Pivotality for AI training</th><th>Monetary incentives</th><th>Externality of AI training</th></tr></thead><tbody><tr><td>Full Pivotality</td><td>100%</td><td>100%</td><td>0%</td></tr><tr><td>No Pivotality</td><td>1%</td><td>1%</td><td>0%</td></tr><tr><td>Full Pivotality-Double</td><td>100%</td><td>100%</td><td>100%</td></tr><tr><td>Full Pivotality-Others</td><td>100%</td><td>0%</td><td>100%</td></tr></tbody></table>

*Notes:* The table provides an overview of the implemented treatments. “Pivotality for AI training” indicates the share of training data the dictator provides for the training of the algorithm in period 31 in the own pair. For example, 1% pivotality means that the subject constitutes only one source of training of the AI out of 100. “Monetary incentives” measures the financial consequences of the dictator’s training of the algorithm for the own pair in period 31. For example, 1% incentives mean that the subjects’ decisions in periods 1–30 contribute only 1% to the decisions that will determine their payoff in period 31. “Externality of AI training” indicates the share of training data the dictator provides for the training of the algorithm in period 31 in the other pair.

## 3.2 Treatments

The experiment comprised four between-subjects treatments that varied the relative impact of the dictator’s decisions on the AI’s training and future prediction, as well as whose payoff was determined by the AI’s choice. These treatments were called Full Pivotality, No Pivotality, Full Pivotality-Double, and Full Pivotality-Others.<fnref n="7" /> For a simplified overview of these treatments, refer to Table 1 and Figure OA1.1 in Online Appendix OA.1.

Our baseline condition was the *Full Pivotality treatment*. It exactly followed the above-described experimental design.<fnref n="8" /> The random forest algorithm solely relied on the 30 choices made by the respective dictator for its predictions, and this data was used exclusively to determine payoffs in period 31. As a result, each dictator in a pair bore complete responsibility for the AI’s training and its subsequent impact on the own pair’s earnings. This baseline, even if it might appear hypothetical, is crucial for our study. While in the real world AI systems often merge data from multiple sources to make recommendations or are pre-trained, there is a growing trend towards personalized AI systems like Custom GPT agents. These systems can be trained on content and data that mirror the preferences and behaviors of specific individuals or audiences. While this full pivotality scenario remains rare outside of controlled experiments, it allowed us to identify the causal effect of pivotality of human decisions when training AI compared with more typical diversified data settings.

In the *No Pivotality treatment*, the training and prediction of the AI in a pair in period 31 relied not only on the dictator’s choices in this pair but also on the training data generated by other dictators in the past. The 30 decisions reflecting the preferences of the current dictator were pooled with the 30 decisions from each of 99 randomly selected previous participants.<fnref n="9" /> Hence, the dictator was only responsible as one out of 100 trainers whose data were used by the algorithm. This condition is consistent with the way training of intelligent systems often occurs. Though AI entirely relies on observed patterns in human behavior, no individual can solely be made accountable for the outcome. Being not pivotal for the AI’s resulting prediction, the dictator had hardly any monetary incentives in how to train the AI. Appendix A.2 describes simulations of the algorithm’s predictions for the Full Pivotality and the No Pivotality treatments, which illustrate the vanishing impact of the dictator for the AI’s decision in period 31.

Note that the No Pivotality and the Full Pivotality treatments differ not only in terms of the degree of pivotality but also in terms of incentives since in the Full Pivotality treatment the decisions of a dictator in periods 1–30 also influence the earnings in period 31 through the AI prediction. So the comparison is:

$$ \text{No Pivotality} - \text{Full Pivotality} = \text{Effect of Removed Pivotality for AI Training} + \text{Effect of Reduced Monetary Incentives} $$

As it is, to the best of our knowledge, technically not feasible to remove pivotality while preserving the full financial consequences of the decisions in periods 1–30 for the own pair’s earnings in period 31, we introduced two additional treatments to separate these two channels. These treatments were not designed to replicate real-world scenarios but rather to isolate the effect of removing the monetary incentives for influencing the AI’s prediction. By incorporating these additional treatments, we can ultimately isolate the causal impact of removing pivotality for the AI’s training, as observed in the No Pivotality treatment.

In the *Full Pivotality-Others treatment*, we used the 30 decisions by the dictator in a pair as training data for the AI that decided for another pair within the same session. Meanwhile, the AI whose prediction determined the earnings of the pair in period 31 was exclusively trained with the 30 decisions of a dictator from another pair in that session. Thus, each pair was matched with

<footnote n="7">⁷ We also preregistered and collected the data from a Shared Pivotality treatment. Here, each dictator trained an algorithm together with another dictator, and the algorithm’s decision was paid out in both pairs. However, this treatment varies two dimensions compared to any other treatment (who trains the AI and whose earnings are affected). Therefore, we have excluded the description and analysis of this condition in the main text. For completeness, we report results on participants’ behavior and revealed social preferences in Table OA1.4 in Online Appendix OA.1. The results are qualitatively similar to and not significantly different from those in the No Pivotality treatment.</footnote>

<footnote n="8">⁸ This baseline, and only this one, is common to both this paper and our companion paper (Klockmann et al., 2022).</footnote>

<footnote n="9">⁹ These participants were informed that their decisions would affect future participants’ earnings through AI training. The impact of this information on behavior is analyzed in our companion paper. Participants in the No Pivotality treatment learned that those 99 other participants stemmed from a previous session and they faced the same set of 30 decisions.</footnote>
two other pairs. In this treatment, the dictator had full pivotality over the AI's prediction for another pair but had no financial influence on the AI's prediction for the own pair. As a result, the weight of the dictator's current decisions in periods 1–30 on their future earnings through AI training was null, making this treatment comparable to the No Pivotality treatment in terms of incentive structure. However, as for responsibility, the decision-making process in this treatment was similar to the Full Pivotality treatment. Additionally, the Full Pivotality-Others treatment provides valuable insights into the distributional preferences participants would want intelligent systems to prioritize when the algorithm's decision does not financially impact them. Hence, the comparison is:

$$ \text{Full Pivotality-Others} - \text{Full Pivotality} = \text{Effect of Reduced Monetary Incentives} + \text{Effect of Externality of AI Training} $$

By introducing monetary consequences of the dictator's training of the algorithm on another pair, the Full Pivotality-Others treatment introduced a new dimension by creating an externality. To ensure that this channel did not influence the comparison between the Full Pivotality and Full Pivotality-Others treatments, we designed the Full Pivotality-Double treatment. This treatment allowed us to isolate the impact of the externality of a dictator's training data on another group. In this treatment, before participants made their allocation decisions in periods 1–30, we informed them that the prediction of the AI in period 31 would not only be paid out in their own pair but also in another pair in the same session. Compared to the Full Pivotality baseline, we retained full responsibility for and monetary interest in the AI's prediction, while also creating financial consequences for a third party, similar to the Full Pivotality-Others treatment. The difference between Full Pivotality-Double and the Full Pivotality baseline lies in the externality of AI training on another group in the latter. That is,

$$ \text{Full Pivotality-Double} - \text{Full Pivotality} = \text{Effect of Externality of AI Training} $$

By comparing treatments, we can identify the driving forces behind participants' behavior. If decisions in the Full Pivotality-Others treatment were closer to those in the No Pivotality treatment, it suggests that the incentive structure drives behavior. On the other hand, if decisions in the Full Pivotality-Others treatment were closer to those in the Full Pivotality treatment, it indicates that responsibility for the AI's training itself has a greater impact. To rule out that the externality of decisions on another pair in the Full Pivotality-Others treatment interferes with this interpretation, we needed to demonstrate that this extra externality did not affect the dictator's decisions. This was the purpose of conducting the Full Pivotality-Double treatment.<fnref n="10" />

Finally, in the No Pivotality and Full Pivotality-Others treatments, the monetary outcome of dictators in period 31 crucially depends on the behavior of previous participants. Therefore, we elicited in these treatments the participants' beliefs about past dictators' decisions and predictions of the AI. After the dictators made their 30 decisions but before they received feedback on the AI's prediction in period 31, participants had to assess whether the random forest algorithm would choose option X or option Y in four decision scenarios. The alternatives in the fourth scenario corresponded to the actual menu of options the AI faced in period 31.<fnref n="11" /> Each accurate answer paid 100 points to the participant. We correlated these beliefs with observed behavior across these treatments to better understand the participants' motivation (see Section 5).

## 3.3 Procedures

We implemented the experiment online using oTree (Chen et al., 2016) with students recruited from the Frankfurt Laboratory for Experimental Economic Research (FLEX) through ORSEE (Greiner, 2015). Each treatment involved 30 dictators and 30 receivers, a number determined through prior power analysis to detect a medium-size effect of 10 percentage points with a significance level of 5% and a power of 80%. For this, we chose a binomial distribution of decisions where we varied the probability of selecting the selfish option X. Using the sample size of 30 dictators per treatment and setting the choice likelihood of option X to 70% in one treatment (as observed in Full Pivotality), we obtain an ex-post minimum detectable effect of about 6.4 percentage points.

A total of 248 participants (124 dictators or independent observations) were recruited between July 2020 and May 2022.<fnref n="12" /> There were 34 dictators in the Full Pivotality treatment, 29 in the No Pivotality treatment, 31 in the Full Pivotality-Double treatment, and 30 in the Full Pivotality-Others treatment. We did not exclude any observation. The average age of the participants was 25.0 years. About 55% were female. Their predominant field of study was economics and they were on average in their 7th to 8th semester. Table B.1 in Appendix presents summary statistics for the elicited control variables, i.e., socio-demographics, education, gender, weekly spending, and participants' familiarity with and confidence in AI. While no significant differences are observed across treatments at the 5% level, a few differences emerge at the 10% level. These are subsequently controlled for in the analysis. Participants earned an average of 14.25 Euro (S.D. 3.60), including the bonus from the belief elicitation, received via PayPal at a conversion rate of 1 Euro per 100 points. Sessions lasted approximately 45 min.

<footnote n="10">¹⁰ An alternative design could involve increasing the stakes in period 31 to equalize incentives between conditions. However, this approach would introduce significant practical and conceptual challenges. Since one of the first 30 periods is always payoff-relevant, raising the stakes only in period 31 would distort the balance of incentives across the experiment. Matching the incentives of a condition where 100 dictators contribute to AI training would require multiplying the stakes by 100, leading to impractically large payouts. Such extreme stakes could bias decisions, shifting the focus from pivotality to participants' responses to unusually high rewards inducing loss aversion or risk-seeking behavior. We thus chose to introduce externalities in other conditions, maintaining consistent incentives while isolating the psychological effects of pivotality.</footnote>

<footnote n="11">¹¹ The other three pairs of options are summarized in Table OA1.3 in Online Appendix OA.1. In the first scenario, option Y was Pareto-dominant. In the second scenario, option Y increased the receiver's payoff and decreased inequality but at a cost for the dictator. In the third scenario, switching from option X to option Y put the dictator in a disadvantaged position, but reduced the absolute difference in payoffs between the two pair members.</footnote>

<footnote n="12">¹² We preregistered the project, the sample size, and our hypotheses on AsPredicted (#44010, https://aspredicted.org/GHF_3SW). Note that the preregistration does not mention the Full Pivotality-Double treatment since we included it in reaction to later comments. While the Full Pivotality, No Pivotality and the Full Pivotality-Others treatments were all conducted at the same time in July 2020, the Full Pivotality-Double treatment was conducted in May 2022. For balance checks, refer to Table B.1.</footnote>
## 4 Behavioral predictions

A model with standard preferences would not predict any differences in the dictators' decisions in periods 1-30: dictators are expected to choose the selfish option in all games, regardless of the treatment. However, the presence of social preferences together with variations in responsibility for how the algorithm determines the allocation of earnings may lead to different predictions. Our design distinguishes between two channels of influence on earnings: direct allocations affecting the dictator's and receiver's payoffs, and AI-mediated allocations shaping the period 31 distribution. Randomly selecting one of the first 30 periods for payment ensured incentive compatibility, holding the direct impact constant across treatments. In contrast, the AI-mediated channel was explicitly varied, introducing a unique psychological dimension: shaping outcomes for others through AI may create a different sense of responsibility than direct allocation choices. Dictators might perceive the AI as an independent agent, creating a layer of separation between their choices and the final outcome.

In the Full Pivotality treatment, the dictator's decisions alone are causally responsible for the AI's allocation rule, making the connection between their actions and resulting inequality highly salient. A dictator with prosocial preferences can actively enhance the fairness of earnings determined by AI by guiding it toward more equitable outcomes through their own egalitarian decisions. In the presence of inequity-averse participants, we would thus expect a part of dictators to choose the non-selfish option. Conversely, in the No Pivotality treatment, dictators' individual influence over the AI's decisions is diluted by the inclusion of choices from 99 other participants. This diffusion of responsibility – both actual and perceived – may reduce the psychological cost of selfishness, providing a justification for prioritizing self-interest. This diffusion can reduce feelings of personal responsibility for the direct harm to the receiver in the first 30 periods, as well. In situations with lower pivotality, individuals can take the opportunity to prioritize their own interests without significant sacrifice of distributional fairness or backlash from others. Based on the literature on diffused responsibility, delegation, and the tendency to downplay the negative consequences of one's actions (as cited in Section 2), we anticipated that in this treatment, the dictators would be less hesitant to allocate ECU to themselves at the receiver's expense compared to the Full Pivotality baseline. The perceived insignificance of individual choices in shaping period 31 allocations may foster more self-serving behavior.

Additionally, the altered incentive structure in the No Pivotality treatment may reinforce selfish decision-making. In each period, the expected utility of the dictator's current decision in the No Pivotality treatment was decreased since it carried a hundred times less weight compared to the Full Pivotality treatment for period 31. This reduction in expected utility might lead to more selfish current decisions as a way to compensate for the loss of expected utility.

**Conjecture 1.** Compared to the Full Pivotality treatment, dictators in the No Pivotality treatment more frequently choose the selfish option.

In the Full Pivotality-Others treatment, dictators exclusively trained the AI for another pair. Unlike the Full Pivotality treatment, the incentive structure in this treatment resulted in a null expected monetary utility from each of the dictator's current decisions for period 31. Nevertheless, the dictator retained full pivotality for the AI's decision. We thus conjectured that dictators might behave more selfishly in this treatment in the 30 decisions to compensate for their powerlessness in influencing their payoff in period 31. If this conjecture were rejected (i.e., players behaved similarly to the Full Pivotality treatment), it would indicate that individuals did not react to the modified incentive structure when training the AI.

**Conjecture 2.** Compared to the Full Pivotality treatment, dictators in the Full Pivotality-Others treatment more frequently choose the selfish option.

We conducted the Full Pivotality-Double treatment to address the potential influence of an externality introduced in the Full Pivotality-Others treatment. In this treatment, compared to the Full Pivotality baseline, we added monetary consequences of one's choices for another pair while still maintaining pivotality and financial incentives for the individual's own pair. We expected that this additional externality would have no influence based on the results of our companion paper (Klockmann et al., 2022). If our conjecture regarding the lack of influence from this externality were supported, we could focus on the aspect of altered incentives while preserving pivotality when comparing the Full Pivotality-Others and Full Pivotality treatments.<fnref n="13" />

Conjecturing that pivotality might matter while externality would not is not contradictory. These two notions capture two related but distinct dimensions of decision-making. Pivotality reflects the extent to which an individual's choices directly determine outcomes, including others' payoffs, while externalities measure the indirect effects of those choices on others' welfare. In our design, pivotality determines how much influence a participant's decisions have on payoffs in later periods (ranging from 1% to 100% for their own pair and 0% to 100% for another pair). Externalities reflect the broader impact of decisions on additional pairs, beyond direct responsibility for one's outcome.

While externalities grow with the number of affected players, pivotality does not necessarily follow the same pattern. A player can generate externalities without being pivotal, and vice versa. Our study focuses on pivotality, leaving the interplay between externalities and pivotality as an open avenue for future research.

<footnote n="13">¹³ In Klockmann et al. (2022), we employed the same baseline condition as the Full Pivotality treatment used in this paper, allowing for the reuse of the baseline data. In an Externality treatment, the dictator's choices generated training data for the AI's allocation decision in their group and for another group that would participate in the same experiment in the future, with no impact on payoffs in the current pair. This treatment is close to the Full Pivotality-Double condition of the current paper. The difference lies in the framing of the other group being in the same session or being part of a new generation of participants. The Offspring treatment was similar to the Externality treatment, except that the earnings of the first pair were affected by the prediction made by the AI for the future pair. Both the dictator and the receiver in the past generation received half of the payoff of the corresponding player in the future generation, in addition to their other earnings. The results showed that the dictators' decisions did not react to the introduction of such externalities.</footnote>
<table><caption>**Table 2**
Overview of the frequency of choices of the selfish Option X across treatments.</caption><thead><tr><th>Treatments</th><th>Dictators</th><th>Option X</th><th>Option X<br>[Restricted Sample]</th></tr></thead><tbody><tr><td>Full Pivotality</td><td>34</td><td>70.29%<br>(0.029)</td><td>66.01%<br>(0.046)</td></tr><tr><td>No Pivotality</td><td>29</td><td>79.20%<br>(0.024)</td><td>80.27%<br>(0.035)</td></tr><tr><td>Full Pivotality-Double</td><td>31</td><td>70.00%<br>(0.027)</td><td>66.31%<br>(0.042)</td></tr><tr><td>Full Pivotality-Others</td><td>30</td><td>70.89%<br>(0.028)</td><td>68.52%<br>(0.043)</td></tr><tr><td colspan="4"><strong>Treatment comparisons (p-values)</strong></td></tr><tr><td>Full Pivotality vs. No Pivotality</td><td></td><td>0.025</td><td>0.019</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Double</td><td></td><td>0.942</td><td>0.962</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Others</td><td></td><td>0.883</td><td>0.693</td></tr><tr><td>Full Pivotality-Double vs. Full Pivotality-Others</td><td></td><td>0.820</td><td>0.714</td></tr></tbody></table>

*Notes:* The table reports the relative frequency of the choice of the selfish option X in each treatment across dictators and periods. Standard errors of means across dictators in parentheses. Each dictator represents one independent observation. Column “Option X [Restricted Sample]” includes only the decisions in games with conflicting interests. *p*-values refer to t-tests for differences in means across dictators.

**Conjecture 3.** *Dictators in the Full Pivotality-Double treatment behave similarly to those in the Full Pivotality treatment.*

## 5 Results

Our analysis aims to identify how varying pivotality in the training data for a machine learning algorithm affected dictators' behavior and, consequently, the overall prosociality of the AI's decisions. To measure prosocial behavior, we focus on the proportion of the selfish option X chosen by the dictators across different treatments and estimate the social preference parameters revealed by those choices using two standard models from the behavioral economics literature (one pre-registered and one exploratory). Moreover, we provide exploratory evidence on the relationship between beliefs and behavior.

### 5.1 Dictators' choices

Table 2 presents pairwise tests that compare behavior across treatments. We conducted our analysis using both the full sample of observations and a restricted sample. The restricted sample included decisions characterized by conflicting interests, where the dictator obtained a higher payoff with option X compared to option Y, while the receiver would have been better off with option Y compared to option X. In Fig. 1, this corresponds to the option pairs represented by lines with a decreasing slope.<fnref n="14" />

We start with comparing the Full Pivotality treatment with the Full Pivotality-Double treatment. This comparison preserved the pivotality for the algorithm's prediction as well as the full monetary incentives in how the AI was trained but introduced an externality on another pair. We could not identify a treatment effect of the additional payout on behavior (*p* = 0.942 for a t-test on the share of Option X in the full sample and *p* = 0.962 in the restricted sample). The introduction of the externality while keeping the impact for own pair constant thus did not alter the participant's decisions. This finding supports **Conjecture 3** and yields **Result 1**.

**Result 1.** *Individuals who trained an AI algorithm only for their pair did not behave differently than those who generated training data that additionally influenced another pair's outcome. There was no significant difference in the frequency of choosing the selfish option X between the Full Pivotality and the Full Pivotality-Double treatment.*

As a next step, we compared the Full Pivotality with the Full Pivotality-Others treatment. In both cases, dictators were fully responsible for training the algorithm but the weight of each current decision on the expected future earnings differed dramatically. At the same time, by influencing the earnings of another pair, the dictator created an externality on others. Here, we found no significant difference in the share of selfish choices (*p* = 0.883 in the full sample and *p* = 0.693 in the restricted sample).

Based on **Result 1**, which indicates that the externality on the other pair did not affect behavior, we can conclude that removing the monetary incentives for selfish training to influence the AI's prediction in the own pair, while keeping pivotality constant, had no effect. We found no evidence of a discrepancy between how participants expected an AI to function for themselves and the behavior they implemented for others.

This analysis contradicts **Conjecture 2**. It is summarized in **Result 2**.

<footnote n="14">¹⁴ Additionally, we refer the reader to Tables B.2-B.4 in the Appendix for descriptive statistics about the relative frequency of choices of the selfish option X, by treatment and relative position of the dictator, by treatment and efficiency, and by treatment and relative inequality, respectively. Moreover, Figures OA1.2 and OA1.3 in Online Appendix OA.1 display the distribution of the shares of selfish option X chosen by the dictators for each treatment, in both the full sample and the restricted sample, respectively. Note that we did not pre-register the analysis of the restricted sample.</footnote>
**Result 2.** Individuals who trained an AI algorithm that exclusively decided for others did not behave differently than those who generated training data that solely influenced their own outcome. There was no significant difference in the frequency of choosing the selfish option X between the Full Pivotality and the Full Pivotality-Others treatment.

Finally, we compared the Full Pivotality with the No Pivotality treatment. By adding the decisions of 99 other dictators to the AI training, we both removed the pivotality and reduced the monetary incentives of the dictator for the algorithmic prediction. Table 2 reveals that reducing pivotality for training data without introducing an externality on another pair played a significant role in dictators' behavior. In the No Pivotality treatment, participants were significantly more likely to choose the selfish option X than in the Full Pivotality treatment, both in the full and the restricted samples ($p = 0.025$ and $p = 0.019$, respectively).<fnref n="15" /> As shown in Result 2, removing monetary incentives while preserving pivotality for the AI's prediction (Full Pivotality vs. Full Pivotality-Others) did not affect behavior. Thus, the behavioral shifts observed in the No Pivotality treatment stem from the absence of pivotality and opportunities for self-excuse, rather than changes in incentives.<fnref n="16" />

This analysis supports Conjecture 1 and leads to Result 3.

**Result 3.** Reducing pivotality for the AI's training induced dictators to behave more selfishly. The frequency of choosing the selfish option X was significantly higher in the No Pivotality than in the Full Pivotality treatment.

Table B.5 in the Appendix reports regression results of the share of option X on treatment dummies and different sets of control variables with the Full Pivotality treatment as the omitted category. The results largely confirm the t-test conducted above.<fnref n="17" />

The differences in the dictators' choices also manifested in the payoffs of both participants in the pair. The difference in period payoffs between dictator and receiver is about twice as large in No Pivotality (88.4 points on average) than in the other three conditions (between 40.8 and 48.0 on average). The increase in payoff inequality when pivotality for AI training is removed is significant ($p = 0.013$ from a t-test comparing mean payoffs in Full Pivotality and No Pivotality), while the other treatment comparisons are not significant ($p > 0.71$).

## 5.2 Revealed preferences and beliefs

Apart from measuring the frequency of choosing the selfish option X, we estimated the parameters of revealed social preferences. We relied on two different well-established models in the behavioral economics literature. First, Charness and Rabin (2002) set up a model of distributional preferences for two players that we fitted to the data, using maximum likelihood, following the approach by Bruhin et al. (2019), as outlined in our pre-registration. The dictator's utility function is given by

$$u_D^{CR}(\pi_D, \pi_R) = (1 - \alpha s - \beta r)\pi_D + (\alpha s + \beta r)\pi_R,$$

where $\pi_D$ denotes the payoff of the dictator and $\pi_R$ the payoff of the receiver.<fnref n="18" /> The indicator functions $s = 1\{\pi_R - \pi_D > 0\}$ and $r = 1\{\pi_D - \pi_R > 0\}$ equal one in case of disadvantageous and advantageous inequity for the dictator, respectively. As in Charness and Rabin (2002), the sign of the parameters $\alpha$ and $\beta$ describe the preference type of the dictator. $\alpha < 0$ indicates that the dictator is envious of the receiver's payoff whenever receiving a lower amount, and it captures behindness aversion. $\beta > 0$ indicates that the dictator seeks to increase the other's payoff whenever receiving a larger amount, which reveals aheadness aversion. The absolute values of $\alpha$ and $\beta$ measure how envious or empathetic the individual is. Further, if both $\alpha, \beta > 0$, the dictator always puts positive weight on the receiver's payoff, independent of her relative position. If $\alpha = \beta = 0.5$, the dictator seeks to maximize total welfare in any case.

In estimating $\alpha$ and $\beta$, we only consider distributional preferences in the training data (periods 1–30) for several reasons. First, accounting for the dictator's influence on period 31 earnings would require multiplying both $\pi_D$ and $\pi_R$ by the same factor. Since each allocation jointly affects the dictator's and receiver's payoffs, this factor cancels out and leaves the estimates of $\alpha$ and $\beta$ unchanged, as the log-likelihood maximization is unaffected by positive scaling of the objective function.<fnref n="19" /> Second, the utility

$$Pr(X|\pi_D^X, \pi_R^X, \pi_D^Y, \pi_R^Y; \alpha, \beta, \sigma) = \frac{\exp(\sigma u_D(\pi_D^X, \pi_R^X; \alpha, \beta))}{\exp(\sigma u_D(\pi_D^X, \pi_R^X; \alpha, \beta)) + \exp(\sigma u_D(\pi_D^Y, \pi_R^Y; \alpha, \beta))}$$

<footnote n="15">¹⁵ To test the robustness of these findings, we additionally adjusted the statistical results for multiple hypotheses testing within each column of Table 2. We used the family-wise error rate (FWER) by employing the Holm-Bonferroni and Holm-Šidák methods (Holm, 1979). We used the false discovery rate (FDR) by employing the Benjamini-Hochberg procedure (Benjamini and Hochberg, 1995). Regardless of the employed procedure, the treatment effect of No Pivotality remains significant at the 10%-level.</footnote>

<footnote n="16">¹⁶ Although the algorithm used varying amounts of data across treatments, this did not increase prediction noise in the No Pivotality treatment (see Table A.1 in Appendix A). Additionally, dictators' assessments of how well the AI reflected their preferences did not differ significantly between treatments.</footnote>

<footnote n="17">¹⁷ The observed treatment difference between Full Pivotality and No Pivotality remains significant at the 10% level when adding controls for gender, economics and weekly spending, where we see differences in our balance checks in Table B.1 (column (2)). The same holds true if we include all control variables elicited in the experiment (column (3)).</footnote>

<footnote n="18">¹⁸ To be precise, we followed the econometric strategy by Bruhin et al. (2019) that builds on a random utility model. When choosing an allocation $X = (\pi_X^X, \pi_R^X)$, the dictator's utility is given by $U'(\pi_X^X, \pi_R^X; \alpha, \beta, \sigma) = u_D(\pi_D^X, \pi_R^X; \alpha, \beta) + \epsilon_X$, where $u_D$ is the deterministic utility from above and $\epsilon_X$ is a random component following a type 1 extreme value distribution with scale parameter $1/\sigma$. The likelihood of choosing allocation $X$ over $Y$ then reads (see Bruhin et al., 2019)</footnote>

<footnote n="19">¹⁹ Any positive multiplication factor in the deterministic utility $u_D$ only inversely proportionally changes $\sigma$ (cf. footnote 18), but leaves the estimated values of $\alpha$ and $\beta$ unchanged.</footnote>
<table><caption>**Table 3**
Average estimated parameters of distributional preferences across treatments.</caption><thead><tr><th>Treatments</th><th>Dictators</th><th>α</th><th>β</th></tr></thead><tbody><tr><td>Full Pivotality</td><td>34</td><td>0.052<br>(0.047)</td><td>0.394<br>(0.057)</td></tr><tr><td>No Pivotality</td><td>29</td><td>-0.061<br>(0.040)</td><td>0.198<br>(0.084)</td></tr><tr><td>Full Pivotality-Double</td><td>31</td><td>0.032<br>(0.058)</td><td>0.390<br>(0.062)</td></tr><tr><td>Full Pivotality-Others</td><td>30</td><td>-0.008<br>(0.061)</td><td>0.396<br>(0.054)</td></tr><tr><td colspan="4"><strong>Treatment comparisons (p-values)</strong></td></tr><tr><td>Full Pivotality vs. No Pivotality</td><td></td><td>0.077</td><td>0.053</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Double</td><td></td><td>0.791</td><td>0.964</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Others</td><td></td><td>0.434</td><td>0.978</td></tr><tr><td>Full Pivotality-Double vs. Full Pivotality-Others</td><td></td><td>0.636</td><td>0.942</td></tr></tbody></table>

*Notes:* The table reports the average estimates of the α (advantageous inequality aversion) and β (disadvantageous inequality aversion) parameters (Charness and Rabin, 2002) across dictators. Standard errors of the mean are in parentheses. *p*-values refer to t-tests for differences in means.

function does not take the possible externality on another pair into account. Indeed, Result 1 reports no effect of the externality on social behavior and suggests that dictators did not factor in the outcomes of the additional pair when making their decisions, possibly due to psychological distance or diminished salience of this externality. This lack of observed behavioral adjustment in our data provides a rationale for excluding the second pair from the utility function. Finally, we did not explicitly incorporate pivotality in the utility function. Our aim was not to test a formal theory of pivotality of decisions, but rather measure how varying pivotality altered choices and the revealed distributional preferences of the dictator.<fnref n="20" />

Table 3 reports the average of the α and β parameters, estimated at the individual level and by treatment.<fnref n="21" />,<fnref n="22" /> While the average α parameter does not differ significantly from zero in any treatment (all *p*-values > 0.13), the average β parameter is significantly different from zero, at least at a 5%-level, in all treatments. The average dictator in the Full Pivotality treatment valued the receiver's payoff positively (β > 0, *p* < 0.001) when the receiver was worse off. Since β > α, they placed greater importance on obtaining a payoff for themselves when they were behind than when they were ahead of the other's earnings. Similar to our findings based on the frequency of chosen option X, we found no significant differences in revealed social preferences when comparing Full Pivotality respectively with Full Pivotality-Double and with Full Pivotality-Others (all *p*-values > 0.43). Neither the externality of AI training nor reduced monetary incentives changed the estimated α and β parameters. However, we found that the estimated weights on the receiver's payoff were marginally significantly lower in No Pivotality compared to Full Pivotality (*p* = 0.077 for differences in α and *p* = 0.053 for differences in β).

**Result 4.** The estimated revealed social preference parameters α and β are (weakly) lower in the No Pivotality treatment compared to the Full Pivotality treatment.

To provide further exploratory evidence on the differences in estimated revealed social preferences, we conducted a finite mixture estimation with *K* = 3 different types of dictators. This approach aims to endogenously identify preference types in the sample without making any assumptions about their properties. Instead, the method estimates separate values of α and β for all types along with their respective share in the population.

Table 4 reports the results of the finite mixture model. The first type of dictator, which we call “altruistic”, has significantly positive, large distributional preference parameters and weights the receiver's payoff positively in all cases. The second type, which we call “selfish”, is characterized by a small weighting of the receiver's payoff; α is insignificantly different from zero, and β is positive, albeit small. Finally, the third type, which we call “inequity-averse”, weights the receiver's payoff negatively when behind (α < 0 and significant) and positively when ahead (β > 0 and significant).<fnref n="23" />

Fig. 2 displays the distribution of the three preference types per treatment, revealing a clear pattern. In the treatments Full Pivotality, Full Pivotality-Double, and Full Pivotality-Others, the distribution is relatively uniform, with each type representing approximately one-third of the population. In contrast, in the No Pivotality treatment, the selfish type dominates, covering almost two-thirds of all individuals. Pairwise t-tests and Fisher's exact tests indicate that the distributions do not significantly differ between

<footnote n="20">²⁰ Simply adding a pivotality parameter multiplying the players' earnings would be ineffective because pivotality affects the calculation of both players' payoffs at the same time.</footnote>

<footnote n="21">²¹ In addition, Figures OA1.4 and OA1.5 in Online Appendix OA.1 display the distribution of estimated α and β, respectively, by treatment.</footnote>

<footnote n="22">²² To assess how the assumed utility function fits the observed choices, Table B.7 in the Appendix displays results from regressing the share of option X on treatment dummies and, in columns 2 and 5, on the estimated values of α and β. When controlling for the distributional preference parameters, all treatment indicators become insignificant and very small, and R² rises from about 6% to almost 78%.</footnote>

<footnote n="23">²³ When estimating the parameters for *K* = 4 types, the finite mixture model yields, apart from the three clusters described above, another altruistic type with significantly positive α and β which is very similar to the first type identified with *K* = 3. We therefore only report results for *K* = 3.</footnote>
<table><caption>**Table 4**
Overview of social preference types.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Type</th></tr><tr><th>Altruistic</th><th>Selfish</th><th>Inequity-Averse</th></tr></thead><tbody><tr><th>α</th><td>0.274<br>(0.033)</td><td>-0.005<br>(0.029)</td><td>-0.186<br>(0.087)</td></tr><tr><th>β</th><td>0.570<br>(0.031)</td><td>0.077<br>(0.024)</td><td>0.545<br>(0.066)</td></tr></tbody></table>

*Notes:* The table reports results of the finite mixture estimation of social preference types with $K = 3$ different types. Standard errors of estimated parameters in parentheses, clustered at the individual level.

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Distribution of the preference types, by treatment.</figcaption></figure>

all treatments except for the No Pivotality treatment. Specifically, the distributions are (marginally) significantly different between Full Pivotality and No Pivotality ($p = 0.072$ from Fisher's exact test), with the share of the altruistic type being significantly lower and the share of the selfish type being marginally significantly higher in the latter treatment ($p = 0.026$ and $p = 0.061$ from t-tests, respectively).

The second model we used for structural estimation is the CES utility by Andreoni and Miller (2002), which combines fair-mindedness with equality-efficiency trade-offs.<fnref n="24" /> Here, the utility of the dictator reads

$$u_D^{AM}(\pi_D, \pi_R) = [(1 - \varphi)\pi_D^\rho + \varphi\pi_R^\rho]^{1/\rho}.$$

Following Andreoni and Miller (2002) and Fisman et al. (2015), the parameter $\varphi$ is the weight put on the receiver's payoff and describes general fair-mindedness. If $\varphi = 0$, the individual is fully selfish, and if $\varphi = 1/2$, the individual is fair-minded since he or she weighs both payoffs equally. The parameter $\rho$ describes the equality-efficiency trade-off. If $\rho > 0$, the individual has distributional preferences towards maximizing efficiency, that is, the sum of both payoffs. If $\rho < 0$, the individual seeks to minimize inequity, that is, the difference between both payoffs.

Table 5 reports the average of the $\varphi$ and $\rho$ parameters, estimated at the individual level and by treatment, again using a maximum likelihood approach.<fnref n="25" />,<fnref n="26" /> In all treatments except No Pivotality, we estimated a significantly positive $\varphi$ at a 1%-level, while the average $\varphi$ in the No Pivotality treatment was not significantly different from zero ($p = 0.170$). The pattern for treatment differences in the revealed fair-mindedness parameter $\varphi$ is similar to the one above for $\alpha$ and $\beta$. While the comparison of the Full Pivotality and the No Pivotality treatments yields statistically significant results ($p = 0.017$), all other differences are insignificant (all $p$-values > 0.75).

Considering the equality-efficiency trade-off, the average estimated parameter $\rho$ is negative for all treatments and only marginally significantly different from zero at a 10%-level for all treatments except Full Pivotality, where $p = 0.103$. This speaks in favor of

<footnote n="24">²⁴ For estimation, we used a maximum likelihood approach analogous to the one described in footnote 18 for the other utility function. This second modeling approach was not pre-registered.</footnote>

<footnote n="25">²⁵ In addition, Figures OA1.6 and OA1.7 in Online Appendix OA.1 display the distribution of estimated $\varphi$ and $\rho$, respectively, by treatment.</footnote>

<footnote n="26">²⁶ We assessed the fit of the Andreoni and Miller (2002) utility function in Table B.7 in the Appendix. Again, controlling for $\varphi$ and $\rho$ made all treatment effects vanish and largely increased $R^2$.</footnote>
<table><caption>**Table 5**
Average estimated Fair-Mindedness and efficiency parameters across treatments.</caption><thead><tr><th>Treatments</th><th>Dictators</th><th>φ</th><th>ρ</th></tr></thead><tbody><tr><td>Full Pivotality</td><td>34</td><td>0.191<br>(0.040)</td><td>-3.297<br>(1.969)</td></tr><tr><td>No Pivotality</td><td>29</td><td>0.054<br>(0.038)</td><td>-2.711<br>(1.431)</td></tr><tr><td>Full Pivotality-Double</td><td>31</td><td>0.193<br>(0.045)</td><td>-9.136<br>(5.086)</td></tr><tr><td>Full Pivotality-Others</td><td>30</td><td>0.173<br>(0.044)</td><td>-9.811<br>(5.199)</td></tr><tr><td colspan="4"><strong>Treatment comparisons (p-values)</strong></td></tr><tr><td>Full Pivotality vs. No Pivotality</td><td></td><td>0.017</td><td>0.816</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Double</td><td></td><td>0.980</td><td>0.272</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Others</td><td></td><td>0.766</td><td>0.225</td></tr><tr><td>Full Pivotality-Double vs. Full Pivotality-Others</td><td></td><td>0.759</td><td>0.926</td></tr></tbody></table>

*Notes:* The table reports the average estimates of the φ (fair-mindedness) and ρ (efficiency concerns) parameters of the CES utility function (Andreoni and Miller, 2002) across dictators. Standard errors of the mean in parentheses. *p*-values refer to t-tests for differences in means.

<table><caption>**Table 6**
Relationship between the Dictators' beliefs and their behavior, by treatment.</caption><thead><tr><th></th><th>Aggregate</th><th>No Pivotality</th><th>Full Pivotality-Others</th></tr></thead><tbody><tr><td>Belief Option X</td><td>0.092***<br>(0.025)</td><td>0.053<br>(0.031)</td><td>0.135***<br>(0.038)</td></tr><tr><td>Constant</td><td>0.593***<br>(0.046)</td><td>0.697***<br>(0.060)</td><td>0.494***<br>(0.066)</td></tr><tr><td>Number of observations</td><td>59</td><td>29</td><td>30</td></tr><tr><td>R<sup>2</sup></td><td>0.194</td><td>0.097</td><td>0.305</td></tr></tbody></table>

*Notes:* The table reports OLS estimates of the percentage of choices of the selfish option X in periods 1–30 on the belief on how frequently option X was selected by the AI in the three scenarios (variable “Belief Option X”). We excluded the fourth pair of alternatives corresponding to the actual menu of options the AI faced in period 31 because this varied across groups. Thus, the variable takes values 0, 1, 2, or 3. Dictators had to guess the prediction of the AI that was trained only with the choices of those dictators whose generated data affected the algorithm’s prediction in their pair. The Aggregate column pools the data from the two treatments. Standard errors are in parentheses. \* *p* < 0.10, \*\* *p* < 0.05, \*\*\* *p* < 0.01.

inequity-minimizing rather than efficiency-maximizing choices. We did not observe significant differences across treatments (all *p*-values > 0.22).

**Result 5.** *The estimated revealed fair-mindedness parameter φ was significantly lower in the No Pivotality treatment compared to the Full Pivotality treatment. There are no significant differences in the estimated equality-efficiency trade-off parameter ρ.*

Finally, we explored the relationships between beliefs and behavior.<fnref n="27" /> Before informing participants about their earnings from the AI’s prediction, we elicited the dictators’ beliefs about the *others’* training data in the No Pivotality and Full Pivotality-Others treatments. We found no significant differences in average beliefs across treatments (*p* > 0.29 from a t-test, see Table B.6). Still, beliefs could relate to behavior differently across treatments. To explore this, Table 6 reports the results of an OLS regression analysis that tested for the relationship between the dictators’ beliefs about the AI’s training and their own behavior. The dependent variable is the relative frequency of the dictator’s choices of the selfish option X in the 30 games and the independent variable is the belief about the number of selfish choices predicted by the AI in the three elicited scenarios (see Section 3.2).

Pooling the data from the two treatments showed that a one-point increase in a dictator’s belief about the AI’s prediction resulted in a significant 9.2 percentage points (*pp*) increase in the dictator’s likelihood of choosing option X. On average, compared to a dictator who believed the AI would always predict the altruistic option Y and is estimated to choose option X in 59.3% of cases (see constant of the regression), a dictator who believed the AI would always predict the selfish option X was 27.6*pp* or 46.5% more likely to choose option X herself.

When estimating the effect by treatment, the strongest correlation between beliefs and behavior appeared in the Full Pivotality-Others treatment. In this treatment, a dictator who believed that the other pair’s dictator put the least weight on the receiver’s payoff (i.e., Belief Option X = 3) picked option X 40.5*pp* or more than 80% more frequently than a dictator who stated a belief of 0 (49.4%, see constant). This suggests that participants did not counterbalance their power position when training an AI for a third,

<footnote n="27">²⁷ These analyses are exploratory and were not pre-registered.</footnote>
independent pair if they expected the participant in the other pair to behave similarly, favoring the dictator's earnings. In contrast, beliefs and behavior were not significantly correlated in the No Pivotality treatment.<fnref n="28" />

This difference in the impact of beliefs across treatments is notable because, in both No Pivotality and Full Pivotality-Others, the dictator's earnings in period 31 were largely determined by others' preferences. The relevance of beliefs about others did not depend on whether one's own earnings were shaped by others but rather on the responsibility for others' earnings. In No Pivotality, dictators lacked this responsibility, while in Full Pivotality-Others, they bore full responsibility. An interpretation is that when knowing they were not pivotal, individuals did not need beliefs about others' selfishness to justify their own selfish choices; which they needed when they were fully pivotal. This is consistent with Falk et al. (2020) who provided evidence that to behave more selfishly while keeping a good image, individuals tend to form motivated beliefs that their actions do not influence an outcome anyway.

The observed correlation between beliefs and actions may also stem from a combination of projection and justification mechanisms. This could alternatively explain why the correlation is stronger in Full Pivotality-Others, where participants are in an identical decision environment, amplifying projection effects. Conversely, in No Pivotality, the asymmetry between the dictators' situations and those whose choices they predict reduces the scope for direct projection, potentially lowering the observed correlation.

We conclude this exploratory analysis with the following final result.

**Result 6.** Individuals who believed that the AI was trained by other selfish dictators behaved more selfishly in generating training data, but only when they were pivotal for others' payoffs.

# 6 Discussion and conclusion

AI systems must be trained on data before making decisions. In contexts like judges using decision support systems for bail, financial firms using robots for investment advice, or human resource systems adopt intelligent automation, machine learning models rely on human-generated data for training. From an ethical standpoint, individuals bear responsibility for this data, influencing AI-based decision-making. In traditional settings, where algorithms do not learn from human actions, decisions typically affect only the immediate outcome or, at most, shape social norms through peer influence. AI training introduces a significant shift – individual decisions no longer terminate with the present but become part of datasets that influence the future behavior of scalable algorithms. This amplifies the impact of individual actions, creating lasting externalities. Yet, the aggregation of data from many individuals may lead to diffused responsibility, weakening the sense of pivotality. Even though one's data may contribute to shaping AI behavior, the scale of aggregation often obscures the perception of direct influence, leading to less prosocial behavior compared to a situation with high perceived pivotality for algorithmic outcomes.

Our findings demonstrate that removing pivotality led to increased selfishness in how humans trained the algorithm. Importantly, this change in revealed social preferences was driven by a shift in individual responsibility (the power over one's own or others' fate) rather than the incentive structures (the expected additional payoff of one's current decisions through the AI's training). Additionally, our findings reveal a positive correlation between participants' beliefs about others' revealed preferences in generating training data and their own AI training choices when they were pivotal for others' payoffs. This pattern points to a potential (false) consensus effect or belief distortion mechanism, where participants justify selfish behavior by assuming others are also selfish, rather than attempting to offset others' selfishness through prosocial actions.

In summary, humans' tendency to behave less prosocial when feeling less accountable or not pivotal extends to AI training as well. This aligns with previous research (particularly Darley and Latané, 1968; Bénabou et al., 2018; Falk et al., 2020) and highlights how undesirable behavioral patterns can be facilitated and even reinforced in the context of AI. If these patterns spread, they could reduce distributional fairness in algorithmic recommendations or decisions in society, contributing to algorithm aversion – where people trust human advice more than algorithmic recommendations (see meta-analysis by Mahmud et al., 2022). Our companion paper (Klockmann et al., 2022) found that when individuals' decisions in AI training affected future generations, decision-makers behaved less selfishly only when they could be harmed themselves by the AI's future decisions. These results underscore the importance of informing people about the risk that machines may adopt less egalitarian models when learning from individuals who feel little personal responsibility for the indirect consequences of their choices in AI design. Just as each vote matters in elections even if individual voters feel powerless, individuals must understand that ethics plays a significant role in every decision they make, even if these individual decisions will be combined with those of many others to train intelligent algorithms.

We acknowledge that our experimental setting has limitations when compared to real-world scenarios. In practice, individuals are often unaware of the broader consequences of their actions. Even when people recognize that their behavior contributes to AI training, the actual impact of their decisions on others or future outcomes may far exceed the minimal effect observed in our No Pivotality treatment. In such cases, the perceived externalities of AI training could be more pronounced, potentially fostering optimism and reducing selfish behavior. Conversely, individuals distanced from the training process – such as those contributing to a large-scale dataset – may feel even less responsible, viewing their role as insignificant among millions of others. An interesting avenue for future research would be to investigate whether participants' behavior changes when they are explicitly informed that

<footnote n="28">²⁸ Since we ask participants to report their beliefs before learning about their payoffs, they might hedge against the risk of receiving low payoffs by stating pessimistic beliefs – specifically, that the algorithm is more likely to choose the unfavorable option Y. While this type of hedging cannot be entirely ruled out, it would likely manifest as a level effect and should not systematically differ between the No Pivotality and Full-Pivotality Others treatments. Therefore, such hedging would not impact the observed differences in the correlation between beliefs about others' selfishness and participants' own selfish choices.</footnote>
their AI training influences the outcomes of many others, potentially amplifying the perceived responsibility and pivotality of their decisions.

To foster socially-oriented algorithmic decision models, two key aspects must be addressed. First, machine designers play a crucial role in addressing the accountability gap in AI training. Often, training data is selected before it is known that it will be used for AI, limiting individuals' ability to internalize the externalities of their decisions. This makes the designer's role in creating fair and transparent AI systems even more critical. Since individuals tend to make less selfish decisions when they feel pivotal, designers must consider these dynamics. Relying solely on revealed preferences may not ensure morally sound AI decisions. By integrating fairness guidelines into the algorithm's design, designers can promote social responsibility and avoid perpetuating selfish behavior. Second, providing information alone may not suffice to prevent the development of scalable algorithms lacking strong distributional fairness preferences, especially when individuals have limited control over their actions, like when AI tracks consumers' searches.

This poses a challenging question for democracies: how can citizens be involved in AI design without compromising moral integrity due to the diffusion of pivotality? Our research highlights a crucial dilemma: while training AI with data from many people may be more democratic, it could also result in less social algorithms. We reopen a broader debate in AI ethics, as mentioned by Coeckelbergh (2020): Should we strive for “idealized” training datasets (as Eric Horvitz of Microsoft, suggests), or mirror real-world human biases? Should we embed strong affirmative action into algorithms to address inequality, or allow algorithms to mimic human decision-making and preferences despite potential increases in inequality? To navigate these ethical complexities, involving additional human intervention in AI decision-making is crucial, as recommended by Chui et al. (2018). A “human in the loop” approach, where experts validate models, check AI decisions, and flag harmful consequences, can provide an added layer of ethical oversight.

Our study does not resolve the normative question of whether AI should mimic typical human behavior or be designed to act more pro-socially. However, it provides empirical evidence on a key factor shaping this debate: how AI training environments influence the behavior captured in training data. If pivotality and perceived responsibility affect decision-making during AI training, structuring environments to emphasize these factors could foster more ethical data inputs. Conversely, training AI in settings where responsibility feels diffuse may reinforce selfish tendencies. While we refrain from prescribing how AI should behave, our findings underscore the need to design AI training contexts that counteract responsibility dilution and promote socially responsible behavior.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Appendix A. Random forest algorithm

### A.1. Technical details

For predicting the out-of-sample choice of the dictator in the 31st period, and as explained in Klockmann et al. (2022), we relied on a random forest algorithm as a standard classification method (Breiman, 2001). A Random Forest consists of several uncorrelated Decision Trees as building blocks. The goal of using a Decision Tree is to create a training model that can be used to predict the class of a target variable. It learns simple decision rules inferred from prior data (training data). In our experiment, the target variable was the decision of the dictator in period 31 and the training data corresponded to the dictator's previous decisions in periods 1 to 30. The algorithm took eight features as input variables to predict the binary outcome option X or option Y in period 31. Apart from the four payoffs for both players from both options, we further added the sum and difference between payoffs for each option as features.

All decision trees have grown under two types of randomization during the learning process. Firstly, at each node, a random subset of features was selected to be considered when looking for the best split of observations. Hereby, we relied on the usual heuristics and allowed up to $\sqrt{8} \approx 3$ features. Secondly, only a random subset of observations was used to build each tree (bootstrapping). For each dictator, a forest consisted of ten different classification trees. To make the final decision on whether option X or option Y was the dictator's hypothetical 31st choice, each tree in the forest made a decision and the option with the most votes determined the final classification.

Due to the Python foundation of oTree, we made use of the random forest implementation of the scikit-learn package (Pedregosa et al., 2011). We further set a fixed random state or seed to ensure reproducible results. To assess the accuracy of the algorithm ex-post, we split the decision data of each dictator into a training and test data set with 24 (80%) and 6 (20%) observations, respectively. For each individual, we thus trained a random forest with 24 randomly selected allocation choices and let it predict the six remaining ones. For all 124 dictators, this yielded an average predictive accuracy of 85.4%, a precision of 89.2%, a recall of 91.0%, and an $F_1$ score of 0.901. Note that this number should be rather taken as a lower bound on the actual accuracy of the algorithm in the experiment that actually used all 30 or 3000 decisions of the dictator(s) for training to make the out-of-sample prediction.

In Table A.1, we report the accuracy, precision, recall, and $F_1$ score of the random forest algorithm in each treatment. We conclude that the noisiness of the AI prediction was not different across treatments. It may seem intriguing that the noise did not decrease when the size of the training dataset was increased by a large scale. In fact, in the No Pivotality treatment, we did not
<table><caption>**Table A.1**
Performance metrics of the random forest algorithm by treatment.</caption><thead><tr><th>Treatment</th><th>Dictators</th><th>Training Obs.</th><th>Accuracy</th><th>Precision</th><th>Recall</th><th>F<sub>1</sub> score</th></tr></thead><tbody><tr><td>Full Pivotality</td><td>34</td><td>24</td><td>85.78%</td><td>90.15%</td><td>88.15%</td><td>0.8914</td></tr><tr><td>No Pivotality</td><td>29</td><td>2994</td><td>83.91%</td><td>96.77%</td><td>83.33%</td><td>0.8955</td></tr><tr><td>Full Pivotality-Double</td><td>31</td><td>24</td><td>84.95%</td><td>88.81%</td><td>90.15%</td><td>0.8947</td></tr><tr><td>Full Pivotality-Others</td><td>30</td><td>24</td><td>82.22%</td><td>85.71%</td><td>90.91%</td><td>0.8824</td></tr></tbody></table>

Notes: The table provides an overview of different performance metrics of the random forest algorithm, separate for each treatment. For each dictator, we made an 80:20 split, i.e., 24 observations for training and 6 observations for testing. The column Training Obs. reports the number of training observations used for each dictator. For the treatment No Pivotality, we additionally trained the algorithm with the 30 decisions from each of 99 randomly selected previous dictators.

only use the dictator's 24 decisions to train the algorithm but also the 99\*30 decisions from previous participants, yielding a total of 2994 training observations. Hence, training data stem from 100 individuals (which might have very heterogeneous preferences), while the test sample still consists of 6 decisions from one single person. So, two forces counteract. More data were used to train the algorithm (i.e., higher quantity, which could lead to less noise) but precise information on that given individual was obfuscated by the huge amount of training data from other individuals (i.e., lower quality, which could lead to more noise).

We further verified that not only did the training data differ across treatments as described in Table 2, but also the predictions of algorithms using these data differed analogously. We repeatedly trained a random forest with randomly selected 80% of the decisions of each dictator and recorded the likelihood of the algorithm to predict option X for the remaining 20% of rounds. This yielded an average likelihood of option X of 72.21% for Full Pivotality, 81.90% for No Pivotality, 70.97% for Full Pivotality-Double, and 74.28% for Full Pivotality-Others. Similar to the patterns identified for dictators' decisions, the only treatment showing a significant difference to Full Pivotality is No Pivotality ($p = 0.0453$), while other comparisons are insignificant ($p$-values above 0.66). Hence, the algorithm mimicked the selfishness of the training data and picked option X favoring the dictator more often in No Pivotality than in the other treatments.

The questionnaire in the final stage included several questions about the participants' attitudes toward AI in general and toward the machine learning algorithm in our experiment in particular. On a scale from 1 to 5, we asked dictators to rate their familiarity with and confidence in this technology (averages of 2.8 and 3.8, respectively), their satisfaction with the prediction in period 31 (average of 4.0), and their assessment of how accurately the AI's decision matched their true preferences (average of 4.1). There were no significant differences across treatments in any of these variables. Satisfaction with and assessed accuracy of the algorithm were not only very high but also strongly correlated (Spearman rank correlation: 0.684, $p < 0.001$).

## A.2. Simulation of predictions

To illustrate the variation in pivotality for the algorithm's prediction between the treatments Full Pivotality and No Pivotality, we simulated the decisions of the random forest algorithm for four participants. We selected the individuals based on their estimated parameters of revealed social preferences ($\alpha, \beta$) and selected those with the most extreme values (marked with a red square in Fig. A.1:

* Prosocial type: positive parameters with $\alpha = 0.386, \beta = 0.998$ (top right)

* Inequity averse type: negative $\alpha = -0.742$ and positive $\beta = 0.767$ (top left)

* Spiteful type: negative parameters with $\alpha = -0.244, \beta = -0.244$ (bottom left)

* Selfish type: parameters close to zero with $\alpha = -0.006, \beta = -0.006$ (center)

We simulated the prediction of the random forest algorithm for the four selected individuals for all six possible out-of-sample choice scenarios listed in Table OA1.2 (100 iterations each). To mimic the Full Pivotality treatment, the algorithm used only the 30 decisions of the respective individual for training. To mimic the No Pivotality treatment, we added the decisions of 99 randomly selected previous participants.

The results of the simulations are illustrated in Fig. A.2. For the Full Pivotality treatment, we observe substantial variation in the frequency of predicting option X across preference types. Intuitively, the algorithm picks option X the least often for the prosocial type (66.83%), followed by the inequity-averse type (83.33%) and the spiteful type (95.00%). For the selfish type with social preference parameters very close to zero, the algorithm always picks option X. This heterogeneity vanishes for the No Pivotality treatment in which the individual's decisions only make up 1% of the training data. The frequency of predicting option X is almost constant across types and varies between 96.67% and 97.00%.

To summarize, the simulations demonstrate that while the own choices in the first 30 periods substantially influence the prediction of the random forest algorithm in period 31, the dictator is no longer pivotal for the algorithm's choices once 99 other sources of training are added.
<figure><img src="image_6.png" /><figcaption>**Fig. A.1.** Scatter plot of social preference parameters.</figcaption></figure>

*Notes:* The figure shows the estimated social preference parameters $(\alpha, \beta)$ for all participants. Those marked with red squares were selected for simulations.

<figure><img src="image_7.png" /><figcaption>**Fig. A.2.** Results of simulations.</figcaption></figure>

*Notes:* The figure shows the frequency of the random forest algorithm to choose option X for all selected types and by treatment. Full Pivotality only uses the training data of the respective individual, No Pivotality adds 99 randomly selected previous participants.

# Appendix. Tables

See Tables B.1–B.7.

# Appendix C. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.euroecorev.2025.105098.
<caption>**Table B.1**</caption>

Summary Statistics, by Treatment.

<table><thead><tr><th>Treatments</th><th>Full Pivotality</th><th>No Pivotality</th><th>Full Pivotality-Double</th><th>Full Pivotality-Others</th></tr></thead><tbody><tr><td>% Females</td><td>60.29</td><td>51.72</td><td>45.16*</td><td>61.67</td></tr><tr><td>Mean age in years</td><td>24.28<br>(0.60)</td><td>25.33<br>(0.53)</td><td>25.47<br>(0.51)</td><td>25.20<br>(0.49)</td></tr><tr><td>% Studies in Economics</td><td>33.82</td><td>48.28*</td><td>43.55</td><td>41.67</td></tr><tr><td>Mean nb Semesters</td><td>7.01<br>(0.42)</td><td>6.81<br>(0.43)</td><td>8.19<br>(0.66)</td><td>6.95<br>(0.48)</td></tr><tr><td>Mean grade</td><td>1.96<br>(0.08)</td><td>2.05<br>(0.08)</td><td>2.01<br>(0.07)</td><td>1.91<br>(0.07)</td></tr><tr><td>Mean weekly spending</td><td>1.41<br>(0.07)</td><td>1.69*<br>(0.09)</td><td>1.66*<br>(0.08)</td><td>1.58<br>(0.09)</td></tr><tr><td>Familiarity with AI</td><td>2.90<br>(0.13)</td><td>2.84<br>(0.15)</td><td>2.85<br>(0.14)</td><td>2.60<br>(0.14)</td></tr><tr><td>Confidence in AI</td><td>3.62<br>(0.10)</td><td>3.76<br>(0.12)</td><td>3.66<br>(0.12)</td><td>3.83<br>(0.12)</td></tr><tr><td>N</td><td>68</td><td>58</td><td>62</td><td>60</td></tr></tbody></table>

Notes: The table displays summary statistics on the participants' sociodemographic characteristics and survey responses, by treatment. Standard errors of means are in parentheses. Grade refers to the German Abitur grade and ranges from 1.0 (best) to 6.0 (worst). Weekly spending is coded by 1 (less than 100 Euros), 2 (between 101 and 200 Euros), and 3 (more than 200 Euros). Familiarity with AI and confidence in AI were elicited using a Likert scale from 1 (not at all/none) to 5 (very good/a lot). The stars indicate significance levels for tests based on comparisons with the Full Pivotality treatment. These tests are Fisher's exact tests for gender, economics, and weekly spending, and t-tests for age, semester, grade, familiarity and confidence. \* *p* < 0.10, \*\* *p* < 0.05, \*\*\* *p* < 0.01.

<caption>**Table B.2**</caption>

Relative frequency of choices of the selfish Option X, by treatment and relative position of the dictator.

<table><thead><tr><th>Treatments</th><th>Nb obs.</th><th>Option X<br>[Advantageous]</th><th>Option X<br>[Disadvantageous]</th><th>Option X<br>[mixed]</th></tr></thead><tbody><tr><td>Full Pivotality</td><td>34</td><td>57.94%<br>(0.0417)</td><td>79.42%<br>(0.0273)</td><td>73.53%<br>(0.0355)</td></tr><tr><td>No Pivotality</td><td>29</td><td>68.62%<br>(0.0426)</td><td>87.93%<br>(0.0213)</td><td>81.03%<br>(0.0240)</td></tr><tr><td>Full Pivotality-Double</td><td>31</td><td>58.39%<br>(0.0407)</td><td>78.39%<br>(0.0271)</td><td>73.23%<br>(0.0312)</td></tr><tr><td>Full Pivotality-Others</td><td>30</td><td>57.67%<br>(0.0392)</td><td>78.67%<br>(0.0270)</td><td>76.33%<br>(0.0297)</td></tr><tr><td colspan="5"><strong>Treatment comparisons (p-values)</strong></td></tr><tr><td>Full Pivotality vs. No Pivotality</td><td></td><td>0.080</td><td>0.020</td><td>0.096</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Double</td><td></td><td>0.940</td><td>0.791</td><td>0.950</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Others</td><td></td><td>0.962</td><td>0.848</td><td>0.553</td></tr></tbody></table>

Notes: This table reports the relative frequency of the choice of option X, by treatment and according to the relative position of the dictator in the game (advantageous, disadvantageous, or mixed), with standard errors of means in parentheses. One observation corresponds to one dictator. *p*-values refer to two-sided t-tests for differences in means.

<caption>**Table B.3**</caption>

Relative frequency of choices of the selfish Option X, by treatment and efficiency.

<table><thead><tr><th>Treatments</th><th>Nb obs.</th><th>Option X<br>[X efficient]</th><th>Option X<br>[Y efficient]</th></tr></thead><tbody><tr><td>Full Pivotality</td><td>34</td><td>96.32%<br>(0.0101)</td><td>48.63%<br>(0.0502)</td></tr><tr><td>No Pivotality</td><td>29</td><td>96.26%<br>(0.0098)</td><td>63.91%<br>(0.0436)</td></tr><tr><td>Full Pivotality-Double</td><td>31</td><td>95.43%<br>(0.0138)</td><td>47.96%<br>(0.0472)</td></tr><tr><td>Full Pivotality-Others</td><td>30</td><td>95.56%<br>(0.0143)</td><td>50.00%<br>(0.0476)</td></tr><tr><td colspan="4"><strong>Treatment comparisons (p-values)</strong></td></tr><tr><td>Full Pivotality vs. No Pivotality</td><td></td><td>0.967</td><td>0.027</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Double</td><td></td><td>0.599</td><td>0.923</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Others</td><td></td><td>0.656</td><td>0.844</td></tr></tbody></table>

Notes: This table reports the relative frequency of the choice of option X, by treatment and according to the efficiency of the option in the game, with standard errors of means in parentheses. Efficiency refers to the sum of payoffs. One observation corresponds to one dictator. *p*-values refer to two-sided t-tests for differences in means.
<table><caption>**Table B.4**
Relative frequency of choices of the selfish Option X, by treatment and relative inequality.</caption><thead><tr><th>Treatments</th><th>Nb obs.</th><th>Option X<br>[X fairer]</th><th>Option X<br>[Y fairer]</th><th>Option X<br>[equal]</th></tr></thead><tbody><tr><td>Full Pivotality</td><td>34</td><td>79.71%<br>(0.0272)</td><td>57.65%<br>(0.0420)</td><td>73.53%<br>(0.0355)</td></tr><tr><td>No Pivotality</td><td>29</td><td>87.93%<br>(0.0207)</td><td>68.62%<br>(0.0440)</td><td>81.03%<br>(0.0240)</td></tr><tr><td>Full Pivotality-Double</td><td>31</td><td>79.35%<br>(0.0270)</td><td>65.88%<br>(0.0319)</td><td>81.47%<br>(0.0180)</td></tr><tr><td>Full Pivotality-Others</td><td>30</td><td>80.33%<br>(0.0277<sup>z</sup>)</td><td>56.00%<br>(0.0411)</td><td>76.33%<br>(0.0297)</td></tr><tr><td colspan="5"><strong>Treatment comparisons (p-values)</strong></td></tr><tr><td>Full Pivotality vs. No Pivotality</td><td></td><td>0.022</td><td>0.077</td><td>0.096</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Double</td><td></td><td>0.928</td><td>0.970</td><td>0.950</td></tr><tr><td>Full Pivotality vs. Full Pivotality-Others</td><td></td><td>0.873</td><td>0.782</td><td>0.553</td></tr></tbody></table>

*Notes:* This table reports the relative frequency of the choice of option X, by treatment and according to whether the option is fairer than the other option or not, with standard errors of means in parentheses. Fairness refers to the absolute difference in payoffs. One observation corresponds to one dictator. *p*-values refer to two-sided t-tests for differences in means.

<table><caption>**Table B.5**
Regression of relative frequency of choices of the selfish Option X.</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th></tr></thead><tbody><tr><td>No Pivotality</td><td>0.0890<sup>**</sup><br>(0.0385)</td><td>0.0695<sup>*</sup><br>(0.0404)</td><td>0.0659<sup>*</sup><br>(0.0395)</td></tr><tr><td>Full Pivotality-Double</td><td>-0.00294<br>(0.0379)</td><td>0.0243<br>(0.0405)</td><td>0.00708<br>(0.0411)</td></tr><tr><td>Full Pivotality-Others</td><td>0.00595<br>(0.0382)</td><td>-0.00727<br>(0.0387)</td><td>-0.0232<br>(0.0383)</td></tr><tr><td>Female</td><td></td><td>0.0424<br>(0.0286)</td><td>0.0386<br>(0.0283)</td></tr><tr><td>Economics</td><td></td><td>0.0585<sup>*</sup><br>(0.0327)</td><td>0.0548<br>(0.0332)</td></tr><tr><td>Weekly spending</td><td></td><td>-0.00476<br>(0.0213)</td><td>-0.0169<br>(0.0216)</td></tr><tr><td>Age</td><td></td><td></td><td>0.00840<sup>**</sup><br>(0.00333)</td></tr><tr><td>Semester</td><td></td><td></td><td>-0.000371<br>(0.00373)</td></tr><tr><td>Grade</td><td></td><td></td><td>-0.0593<sup>**</sup><br>(0.0244)</td></tr><tr><td>Familiarity</td><td></td><td></td><td>-0.00446<br>(0.0133)</td></tr><tr><td>Confidence</td><td></td><td></td><td>0.0146<br>(0.0164)</td></tr><tr><td>Constant</td><td>0.703<sup>***</sup><br>(0.0261)</td><td>0.669<sup>***</sup><br>(0.0424)</td><td>0.561<sup>***</sup><br>(0.108)</td></tr><tr><td>N</td><td>124</td><td>124</td><td>124</td></tr><tr><td>R<sup>2</sup></td><td>0.059</td><td>0.094</td><td>0.172</td></tr></tbody></table>

*Notes:* The table reports OLS estimates of the percentage of choices of the selfish option X in the 30 games on treatment dummies, demographics, and survey answers. The constant report the relative frequency of option X in the omitted treatment Full Pivotality. Standard errors are in parentheses. \* *p* < 0.10, \*\* *p* < 0.05, \*\*\* *p* < 0.01.
<table><caption>**Table B.6**
Distribution of beliefs about other's behavior across treatments.</caption><thead><tr><th rowspan="2">Treatments</th><th colspan="4">Belief about the choice of option X</th></tr><tr><th>0</th><th>1</th><th>2</th><th>3</th></tr></thead><tbody><tr><td>No Pivotality</td><td>6.90%</td><td>20.69%</td><td>58.62%</td><td>13.79%</td></tr><tr><td>Full Pivotality-Others</td><td>6.67%</td><td>26.67%</td><td>66.67%</td><td>0.00%</td></tr></tbody></table>

**Notes:** The table reports participants' beliefs about how frequently option X was selected in the three scenarios presented to the dictators during the belief elicitation task (from never to all three choices). We excluded the fourth pair of alternatives corresponding to the actual menu of options the AI faced in the 31st period because it varied randomly across pairs. Participants were asked to guess the decision of the AI that was trained with the choices of the 99 other dictators in the No Pivotality treatment and with the choices of the dictator who served as the only source of training data in Full Pivotality-Others.

<table><caption>**Table B.7**
Predictive power of estimated social preference parameters.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Full sample</th><th colspan="3">Restricted sample</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th></tr></thead><tbody><tr><td>No Pivotality</td><td>0.0890**<br>(0.0385)</td><td>0.00426<br>(0.0194)</td><td>0.0183<br>(0.0232)</td><td>0.143**<br>(0.0591)</td><td>0.0168<br>(0.0324)</td><td>0.0367<br>(0.0377)</td></tr><tr><td>Full Pivotality-Double</td><td>-0.00294<br>(0.0379)</td><td>-0.00821<br>(0.0185)</td><td>0.00316<br>(0.0224)</td><td>0.00295<br>(0.0581)</td><td>-0.00467<br>(0.0311)</td><td>0.0102<br>(0.0364)</td></tr><tr><td>Full Pivotality-Others</td><td>0.00595<br>(0.0382)</td><td>-0.00570<br>(0.0187)</td><td>0.00276<br>(0.0226)</td><td>0.0251<br>(0.0586)</td><td>0.00848<br>(0.0314)</td><td>0.0181<br>(0.0368)</td></tr><tr><td>α</td><td></td><td>-0.206***<br>(0.0235)</td><td></td><td></td><td>-0.294***<br>(0.0395)</td><td></td></tr><tr><td>β</td><td></td><td>-0.314***<br>(0.0191)</td><td></td><td></td><td>-0.473***<br>(0.0320)</td><td></td></tr><tr><td>φ</td><td></td><td></td><td>-0.510***<br>(0.0354)</td><td></td><td></td><td>-0.764***<br>(0.0575)</td></tr><tr><td>ρ</td><td></td><td></td><td>0.000911**<br>(0.000392)</td><td></td><td></td><td>0.00103<br>(0.000638)</td></tr><tr><td>Constant</td><td>0.703***<br>(0.0261)</td><td>0.837***<br>(0.0148)</td><td>0.803***<br>(0.0168)</td><td>0.660***<br>(0.0401)</td><td>0.861***<br>(0.0248)</td><td>0.810***<br>(0.0273)</td></tr><tr><td>N</td><td>124</td><td>124</td><td>124</td><td>124</td><td>124</td><td>124</td></tr><tr><td>R<sup>2</sup></td><td>0.059</td><td>0.778</td><td>0.680</td><td>0.059</td><td>0.735</td><td>0.640</td></tr></tbody></table>

**Notes:** The table reports OLS estimates of the percentage of choices of the selfish option X in the 30 games on treatment dummies and individual social preference parameters. The omitted treatment is Full Pivotality. Standard errors are in parentheses. * $p < 0.10$, ** $p < 0.05$, *** $p < 0.01$.

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