Benchmarking Cognitive Biases in Large Language Models as Evaluators (2024)

Abstract: Large Language Models (LLMs) have recently been shown to be effective as automatic evaluators with simple prompting and in-context learning. In this work, we assemble 16 LLMs encompassing four different size ranges and evaluate their output responses by preference ranking from the other LLMs as evaluators, such as System Star is better than System Square. We then evaluate the quality of ranking outputs introducing the COgnitive Bias Benchmark for LLMs as EvaluatoRs (COBBLER)1, a benchmark to measure six different cognitive biases in LLM evaluation outputs, such as the EGOCENTRIC bias where a model prefers to rank its own outputs highly in evaluation. We find that LLMs are biased text quality evaluators, exhibiting strong indications on our bias benchmark (≈ 40% of comparisons made by all models) within each of their evaluations that question their robustness as evaluators. Furthermore, we examine the correlation between human and machine preferences and calculate the average Rank-Biased Overlap (RBO) score to be 44%, indicating that machine preferences are misaligned with humans. According to our findings, LLMs may still be unable to be utilized for automatic annotation aligned with human preferences.

heading: 1 Introduction
text: Large language models (LLMs) (Brown et al., 2020; Ouyang et al., 2022) adapted to follow various kinds of instructions have been popularly utilized for several natural language tasks. The general standard for testing a model’s capabilities is benchmarking its performance on static evaluation suites such as Fan et al. (2019) and Wang et al. (2020). With the increased usage of language models as general-purpose assistants and their artificial nature (Das et al., 2024), current task-specific benchmarks are insufficient to measure the quality of generated texts in the wild.
1Our project page: https://github.com/minnesotanlp/cobbler
Recent studies have shown that LLMs can serve as evaluators themselves: Wu and Aji (2023) utilize LLMs as self-evaluators to automatically judge the quality of open-ended generations and compare them with human judgments via an Elo-score calculation. Other works, such as AlpacaEval (Li et al., 2023b), also utilize LLMs, such as GPT-4 (OpenAI, 2023), as automatic evaluators to reduce the time and cost overhead of human annotations. As noted by these works, such automatic evaluation leaderboards have a number of limitations, including a preference for long outputs or outputs that are more similar to the evaluators’ generation qualities.
In this work, we propose COBBLER, the COgnitive Bias Benchmark for evaluating the quality and reliability of LLMs as EvaluatoRs, as depicted in Figure 1. We collect a set of 50 questionanswering instructions from two well-established benchmarking datasets: BIGBENCH (Srivastava et al., 2023) and ELI5 (Fan et al., 2019). We then generate responses from 16 open- and closedsource LLMs and conduct a round-robin over every possible unique pair between each of the model responses, prompting each model to evaluate its own and other models’ responses.
We then test six different biases to benchmark their evaluation quality and categorize the model biases into two groups: (1) Implicit Biases, which can be implicitly extracted from each model’s evaluation via a vanilla prompt, and (2) Induced Biases, which add modifications to the original prompts akin to induce negative behaviors. As shown in Figure 2, we find that the majority of the models strongly exhibit several of the different biases, which may compromise the credibility of their role as evaluators.2 Furthermore, we conduct experiments for human preferences by crowdsourcing six human annotators and collecting each of their rankings for a total of 300 annotations. From
2In total, 42K samples are analyzed across six biases for each model totaling 630K samples.
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our findings, we observe a low correlation between human and machine judgments via Rank-Biased Overlap (RBO), indicating that machine and human preferences are generally in low agreement.
Our core contributions are as follows:
• A new benchmark (COBBLER) for evaluating LLMs to perform unbiased evaluations within the QA setting. • An examination of an exhaustive list of 6 (cognitive) evaluation biases that have not been covered by previous studies. We find that most LLMs cannot perform as unbiased evaluators. • A comprehensive lineup of models (sizing from 3B to >175B parameters) as evaluators, encompassing the current state-of-the-art language models covering over 630k comparisons.
From our benchmark, we find that most models exhibit various cognitive biases when used as automatic evaluators, which may negatively impact evaluation quality. Thus, we propose our benchmark (COBBLER) for measuring the capabilities of language models as evaluators to enable more reliable evaluations that are well-aligned with human judgment.
We note that our use of biased and unbiased preferences does not allude to the ability to make completely impartial judgments but rather the amplification of human-like biases within language models. As most models are tuned on human data, our study aims to estimate this gap between model and human judgment such that they can be refined more effectively to mitigate against these biases. As such, we also aim for our benchmark to be applied towards the development of future models, as in discovering new gaps or finding that existing gaps are still unresolved.

heading: 2 Related Work
text: LLMs as Evaluators. Owing to the effectiveness of LLMs, many recent research works have investigated their utility in various downstream tasks, such as machine translation (Kocmi and Federmann, 2023), summarization (Shen et al., 2023; Gao et al., 2023), code generation (Zhuo, 2023), writing assistance (Schick et al., 2023; Raheja et al., 2023), factual consistency (Cohen et al., 2023; Gekhman et al., 2023; Luo et al., 2023), and more. Additionally, many studies have leveraged LLMs for general-purpose NLG evaluation. For instance, Liu et al. (2023); Chen et al. (2023); Wang et al. (2023a) investigated the effectiveness of GPT-4 and ChatGPT against reference-free evaluation methods, whereas Fu et al. (2023) proposed an evaluation framework, GPTSCORE, to score generated texts. Recently, Li et al. (2023a) and Zheng et al. (2023) conducted similar experiments by employing LLMs as evaluators to judge the quality of generations in a pairwise setting. Although these works present promising results for LLMs as automatic evaluators, our work takes a closer look at machine artifacts that could be detrimental to data quality by benchmarking an exhaustive list of biases impacting LLMs-as-evaluators.
LLM Evaluation Benchmarks. It is becoming increasingly challenging to evaluate open-source LLMs as they become more powerful and performant. As a result, there has been an increasing need to develop better evaluation benchmarks for measuring the performance of LLMs. However, most of these benchmarks, such as LM-EVALHARNESS (Gao et al., 2021), MMLU (Hendrycks et al., 2021), HELM (Liang et al., 2022) and BIG-

heading: Bias Bias Behavior Example
text: ORDER BIAS The tendency to give preference to an option based on their order (e.g. first, second, or last). System Star: x System Square: y System Square: y System Star: x

heading: COMPASSION
text: FADE
The tendency to observe different behaviors when given recognizable names as opposed to anonymized aliases. Model Alpaca: x Model Vicuna: y Model Vicuna: y Model Alpaca: x

heading: EGOCENTRIC
text: BIAS
The inclination to prioritize one’s own responses regardless of response quality. Model Star (You): x Model Square: y

heading: SALIENCE
text: BIAS
The tendency to prefer responses based on the length of the response (i.e., more often preferring longer responses over shorter ones). System Star: The quick brown fox jumps over the lazy dog. System Square: The fox jumped.

heading: BANDWAGON
text: EFFECT
The tendency to prefer majority belief without critical evaluation. 85% believe that System Star is better.

heading: ATTENTIONAL
text: BIAS The inclination to give more attention to irrelevant or unimportant details. System Square likes to eat oranges and apples
Table 1: We display the characteristic format for each bias and bold answers that indicate behavior influenced by the bias. For example, in COMPASSION FADE (recognizable names) Model Alpaca and Model Vicuna are associated with System Star and System Square respectively, in which the preferred response (bolded) is inconsistent with the preferred response from ORDER (anonymized names). Specific prompt details are viewed in Appendix C.
BENCH (Srivastava et al., 2023), only focus on general LLM performance but do not explore their capabilities as evaluators. Our work in this direction overlaps directly with Bai et al. (2023) and Zheng et al. (2023), who propose a Language-Model-asan-Examiner benchmark and LLM-as-a-judge to study the capability of LLMs to emulate human preferences. While our experimental setups are similar, we highlight key differences. We cover a wider demographic of current popular language models and an overall different focus on QA as opposed to other domains such as math and reason. Furthermore, our benchmark emphasizes a wider range of biases (implicit/induced) to better describe machine artifacts when used as automatic evaluators. Specifically, COBBLER measures the extent to which each LM-as-evaluator is impacted in each decision by certain artifacts within prompts (i.e., prompting format, prompt information) over a comprehensive list of cognitive biases.
Cognitive Biases in LLMs. While biases have been well-known to exist in LLMs (Wang et al., 2023b; Talboy and Fuller, 2023; Wu and Aji, 2023), many recent works investigating the behaviors of LLMs have also uncovered similarities with cognitive biases. Some recent works (Zhao et al., 2021; Liu et al., 2022; Lu et al., 2022) have shown that the order of training examples in GPT-3 could lead to differences in accuracy between near chance and near state-of-the-art. Jones and Steinhardt (2022) captured failures in GPT-3 and Codex and found
that error patterns of LLMs resemble cognitive biases in humans. Our work overlaps with these in some of the biases we cover, but we present a much more holistic and comprehensive evaluation of LLMs. Along this aspect, while our work is close to Wu and Aji (2023), who investigate biases related to fabricated factual and grammatical errors, our work is much more comprehensive in terms of the number of LLMs analyzed, the types of biases analyzed and the creation of an open benchmark.

heading: 3 COBBLER: Cognitive Bias Benchmark for LLMs as Evaluators
text: The following criteria are used to select each type of evaluation bias:
• General Applicability. Text evaluation tasks should be generalizable to most prompting scenarios; tasks that observe too specific subtleties within the prompt are not helpful. • Impartiality. The prompt should not involve any leading statements to extract some desired quality of the evaluations • Memorylessness. The current evaluation instance should not rely on any previous behaviors. Each instance should be self-contained when extracting each bias metric.
We carefully hand-select these biases based on the above three criteria such that they can be widely applicable to most evaluation settings in assessing the performance of LLMs as automatic evaluators.
Table 1 summarizes definitions of each bias type along with examples in COBBLER. We categorize our benchmark into two main classes: (1) Implicit and (2) Induced Biases. For implicit biases, we feed a general prompt that shows system outputs in a pairwise manner to extract any biased behaviors within the model’s evaluations implicitly. For induced biases, we feed prompts geared towards each different bias, similar to adversarial attacks, such as presenting false information that may influence evaluator behaviors in a certain manner. Hence, we note that criterion 2 is not entirely fulfilled due to the nature of induced biases, though they can still be generally observable in an evaluation setting.

heading: 3.1 Implicit Biases
text: We categorize biases as “implicit” if they can be witnessed without including any additional information other than instructing the model to judge the quality of two given generated texts.
Order Bias is an evaluation bias we observe when a model tends to favor the model based on the order of the responses rather than their content quality. Order bias has been extensively studied (Jung et al., 2019; Wang et al., 2023a; Zheng et al., 2023), and it is well-known that language models can be influenced by the ordering of the responses in their evaluations. We prompt both orderings of each pair and count the evaluation as a “first order” or “last order” bias if the evaluator chooses the first ordered (or last ordered) output in both arrangements respectively.
Compassion Fade (Naming). (Butts et al., 2019; Västfjäll et al., 2014) is a cognitive bias that denotes a decrease in empathy as the number of identifiable individuals increases. To this phenomenon, we modify the definition for our use case to measure whether model evaluations are affected by real/identifiable names as opposed to evaluations with anonymous aliases (e.g. System A). Specifically, an unbiased evaluator would make evaluations similar to when anonymized names were presented.
Egocentric Bias (Self-Preference). (Ross and Sicoly, 1979) is a cognitive bias that refers to the tendency to have a higher opinion of oneself or to more easily accept ideas if they match one’s own. We define an evaluator to be egocentrically biased if, for each instance, the evaluator prefers its own response over others. We note that an unbiased evaluator would choose between themselves
and other comparand models equally in proportion. However, we highlight that some models would naturally generate higher quality responses (e.g., GPT4 vs. KOALA), resulting in a stronger inclination for such evaluators to choose their own responses.
Salience Bias (Length). (Schenk, 2010; Zheng et al., 2023) The evaluator tends to favor responses that are either shorter or longer in length. An unbiased evaluator would be split evenly between responses that are shorter or longer in length. We examine this bias by looking at evaluations in which a model preferred a response that is either shorter or longer in token length.

heading: 3.2 Induced Biases
text: We categorize a bias as “induced” when it requires modifications to the primary prompt or the inclusion of additional information with the original instructions. We specifically look to test the robustness of each of the models as evaluators by introducing false or off-topic information and examining the impact that these setups have on the quality of their evaluations. For both biases below, we would expect an unbiased evaluator to generally pick responses highlighted by BANDWAGON and ATTENTIONAL ∼25% of the time (calculated RANDOM threshold).
Bandwagon Effect. (Schmitt-Beck, 2015) The evaluator’s preferences are influenced by the collective preference rather than being based on their own independent judgments. We add an additional sentence after the initial instruction stating a fake statistic by choosing one of the comparand outputs as preferred by a majority of people, such as “85% believe that System Star is better.”. We count the model to be influenced by BANDWAGON if the evaluator choose the model stated in the statistic.
Attentional Bias (Distraction). In addition to the original instruction, we follow a similar setup from (Shi et al., 2023) where we include irrelevant information about one of the comparand models to test the ability of evaluators. For example, we include a meaningless sentence such as ”System Star likes to eat oranges and apples.” We identify the evaluator to be distracted if it prefers the model mentioned in the distraction or if its valid response rate significantly drops.

heading: 4 Experiment Setup
text: In this section, we discuss our evaluation framework for benchmarking each of the different biases in LLMs as evaluators for text quality comparison.

heading: 4.1 Datasets and Models
text: Datasets We choose two widely used datasets (Eli5 (Fan et al., 2019) and BigBench (strategyQA)) (Geva et al., 2021; Srivastava et al., 2023)) employed to train and benchmark instruction-tuned models, creating a set of 50 question-answering instructions (taking 25 random instructions from each). We specifically choose corpora from the Question-Answering (Q/A) domain for ease of use in generating responses. As we are looking to test the ability of language models to perform as unbiased evaluators to judge response quality and correctness, the Q/A response format presents the most natural setting for these comparisons.
Models We assemble 16 popular models based on the HuggingFace OpenLLM leaderboard (Beeching et al., 2023), API-based models, and recent open-source models: • (>100B parameters): GPT-4, CHATGPT, IN-
STRUCTGPT (OpenAI, 2023) • (>40B parameters): LLAMAV2 (Touvron
et al., 2023), LLAMA (Touvron et al., 2023), COHERE, FALCON (Almazrouei et al., 2023) • (>10B parameters): ALPACA (Taori et al., 2023), VICUNA (Chiang et al., 2023), OPENASSISTANT (Köpf et al., 2023) • (<10B parameters): MISTRAL-INSTRUCT (Jiang et al., 2023), OLMO (Groeneveld et al., 2024),BAIZE (Xu et al., 2023b), KOALA (Geng et al., 2023), WIZARDLM (Xu et al., 2023a), MPT (Team, 2023)

heading: 4.2 Text Evaluation Setting
text: Response Generation Figure 1 demonstrates our generation and evaluation pipeline for COBBLER. Here, we define “models” and “evaluators” interchangeably. We first generate the responses from each model by prompting 50 instructions from the combined dataset for a total of 800 generations.
Pairwise Evaluation After we collect all the model responses, we then prompt each evaluator to compare the anonymized generations in a pairwise manner. We generate all ( 15 2 ) unique pairs
amongst all models3 for each of the 50 instructions, creating a total of 5250 examples for each evaluator to rank. We then prompt the evaluator to compare generations based on the coherence of each of the responses in terms of correctness of content and alignment to the instruction/reference provided. The evaluation prompts for each bias benchmark are viewable in Appendix C. To mitigate against potential confounding factors, we run each pairwise instance twice in both arrangements to validate consistent behavior.
Additionally, we conduct a list-wise ranking amongst 4 models. However, we find that most LLMs of size <40B have trouble generating a valid list of rankings (Appendix B) due to increased task complexity (Dziri et al., 2023).
Benchmarking As the comparisons are limited to a pair-wise fashion, we empirically calculate a ”bias threshold” via random selection. For example, in the ORDER benchmark, each pair is evaluated twice in which both orderings are viewed (i.e. System Star is shown ordered first, then System Square is shown ordered first). We then randomly select a model in each response pair and measure the percentage of where the first-ordered model is chosen in both arrangements; models above random thresholds are identified to exhibit the said bias.
The random threshold provides a rough basis for the proportion of evaluations, for example, with respect to Order bias, which would be labeled “first order bias” if one randomly selects a response. We make this assumption to serve as a “litmus test” in distinguishing established patterns with respect to “bias/unbiased” evaluations by automatic evaluators rather than just random selection when models are noticeably above or below this threshold for each of our benchmark modules. We conduct a statistical test in Appendix B.5 to determine the significance of each proportion of biased evaluations from each automatic evaluator with the random baseline.

heading: 4.3 Human Preference Study
text: We collected human preferences from six workers on Amazon mechanical Turk (AMT) platform. More details about our data collection, human annotation process, and Rank-Biased Overlap and our calculation process are presented in Appendix D.
3We say all pairs from 15 models, as LLAMAV2 was added later, which alone evaluated ( 16 2 ) unique pairs

heading: Vicuna
text: Agreement between Human Preference and LLM Evaluation We calculated the RankBiased Overlap (RBO) score (Webber et al., 2010) to measure the agreement between human preferences and model evaluations in ranking-generated texts across 16 different LLMs. RBO, which can vary from 0 (non-conjoint) to 1 (identical), assigns more weight to the top k items in the ranked lists being compared 4. Higher RBO score means higher agreement. Further mathematical details of RBO setup can be found in Appendix D.2. To properly compare machine and human preferences, we construct a ranked list for each evaluator by counting each model wins5 from every pairwise comparison and then calculated the RBO. Here, we computed the RBOs between each individual annotator and machine preferences and averaged them.
Identifying Biases in Pairwise Human Preference To validate the gap between model judgment and humans, we conduct another study to measure the degree of bias in human evaluations as well. We mirror the pairwise model evaluation setting from Section 4.2 for ORDER BIAS, SALIENCE BIAS, BANDWAGON EFFECT, and ATTENTIONAL BIAS for a separate human study. To obtain an
4We concentrated 86% of all weights on the top 5 list positions, following Webber et al. (2010).
5At the time of human experiments, LLAMA2, MISTRAL, and OLMO were added later and instead involved responses by REDPAJAMA and DOLLY. Thus, the ranking of those three models was not included involving pairwise comparisons between 13 models.
effective metric, and due to the vastness of the pairwise model comparison settings, we randomly sampled 750 pairs from 25 different instructions. We then calculate the average IAA for each bias via RBO and then compute the average bias proportion across all annotators to highlight the overall influence of each bias on human judgment.
To maintain consistency with the initial study, where we used RBO as an IAA metric among human annotators for the previous N-wise ranking human experiment, we employed the same approach for the pairwise human bias experiment as opposed to Fleiss’ Kappa or other pairwise agreement scores. This involved converting all pairwise rankings by humans into a ranked list of models and computing the IAA scores among the human annotators for each of the three bias experiments. However, we randomly paired models for each instruction and thus generated 750 model pairs per bias 6, with some models appearing either multiple times or none in those pairs. As some models may be overrepresented, we compensate for the absence of some models by applying a normalization to the rankings of appearing models across all judged pairs per human annotator. More details are described in Appendix D.3, D.4, and D.5.
6Note that there are 25 batches in total for 750 pairs per bias and 75 human annotators
Model Size ORDER COMP. EGOC. SAL. BAND. ATTN. First Last First Last Order Comp.

heading: 5 Results and Discussion
text: For each bias, we analyze the performance of each of the 16 models as evaluators. We provide a visual breakdown of the proportional impact of the average performance of each model as unbiased evaluators in Fig. 2 based on the results relative to the RANDOM baseline in Table 2. On average, we see that models within the 10B size range are most affected by each bias benchmark in Fig. 2a. Notably, we see that the implicit biases contribute similarly to each models’ overall bias scores, indicating that scaling model size does not reduce implicit biases in evaluators.

heading: 5.1 Bias Analysis
text: Implicit Biases We first examine the performance of each evaluator on the implicit bias benchmarks for ORDER BIAS, COMPASSION FADE, SALIENCE BIAS and EGOCENTRIC BIAS. For the ORDER BIAS benchmark in Table 2, we observe that most models (11/15) tend to be drawn towards either the first- or last-ordered model in each of the pairwise comparisons. Notably, within the second size group (>40B), the first-ordered system was strongly favored in over 50%.
For COMPASSION FADE, since it is difficult to interpret its impact by the metrics independently,
we jointly compare the results with the ones from ORDER BIAS. For an unbiased evaluator that is not influenced by identifiable names, we expect the results for COMPASSION FADE to be relatively similar to the ORDER BIAS benchmark. However, we see in Table 2 that all models are dramatically influenced by real model names. Although this phenomenon may be akin to injecting random names, the disparity between ORDER and COMPASSION FADE results support our hypothesis that recognizable names influence evaluations in contrast to anonymized ones. In addition, we also note that OLMO sees a drastic decrease in performance. This might be attributed to the model’s inability to follow more complex instructions from its training.
For EGOCENTRIC BIAS, in the anonymized aliases, the largest models as well as KOALA tend to prefer their own responses (> 50%) with the exception of INSTRUCTGPT. However, with real model names (COMPASSION), we see a large drop in self-preference for models in the largest size group (>100B) models, but this may be attributed to a large increase in bias for each position. On average, we see an increase in self-preference with real model names amongst the two smaller size groups, notably KOALA sees a 100% increase in preference.
For SALIENCE BIAS, we observe that the larger models in the first and second size groups are more strongly affected by longer responses, which align with findings from other works (Wu and Aji, 2023; Zheng et al., 2023). However, smaller models (excluding MPT) tend to be less influenced by the length of the responses, suggesting that smaller models in the third and fourth size groups are less impacted in their evaluations in consideration of the length of the text.
For models such as ChatGPT, the EGOCENTRIC BIAS may be unfair because their generations are indeed better, or in SALIENCE, the longer generations indeed have higher quality. For further insight in decoupling these factors, we include supplementary experiments viewed in Appendix B.

heading: 5.1.1 Identifying Egocentric and Salience Bias
text: We also discuss the evaluation criteria for identifying EGOCENTRIC and SALIENCE biases, which may be more appropriately evaluated conditioned on underlying generation quality and model size.
We select a few model representative models for clarity viewed in Table 3. Generally, most models stay consistent with their preference for longer/shorter responses conditioned on either generation’s quality, although some flip their preferences (to only a small effect however). For further insight, we compute the generation quality using reference-based metrics via BERTScore. From this, all models produce nearly the same quality of generations with respect to the reference answer (∼0.81 to 0.86 for F1), highlighting that identifying EGOCENTRIC or SALIENCE bias is most likely not dependent on generation quality.
Induced Biases Next, we evaluate the performance of each evaluator on the induced bias benchmarks: BANDWAGON EFFECT and ATTENTIONAL BIAS. For BANDWAGON EFFECT, we observe that almost all models (11/15) are heavily influenced in
which > 70% of evaluations on average followed the bandwagon preference regardless of text quality. Although we only included a simple fake statistic (e.g. 85% of people preferred “System Star“), we see that evaluators can be heavily influenced by this external information. To observe a correlation between the biased tendency and the percentage, we include additional results in Appendix B.1
For ATTENTIONAL BIAS, we see that around half of the models’ rankings are influenced by irrelevant information. Specifically, we see that models in the third size group (>10B) were the most strongly impacted by the distracting information, with > 80% of evaluations being counted as distracted. On the other hand, API-based models such as CHATGPT and COHERE remained robust against these distractions in their rankings. We include the list of distractions we use in Appendix C.
Lastly, we address specific models such as LLAMAV2, LLAMA, KOALA, and OLMO that show abnormal results on most of the benchmarks. This can be attributed to their low valid response rates, displayed in Table 12 in Appendix B, which may be explained by our prompting format or the capabilities of the model themselves, likely as they are not instruction-tuned. Although these models display lower performance when extracting evaluations, if a model is not strong enough to produce valid outputs, we assume those models are not strong enough to be used for evaluations. And as we don’t consider invalid responses within the study, we only apply our findings to ones that produced valid evaluations, in which most models exhibit cognitive biases from our benchmark. Although the correlation between valid response rates and bias can provide more insight into model capabilities, it is not within the scope of our findings.

heading: 5.2 Agreement Between Human Preferences and Model Evaluations
text: N-rankwise Human Preference (N=13) The average RBO among the six AMT workers is 0.54, which signifies a modest but reasonable consensus among workers in ranking the LLM outputs, given the challenges of ranking all LLM-generated outputs. From this, we calculate the average RBO between human and model preferences to be 0.44, indicating that model evaluations do not closely align with human preferences.
Figure 3 presents the average RBO scores be-
tween a model and each of human preferences. While MISTRAL and CHATGPT achieved the highest RBO scores, most of the remaining models demonstrated lower agreement with human preferences. Smaller models also tend to misalign with an overall human preference, as the average RBO of models of size greater or smaller than 10B are 0.37 and 0.41, respectively, compared to >40B (0.49) and >100B (0.48).
Furthermore, we present additional results on the variance of pairwise RBOs based on our annotations by six human annotators for the N=13-wise ranking experiment. Table 5 presents that the variance of all pairwise RBOs among humans is 0.004, indicating minimal disparity amongst all annotators. It is more clearly observed that any pairwise RBO between two annotators is higher than the average agreement between humans and models (0.44).
Bias in Pairwise Human Preference The average RBO scores were 0.39 (ORDER BIAS), 0.50 (BANDWAGON EFFECT), and 0.43 (ATTENTIONAL BIAS), indicating modest agreement 7 amongst human annotators in a pairwise selection setting. The average proportion of biased responses across all human annotators for ORDER BIAS, SALIENCE BIAS, BANDWAGON EFFECT, and ATTENTIONAL BIAS are presented in Table 4. Compared to humans, VICUNA shows higher or similar bias proportions on all of the four bias types, where its
7Note that we considered these scores, which might initially appear low, as relatively high when considering the impact of biases that can affect individuals to varying degrees.
ATTENTIONAL BIAS proportion particularly exceeds humans by more than twice.
We view that humans still exhibit biases when making their preferences on pairwise LLM evaluations, but less than LLM evaluators on average. Similarly, on the induced bias benchmarks, humans were less affected by BANDWAGON EFFECT and ATTENTIONAL bias, highlighting a prevalent gap between model judgment capabilities and human ones, in which human-like biases are more intensified.

heading: 6 Conclusion
text: In this paper, we analyze 16 recently developed LLMs for their suitability as automatic text quality annotators in Q/A settings. We introduce a new benchmark COBBLER to assess their evaluation performance against 1) Implicit and 2) Induced biases. Additionally, we compare LLM evaluations to human preferences and find only a 44% average agreement. Our results indicate that most LLMs exhibit cognitive biases to a greater extent than humans, suggesting that LLMs are still unsuitable as fair and reliable automatic evaluators. In the future, potential de-biasing methods provide another area of interest in reducing each bias. For example, techniques such as chain-of-thought (CoT) reasoning or other alignment methods can perhaps be employed to reduce the bias for current models.

heading: Limitations
text: We acknowledge a few limitations within our study. Some models reach very low valid response rates, which may be due to the prompting format. With model-specific prompts, we may be able to extract more clear results for each bias. Additionally, we address the fairly subpar IAA within our human judgment study. This may be due to the difficulty of the task, asking MTurk annotators to rank 15 models to limit the number of comparisons required in a pairwise format, but also increases the complexity of the task itself, which may have caused lower quality in the annotations.
We also highlight the stability of our findings in the long term. As LLM research is rapidly growing, the capabilities of language models can scale exponentially with time. As such, with new developments being discovered frequently, previous LLM performance on our bias benchmarks may quickly become outdated (i.e. INSTRUCTGPT can be considered an "outdated LLM," as the API is also no longer offered on OpenAI’s platforms).

heading: Acknowledgements
text: This work was mainly supported by the research gift from Grammarly. We also thank Minnesota NLP group members for providing us with valuable feedback and comments on the initial draft.

heading: A Experimental Setup

heading: A.1 Model Hyperparameters
text: We set the same hyperparameters across models for each evaluation generation and response generation for consistency across all of the models. We limit the max new tokens generated to 128 tokens and set the temperature to 1.0. For Huggingface models, we set a repetition penalty of 1.2 and set the number of beams to 3.

heading: A.2 Experimental Settings
text: For models that are supported (ChatGPT, InstructGPT, GPT-4, Vicuna), we utilize Microsoft Guidance to better control LLM generations. Otherwise, we utilize the transformer pipeline library from Hugginface to retrieve each evaluation generation. Regardless of whether a models generation was collected from guidance or using the transformer pipeline, all parameters were the same. Model generation times for response generation ranged from 1 to 8 hours, and for evaluation generations ranged from 3 to 24 hours for each bias benchmark. All experiments were run on either A5000 or A6000 GPUs for models under 40B parameters. For models over 40B, A100 GPUs were utilized if an API service was not available (e.g. OpenAI, Cohere).

heading: A.3 Datasets
text: Eli5 (Fan et al., 2019) is a long-form questionanswering dataset constructed from 270k threads from the “Explain Like I’m Five” Reddit forum. The online forum consists of a community for individuals to ask various questions, and answers are provided in a format that is comprehensible to five-year-olds, along with assigned scores based on community votes. For our purposes, we only utilize the questions and their highest-rated answers to generate responses and benchmark automatic evaluators for text-generation quality.
BigBench (Srivastava et al., 2023) is a collection of benchmarks that look to probe the abilities of language models over a diverse range of tasks. We specifically utilize the strategyQA (Geva et al., 2021) dataset, which was constructed by crowdsourcing questions from writers as well as their responses with short justifications. We choose the strategyQA dataset to generate responses that require multi-step reasoning to effectively benchmark the ability of models to comprehend and compare the quality between two different explanations.

heading: B Supplementary Results

heading: B.1 Correlation between BANDWAGON and Percentage
text: In an additional experiment, we show a modified statistic for the biased model: "0% of people prefer {model}.” If bias tendency were indeed correlated with the statistic, we would expect the evaluator model to have 0 preference for bandwagon response. Due to limited computation resources and time, we ran the additional experiments for two representative models at each size range (+ all API-based models) and presented the results below in Table 6.
Here, one can observe that the preference choices for the bandwagon statistic greatly change (besides GPT4 and VICUNA) which suggests that indeed the biased tendency is correlated with the bandwagon statistic. However, we see that VICUNA, in particular, is not greatly affected by the statistics. This suggests that within the prompt, the model only focuses on the phrase “people believe that {model} is better” instead of the statistic. Similarly, this may be the case for Alpaca and InstructGPT as well. We also present the results of the bandwagon test by randomly choosing a percentage between 50% and 85% in Table 7. We continue see that most models demonstrate biased tendencies.

heading: B.2 Diverse Prompts
text: We additionally ask each evaluator to analyze generation quality along several different aspects such as “coherence, accuracy, factuality, and helpfulness” following (Bai et al., 2023) and (Zheng et al., 2023). As opposed to our single-aspect format in the main section, we conjecture that these cognitive biases remain regardless of evaluation aspects. To validate this, we constructed an extended prompt viewable in C.5 that incorporates different dimensions of evaluation criteria into our pairwise evaluation prompt and reported their results in Table 8 on the ORDER benchmark. We see that by including diverse perspectives in the evaluation setting, some metrics become more pronounced (i.e. COHERE for EGOCENTRIC) or bias decreases (i.e. VICUNA for EGOCENTRIC). However, we see that the proportion of biased evaluations stays relatively consistent for most models on all benchmarks. Hence, our findings remain that models still show a large skewness in bias tendency as evaluators.

heading: B.3 Prompting with Ties
text: We present a modified version of the prompt in B.3 that considers ties in each pairwise preference. Note that for SALIENCE, if a pairwise sample was labeled as “Tie,” we do not consider it for length bias. From Table 9 we see that the inclusion of the tie option does view a considerable change in the bias benchmarks. Notably, the strongest and smallest models (GPT-4, CHATGPT, BAIZE, WIZARDLM) do not exhibit any change. However, we see that the mid-range models (ALPACA, VICUNA) and INSTRUCTGPT display a large preference for assigning the tie label (≥∼ 90%) that does not present any valid results, to which we had originally only prompted two options for each evaluator to avoid this issue. The only model that demonstrated an improvement from previous bias behavior was COHERE.

heading: B.4 Decoupling Confounding Factors
text: We particularly focus on decoupling EGOCENTRIC and Salience, which are the most prone to having large correlations with each other (i.e. longer generations may indeed have overall higher quality generated by much stronger models).We highlight two important aspects regarding the identification of these biases:
• If multiple models have a large proportion of evaluations preferring their own responses (as the evaluated pool of pairwise instances is the same for each evaluator), we reason that this may suggest “egocentric” qualities within involved evaluators, regardless of the objective strength of the models. Moreover, we see this effect is especially demonstrated between the more powerful models as well (GPT4 & CHATGPT) that suggest the presence of EGOCENTRIC evaluations from their disagreement.
• We employ various strategies to mitigate these confounding variables and isolate each analysis as much as possible. For example, we employ a “hierarchical” rubric, where some biases take priority in an evaluation. Specifically, if an evaluation shows signs of order bias by choosing A in (A first, then B) and B in (B first, then A), we do not evaluate it for SALIENCE or EGOCENTRIC bias.
To get further insight into decoupling them, we examine additional statistics in Table 11 displaying the proportion of EGOCENTRIC samples where the model’s generation was longer/shorter than the other generation. In particular, since OLMO only won once, and LLAMA never won, their EGOCENTRIC ratios look weird. Otherwise, we view overall that most models (9/16) exhibit a self-preference for their own generations often when their own generations exhibit longer token length.
As above, we see that SALIENCE may be associated with higher quality generations, as we see that the strongest models (GPT4, ChatGPT) often prefer their own responses when their generations are longer. Nevertheless, even in smaller models (e.g., Cohere, Koala), preference for their own generations occurs more often when they are longer. However, as we previously emphasized, if multiple models observe a self-preference for their own generations, it is difficult to associate with SALIENCE as there is disagreement that is indicative of an EGOCENTRIC bias.

heading: B.5 Significance of Results
text: We adapt two statistical hypothesis tests based on the random bias threshold for the Order bias (firstorder and last-order) benchmark in Table 10. Since we have binary outputs (bias, not biased), we conduct a two-sample Z test of proportions to determine the significance of each proportion of biased evaluations from each automatic evaluator with the random baseline. We conduct the test with the null hypothesis defined to be that “evaluator X is just as likely to make the mistake of flipping its preference according to the order of the response to the first-order as the random baseline” or equivalently:
H0: the mean of Evaluator X for first-order bias is not any different from random selection.
On almost all of the ORDER benchmarks, the proportions of biased evaluations are statistically significant from ones by the random score. Notably, the p-values are critically small (z-scores are blown up) due to our large sample size. Also, we note that the p-value is actually not statistically significant for last-order bias in InstructGPT; however, the first-order proportions are statistically significant, indicating that one must consider the test for both positions to get the full picture of the evaluator’s tendencies in reference to the random baseline. For example, if both first-order and last-order were not statistically significant from the random
proportions, we might find that the evaluator is “unbiased,” but the following may also undermine the capabilities of the automatic evaluator reduced to just random choice.

heading: B.6 LLM Performance and Agreement
text: We detail the general agreement between machine preferences as similarly conducted in the humanmachine correlation study. Figure 5 visualizes the average Rank-Based Overlap between LLMs. We find that LLMs in their own size group (excluding the smallest size group) have a relative agreement with each other. For example, models in the largest size group (>100B) are more in agreement amongst themselves than with models from other size groups. Furthermore, we also show the average valid response rate from different bias promptings in Table 12. We gather the proportion of valid responses by post-processing each “eval-gen” via pattern matching. After post-processing, we then label each output as a valid or invalid response, such that if a response is valid, we give one point to the preferred system.

heading: B.7 Model Size
text: We conduct a supplementary experiment analyzing the impact of each bias for different models scaled by size in Table 13. We present results from a range of model sizes with LLAMAV2 and VI-
CUNA. Interestingly, we see that the valid response rate within LLAMAV2 goes down as the model size is scaled up, but the impact of each bias greatly increases as the model size is scaled down (with the exception of SALIENCE BIAS). On the implicit bias benchmarks, LLAMAV2 exhibits more robust performance with the proportion of responses affected by each bias SALIENCE BIAS in which longer responses are much more strongly preferred. For the induced bias benchmarks, a similar trend is viewed in which the effect of each bias on the model as an evaluator is dampened in correlation to the model scale. On the contrary, VICUNA exhibits a stronger valid response rate as the model size is scaled; however, certain implicit biases are much more amplified, such as ORDER BIAS and SALIENCE BIAS. For implicit biases, VICUNA tends to prefer itself when actual model names are used as size is scaled smaller while tending to prefer much more verbose responses as model size is scaled higher. Across the induced biases, VICUNA performs more resiliently proportionally to scale, although still strongly influenced by BANDWAGON EFFECT but much less affected by ATTENTIONAL BIAS. We include another visualization correlating the overall performance on each of the bias benchmarks with model size for the main results in Figure 2a.

heading: B.8 N -Rankwise setting: N = 4
text: We show the results and average rankings between four different models representing each of the different size groups: CHATGPT (>100B), FALCON
(>40B), ALPACA (>10B), VICUNA (<10B). For the experimental setup, we conduct a smaller study, generating 100 responses from each of the 4 different LLMs using the Databricks Dolly15k dataset (Conover et al., 2023) via the same instruction prompt template from Appendix C and the same evaluation prompt template from the ORDER bias.
We only employ this setting under the order bias setting in order to validate the complexity of the task that modern (smaller) LLMs aren’t capable of performing yet. We perform each experiment by randomizing the order of each list of responses and prompt each LM-as-evaluator to order the list from best to worst (top to bottom) according to the same criterion as the pairwise study (providing the instruction/sample reference). Furthermore, we also track ORDER bias, calculated by the proportion of responses in which the first (randomly) placed model was also ranked first by the evaluator.
As viewed in Table 14, we find that most models besides the closed-source API models (e.g. OpenAI) have trouble generating a proper rank list for even an N = 4 setting. This may be due to the increased complexity of the task (Dziri et al., 2023) where the ranking of N generations may become much more difficult as N gets larger (since the task complexity increases).

heading: C Prompt Templates
text: We present each evaluation prompt utilized for models to evaluate the quality between two generations. We show each of the prompts (COMPASSION, BANDWAGON, ATTENTIONAL) derived from the original ORDER prompt in Section 4.2. We highlight each modification made from the original template.
Our generation instruction template looks like the following:
### Instruction: ### Response:
For evaluation, bias-specific prompts are formatted as follows:

heading: C.1 Order
text: ### Instruction: Which system’s response is more coherent considering the reference and instruction?
The instruction is: {{instruction}} The reference is: {{reference}} “‘ System Star: System Square: “‘ Please respond in the following format strictly: System _ is better Do not provide any additional text or explanation: ### Response:
Also, we underline that EGOCENTRIC bias was extracted under two dimensions, hence its double column for (ORDER / COMPASSION) in Table 2. Since EGOCENTRIC is a bias extracted implicitly, it involves two different prompts from C.1 (Order) and C.2 (Compassion Fade). In the case of C.1, since model names are completely anonymous, the addition of “(You)” is omitted (as shown in Table 1, and models cannot tell if they are self-evaluating. In contrast, C.2 shows recognizable names; thus, “(You)” is appended to the system name when selfevaluating. We highlight that the added “(You)” within the EGOCENTRIC example in Table 1 serves to explicitly communicate an example of an egocentric bias to the reader and not necessarily the prompt itself.

heading: C.2 Compassion Fade
text: ### Instruction: Which system’s response is more coherent considering the reference and instruction?
The instruction is: {{instruction}} The reference is: {{reference}}
“‘ {model1_name}: {model1_response} {model2_name}: {model2_response} “‘ Please response directly in the following format: System _ is better Do not provide any additional text or explanation: ### Response:

heading: C.3 Bandwagon Effect
text: ### Instruction: Which system’s response is more coherent considering the reference and instruction?
The instruction is: {{instruction}} The reference is: {{reference}}
“‘ System Star: {model1_response} System Square: {model2_response} “‘ 85% of people believe that {system} is better.
Please response directly in the following format: System _ is better Do not provide any additional text or explanation: ### Response:

heading: C.4 Attentional Bias
text: ### Instruction: Which system’s response is more coherent considering the reference and instruction?
The instruction is: {{instruction}} The reference is: {{reference}}
“‘ System Star: {model1_response} System Square: {model2_response} “‘ {distraction}
Please response directly in the following format: System _ is better Do not provide any additional text or explanation: ### Response:
Attentional Bank
{System} likes to eat apples and oranges.
The coolest thing that {System} can do is a 60 second handstand.
{System} plays a lot of soccer and basketball.
{System} has been all around Europe two times.

heading: C.5 Diverse Prompt
text: ### Instruction: Which system’s response is more coherent, accurate, factual, and helpful considering the reference and instruction?
The instruction is: {{instruction}} The reference is: {{reference}}
“‘ System Star: {model1_response} System Square: {model2_response} “‘ Please response directly in the following format: System _ is better Do not provide any additional text or explanation: ### Response:

heading: C.6 Tie Prompt
text: ### Instruction: Which system’s response is more coherent considering the reference and instruction?
The instruction is: {{instruction}} The reference is: {{reference}}
“‘ System Star: {model1_response} System Square: {model2_response} “‘ If you believe each response is equally sufficient simply respond with: Tie
Please response directly in the following format: System _ is better Do not provide any additional text or explanation: ### Response:

heading: D Human Preference Study

heading: D.1 Annotator Recruitment & Annotation Process
text: N=13-rankwise setting We recruited six workers from the Amazon Mechanical Turk (AMT) platform, each of whom had a U.S. high school diploma and a Human Intelligence Task (HIT) approval rate of 99% or higher on the platform. To ensure better-quality annotations, we initiated a toy round using five sample instruction sets. Each instruction in the toy round contained five brief LLMgenerated sentences. Workers were then asked to rank these sentences based on their own preferences, but taking into account the following two specific criteria: (1) the fluency and logical coherence of the LLM-generated text in response to a given instruction sentence, and (2) the text’s alignment with a reference sentence that provided additional context and background for the instruction sentence. Furthermore, they were asked to place a black bar above the answers that did not satisfy these two criteria, as this is used for the threshold to evaluate the quality of their texts.
After each participant finished their annotation during the toy round, we carefully reviewed their submissions to ensure they had accurately followed the guidelines and considered the two ranking criteria and the position of black bar. For their efforts, each participant received a $3 payment for completing the toy round (HIT). Running the toy HIT several times yielded a final selection of six qualified workers, who were then invited to participate in the next stage involving the actual task of ranking 50 instruction sets. Each of these sets included 13 texts generated by 13 different LLMs. Note that LLAMA2, MISTRAL, and OLMO were not included yet at the time of our human study.
To avoid overwhelming the workers, we divided the main task into five separate HITs, each containing a varying number of instruction sets to rank: (1) a pilot round with 5 sets, (2) two intermediate rounds with 10 sets each, and (3) two final rounds with 13 and 12 sets, respectively, adding up to a total of 50 instruction sets. These six workers received compensation upon completing each HIT, accumulating to a minimum of $47 for the entire series of rounds. This averaged out to approximately $1.05 per instruction set. Additionally, on average, it took each of the six workers about 5.8 minutes to complete a single instruction set. Lastly, considering the level of difficulty for the workers to
rank 13 outputs per instruction set, we also remunerated them with a bonus of at least $5 per round, based on the quality of their performance. Lastly, we checked that our collected data did not include any personally identifiable information or offensive content and that the AMT responses were already anonymized.
Bias in Pairwise Human Preference For each bias, we collected human preferences from 75 experienced AMT workers who had HIT approval rates over 97%, had completed more than 10,000 HIT tasks, and resided in five major English-speaking countries (e.g., the United States, Canada, United Kingdom, Australia, and New Zealand.) These workers were then grouped into 25 sets of 3, with each group assigned a HIT task encompassing 30 model pairs randomly sampled from an instruction. Consequently, we generated 25 HITs for each bias. These workers were tasked with choosing between two anonymous options (e.g., System A and B) for each of the 30 pairs. Their decisions were purely based on their preference, but we also asked them to consider the alignment and coherency with the instruction and reference sentences of each set.
To employ a pre-task and training session, we asked the participating workers of each HIT to complete a qualification round, which asked three example instructions to complete and pass. Only workers who passed this round were allowed to start the main tasks of annotating 30 pairs, ensuring that the workers were able to understand the HIT. Each worker who participated in a HIT received a compensation of $2.5. Note that SLIENCE BIAS were computed using the annotations from ORDER BIAS experiments on the AMT platform.
Similarly, we confirmed that our collected data did not include any personally identifiable information or offensive content and that the AMT responses were already anonymized.

heading: D.2 Details on using RBO
text: Rank-biased overlap (RBO) 8 is a widely used metric for evaluating the similarity between two ranked lists and is particularly relevant for tasks in information retrieval (Oh et al., 2022; Sun et al., 2023). The RBO value ranges from 0 (non-conjoint) to 1 (identical). In more detail, 0 indicates that there is no intersection or similarity, while 1 indicates a total intersection and complete similarity between
8We implemented RBO using the python package ‘rbo’: https://pypi.org/project/rbo/.
two ranked lists, A and B, in terms of ranked elements and order. Unlike classical correlation-based metrics such as Kendall’s tau or Spearman’s rank correlation, RBO is intersection-based, so there is no criteria range of value for RBO regarding the interpretation of its score. Rather, a higher continuous value of RBO means a higher ranking similarity between A and B.
In addition, unlike traditional correlation-based metrics like Kendall’s τ or Spearman’s ρ, RBO allows for greater weighting of the top k elements in the ranked lists being compared. This feature makes RBO well-suited for our experimental setup, where AMT workers were tasked with reading and ranking 13 outputs generated by LLMs. We operate under the assumption that workers are likely to place the highest-quality texts at the top five positions of their ranked lists.
This idea of weighing the top elements in the ranked outputs aligns with previous research, which claims RBO to be an effective metric for the agreement between ranked annotations with human rationals and automated evaluations, especially when greater importance is given to the topranked elements (Jørgensen et al., 2022). Given these considerations, which are highly relevant to our own study, we decided to use RBO as the metric for assessing agreement between human preferences and LLM evaluations.
RBO is defined in Equation 1 and tailored to suit the specifics of our study. Here, H and L represent two ranked lists of shape (1, 13), corresponding to human preferences and LLM evaluations for each instruction set, respectively. The maximum depth for H and L is set at 13, and p is a tunable parameter that determines the degree of top-weightedness in the final RBO calculation. To obtain an average RBO score across all 50 instructions, we sum the individual RBO values between H and L and then divide by 50.
RBO(H,L) = (1−p) 13∑
d=1
pd−1 |A[1 : d] ∩B[1 : d]|
d
(1) Following the work of Webber et al. (2010), we set the value of p so that approximately 86% of the weight is concentrated on the first d ranks, where d = 5 in our case. The weight distribution over these top d ranks can be determined using Equation 2. This means that the value of Equation (2) given d = 5 should be 0.86. In our experimental setup,
we found that p was approximately 0.8.
(1− pd−1) + (1− p p
) · d · ( ln 1
1− p − d−1∑
i=1
pi
i
)
(2)

heading: D.3 Details on Pairwise Human Preference Experiments
text: In pairwise human preference experiments, we did not test the COMPASSION FADE and EGOCENTRIC BIAS as they cannot be applied to human cases, because humans are not likely to be impacted by the anonymity of model names and the texts used in our setups are not generated by humans as well.
Unlike pairwise model evaluation as described in Section 4.2, we were not able to evaluate with humans all possible 5,250 model pairs. Instead, we first randomly selected 25 of the 50 total instructions. Then for each instruction, we produced 15 pairs of randomly sampled model outputs and created another 15 pairs by reversing their order (for ORDER BIAS) or switching the bias-induced sentence between A or B (for BANDWAGON EFFECT and ATTENTIONAL BIAS). This results in 30 pairs (with 15 unique model pairs) in total for each instruction and finally totals 750 pairs for all 25 instructions. Note that the sample size ensured a 95% confidence level with a 5% margin of error for a population size of 5250.
Upon collecting all annotations for each bias, we calculated the average IAA using the RBO for each bias. Each instruction consisted of uniquely (but randomly) sampled model pairs, with some models appearing multiple times. Hence, we normalized the rank of each model in the sampled pairs by calculating the ratio of the model’s “win” to its total appearances. With this data, we re-ranked each model in the sampled pairs per instruction. Afterward, we computed the mean RBO among the ranked model lists from each group of three AMT workers per instruction. We then averaged these RBO values over all 25 instructions to calculate the IAA scores for each bias experiment.
Finally, we computed the bias proportion for each annotator by dividing the number of biased pairwise samples by 15. Following these steps, we aggregated the bias proportions across all annotators, showing the degrees of impact of bias on human preference in pairwise selections. For SALIENCE BIAS, we leveraged annotations from ORDER BIAS experiments and calculated proportions for shorter and longer preferred responses.
We then reported the preference with a higher average proportion that was computed all across annotators, indicating whether humans were more influenced by shorter or longer length bias.

heading: D.4 Details on Pairwise Human Preference Samples
text: We clarify that for each one of the three bias measurements, a random sample of 750 model pairs was tested by three annotators in the pairwise human experiment setup, totaling 2250 samples for 3 annotators. More formally, we define:
• B(= 3): Number of bias experiments (B_salience, B_order, B_bandwagon)
• S(= 25): Number of samples selected for each bias experiment
• P (= 15): Number of original model output pairs (Model A - Model B) for each sample
• M(= 2): Multiplier for both orderings of each pairwise sample (i.e., for each A-B we also add B-A)
• A(= 3): Number of human annotators evaluating each model pair
Tpairs = Total # of model pairs for one bias
= S × P ×M = 750
Tevals = total # of human evaluations for one bias
= Tpairs ×A = 750× 3 = 2250
Thus, we analyze 2250 × B = 6750 samples across all bias setups.
D.5 Interface Design We present the interface design temple for each of the human preference experiments setups on the AMT platform, including (1) N-rankwise setups (N=13) and (2) bias in pairwise human preference, as described in Section 4.3. The original prototype of the interfaces that we used for the Nrankwise experiments, as in Figure 6 is based on https://github.com/mtreviso/TextRankerJS. For the pairwise human bias experiments, we referenced the interface design from Hayati et al. (2021).

heading: Future Work
text: In the future, potential de-biasing methods provide another area of interest in reducing each bias. For example, techniques such as chain-of-thought (CoT) reasoning or other alignment methods can perhaps be employed to reduce the bias for current models