Data Pricing Mechanism Based on Property Rights Compensation Distribution
Authors: shiqian Liu
Peizheng Wang
Chao Wu
Venue: Submitted to ICLR 2023 (2023)
Keywords: data valuation
game theory
data ownership
modern property rights theory

Abstract: While machine learning (ML) benefits from data, it also faces the challenges of ambiguous data ownership, including privacy violations and increased costs of using data. Yet existing approaches to data valuation may focus on preventing privacy breaches, but do not truly protect data ownership. This is because a data trading marketplace that protects data ownership should achieve this goal: once data is traded, its ownership does not transfer to a new owner but merely enlarges its coverage. Considering that the transfer of property rights in the process of data trading makes compensation necessary, this paper proposes the first data valuation mechanism based on modern property rights theory. Specifically, we propose the integration of property rights to improve the final revenue of the entire workflow called the “data chain” while compensating process executors who lost ownership after integration. Then, we consider the expectations of both the integrator and the integrated party during the compensation allocation. For the former, we apply compound interest to assess a total compensation equivalent to the time value for the Data chain. For the latter, we respect and meet their expectations as much as possible. To achieve this, we provide the framework based on Least-core to assign the compensation and prove that our framework can also work compared to existing algorithms. Finally, to cope with more complex situations, we adjust the traditional Least-core and demonstrate theoretically and experimentally that the compensation mechanism is feasible and effective in solving the data pricing problem.

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DATA PRICING MECHANISM BASED ON PROPERTY RIGHTS COMPENSATION DISTRIBUTION CONFERENCE SUBMISSIONS
Anonymous authors Paper under double-blind review
ABSTRACT
While machine learning (ML) benefits from data, it also faces the challenges of ambiguous data ownership, including privacy violations and increased costs of us- ing data. This suggests that the value created by data is determined not only by its utility but also by the cost of using the data (negative externalities). The exist- ing pricing methods mainly value data based on its utility but ignore the negative externalities caused by fuzzy ownership, therefore can not design an efficient pric- ing mechanism. Throughout the data life cycle (creation, pre-processing, training, etc.), the usufruct and ownership of the data are transferred at the same time, so the benefits and costs are generated simultancously. Considering that data rights confirmation and data pricing cannot be separated independently in the process of data transaction, we propose the first data valuation mechanism based on mod- ern property rights theory in this paper. Specifically, we propose to clarify the ownership of property rights through the integration of property rights and im- prove the final revenue of the whole workflow "data link" through the form of the whole collective, while compensating process performers who lose ownership af- ter the integration. Then, consider the expectations of both the integrator and the integrated party during the compensation allocation. For the former, we apply compound interest to assess total compensation equivalent to the time value for the Data chain. For the latter, we respect and meet their expectations as much possible. To achieve this, we provide the framework based on Least-core assign the compensation and prove that our framework can also work compared existing algorithms. Finally, cope with more complex situations, adjust the traditional Least-core and demonstrate theoretically and experimentally that the compensation mechanism is feasible and effective in solving the data pricing problem.
INTRODUCTIOIN
While MI. benefits from data, it also faces challenges brought by the ambiguity of data owner- ship (Maini et al.) (021). According to the life cycle, data is generated by the producer and then passes through agents such as data preprocessors and model pre-trainers, and finally generates value through model training. In this process, data ownership and access are transferred simultancously, which makes the utilization of data have cost: On the one hand, this makes the subject of privacy protection unclear, posing the potential for privacy violations. The Cambridge Analytica scandal, for example, where Facebook and Cambridge Analytica collected the personal data of up to 87 mil- lion Facebook users without their consent (Kelly), gave rise to an unprecedented discussion privacy. On the other hand, even though a large number of data pricing models are already available in the data marketplace to value data (Chen et al. 2019 Liu 2020 Li et al., 2013) Koutris et al.) 2013 2015), each use of a dataset requires a valuation, since datasets behave differently in different models. This increases the negative externalities of ML (e.g., huge computational volumes).
data
The imbalance between the benefits of data and the costs of using it makes clarifying property rights an important issue. Demsetz/ (9677) points out that the generation of property rights is essentially tradeoff. Property rights arise when the benefits of internalizing externalities by defining property rights are greater than the costs of engaging in the act. Furthermore, the purpose
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of clarifying property rights is to maximize returns by internalizing externalities. Taking the data life cycle as an example, the concrete task of confirming the ownership is to delineate the controllable rights and clarify the owner of the rights (Asswad & Marx Gómez 202T), whose purpose is to internalize externalities to the maximum extent. In other problem setting, such as feature selection or data source valuation, giving the most valuable feature data source ownership can internalize externalities ( (.g., reduce computations after setting the appropriate utility functiin ) and improve the performance. should be noted that the revenue of data transactions under the premise of data ownership includes both traditional revenue and the cost caused by negative externalities that need to be subtracted. And the purpose of rights confirmation is to maximize the revenue of data at this time.
The existing data marketplace always assumes that the ownership of data belongs to its producer, and attributes the costs of data transactions to privacy protection, making data privacy protection becomes an issue juxtaposed with data pricing rather than unified. Specifically, traditional data
pricing schemes including data-based pricing, model-based pricing (Chen al. 2019 Liu 2020).
and query-based pricing (Li et al.) 2013 Koutris et al. 2013: 2015). have paid varied degrees of attention to avoiding privacy leaks. The marketplace with data- based pricing allows the customers to access datasets entries directly, which makes it challenging for ownership protection. To address this challenge, the model-based pricing framework propose creating different query versions by carefully adding different noise (Chen et al.) 2019) or sells a series of differentially private models to respect data owners' privacy restrictions (Liul (020). In terms of the query-based pricing framework, makes decisions about the restrictions on data usage (Li et al. 2013)), which partially alleviate the
shortcomings of privacy protection. However, their pricing mechanism still reflects the value of the data by quantifying the utility of the data or quantifying the model training examples, which, incidentally, avoids the data owner's privacy from being breached. Such passive protection can only strive to prevent privacy leaks but fail to integrate more negative externalities.
In this case, we propose a data pricing method based on property rights compensation, which different from the previous pricing mechanism. Our contributions are mainly reflected in:
Clarifying the data ownership. Through the introduction of modern property rights theory, we answer the question of maximizing the internalization of externality: integrate the co- operative parties into a whole, and the one who makes the most marginal contribution holds the overall data ownership. In fact, according to the logic of modern property rights theory, ownership can be determined for all agents with cooperative relations through integration. The effect of it will be improved with the increase of marginal contribution difference of agents, which can extend our framework to the whole life cycle of data. In this paper, we take the background of feature selection and data source pricing as example to prove the feasibility of the method.
Discussing the Data pricing from the perspective of compensation that the transfer of data property rights necessitates the payment of compensation. Since the use of data brings both benefits and costs, we propose that the valuation of data should not only be based on benefits but also consider its costs. Although the cost cannot be directly quantified, we internalized externalities furthest through property rights integration maximize the value of the data. On this basis, the compensation for distorted ownership is estimated by the time value of the data. Experimental results show that this method can still complete the task of data pricing.
We propose using the least-core rather than other concepts in cooperative games to solve the allocation scheme. Since the process of ownership integration requires the integrated party to transfer ownership to form a grand coalition, the withdrawal of either agent will increase the negative externalities of the coalition. We are more inclined to realize the stability of the distribution scheme through the core. In this process, we balance the ex- pected compensation of both the integrator and the integrated party. Finally, we discuss the feasibility of this framework under different conditions by adjusting the coefficients of the deficit parameter.
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RELATED WORK
Data ownership in Machine Learning. Research in the field of machine learning attaches some importance to the ownership of data or models. Specifically, the work revolves around ownership utilization and protection. For the former, the work of Maini et al.] (202T) has achieved determine whether potentially stolen model was derived from an owner's model or dataset. And for the latter, the existing measures for protecting data ownership the data marketplace include legal means and technical means.
For the former, countries have been experimenting with relying on the traditional model of "empowerrenn--iolation to provide a legal basis for data property rights protection, and have achieved some practical results, such as the well-known General Data Protection Regulation(GDPR) and the California Consumer Protection Act(CCPA). Using the GDPR one of the patterns, the pro- ducers of data are endowed with data ownership. The existing law regulates data rights and legal obligations. Although, the law provides a powerful weapon for data property rights, it continue to face constraints in practical application. For instance, GDPR highlighting that it may fundamentally change the way big data analysis is done, making a suboptimal and inefficient method of protec- tion (Zaskky 2017). Additionally, the number of cases filed by parties is limited and is difficult to obtain satisfaction of claim real life. Thus, the protection of data ownership has not achieved the expected performance despite rapid legislative progress (Li et al.) 2019). The legislation has established legal basis for the ownership issue, but still unable to protect favorably. This poses a significant hidden risk to the establishment of a healthy data trading market.
For the latter, the fundamental technical solution is to shift from centralized paradigm to decentral- ized paradigm. And the key technologies to the decentralized paradigm include Federated learning, Secure Multi-Party Computation (MPC), Blockchain, etc. In federated learning, clients collabo- ratively train a shared model under the orchestration of central server, while keeping the training data decentralized (Li et al,, 2020). Due to its advantages in privacy protection, there are increasing works that have been proposed to use federated learning in healthcare (Xu & Wang/ 2021), city management (Jiang et al., 2020), etc. MPC enables participants jointly compute a function with their data while keeping data private. tamper-proof ledger using the blockchain may be used to record digital interactions (Wirth & Kolain, 2018). These interactions not only contain operations on the data but can also record the process of data modeling and analysis (Wang et al. (0188). If the complexity of these technologies is not taken into account, we could embed privacy into the entire engineering process, with these technologies effectively involved the loop (Martín Kung 2018).
Compensation distribution. There are a number of compensation distribution criteria proposed from the area of cooperative games. The acquiescent baseline to assign the data importance/value to model is leave-one-out (LOO). Another conception, Shapley value (Shapley 1953). the most common one amongst all of the valuation criteria. It satisfies some proven theoretical properties, provides an efficient and fair solution to distribute contributions among players (clients or partic- ipants) by assigning to each real value which denotes its influence (profit). It is Ghorbani & Zou 2019) who developes a principle framework to address data valuation in the context of supervised machine learning. More precisely, given learning algorithm trained on n data points to produce a predictor, data Shapley was first proposed to quantify the value of each training datum to the predictor performance. Besides, solve this question of fairly distributing profits among multiple data contributors, Jia et al. (2019) proposed novel approach, which addresses the problem of data valuation by utilizing the Shapley value. Furthermore, Kwon et al.) (202T) derives the first analytic expressions for DShapley for the canonical problems, and proposed an algorithm several orders of magnitude faster than D-shapley.
PRELIMINARIES AND BACKGROUND
In this section, we introduce the background and preliminaries of the framework. First, we introduce the definition and generation of the data ownership to help understand the importance of clarifying property rights. Then we formalize the data workflow and introduce the theory to identify ownership. Finally, we introduce the solution to distributing the compensation. The notations used frequently showed in Table
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Table 1: The summary of notations
NOTATION
DEFINITION
DC
Data chain
DP
data product (performance of the machine learning) the jth action of Data chain the agent conducting the 1th action the expected compensation of the 1th agent the time value of the j agent at time / the compensation for DC estimated by the integrator time the compensation for the hth agent estimated by the integrator time
A
a
W;
C
Bt
B;
bi
the payoff of the 1th agent at time È the compensation allocated to the 1th agent
1/
the contribution of the jth agent the contribution rate the 1th agent the deficit parameter in least core
%
d
3.1 OWNERSHIP OF DATA
Despite the absence of unified view on the definition of the data ownership. is widely agree that the rights of it including, but not limited to access, creation, generation, modification, analysis, use, sell, or deletion of the data, addition the right to grant rights over the data to others (Asswad) & Gómez 202T). If we explain the generation of data property rights according to the theory of property rights, shows that the benefits of internalizing externalities in the process of data value extraction have been greater than the costs of direct stepwise training data. The property right of an asset needs be defined either because the income of defining the ownership becomes larger, or because the cost of it becomes smaller. The reasons for the emergence of data property rights include the above two aspects: on the one hand, with the widespread usage of new information and communications technologies (ICTs) such highspeed networks, cloud computing, and pervasive data collection (Hashem et al.; 2013), we now have a vast amount of data available. At the same time, upgrades in computer hardware and improved algorithms have substantially increased the power of analytical techniques, and thus the value of data has been better derived. On the other hand, the distributed frameworks including blockchain also provide way protect owners from the transfer, reducing the cost of defining ownership.
3.2
DATA CHAIN
Data has value, but the value of a data-driven product or service depends not only on the data, but also on the model upon data, making it difficult understand the value of data before modeling. ii) The value of data can be augmented with other data, in a nonlinear manner. iii) The utility of data-driven product of service also depends the user of it. To this end, we propose that the realization of data value extraction needs workflow. It is in this workflow that the process of data circulation is accompanied by the movement of data ownership and usufruct of
get from data is non-linear and unpredictable as: i) The utility
Definition 1. A data chain DC' is consequence of actions (2,, An) upon data to create data product DP, which creates payoff B, at time
3.3 THEORY MODERN PROPERTY RIGHT
We introduces Modern Property Rights Theory in the field economics to provide a theoretical basis for ownership integration in the Data chain. After integration, the property rights are further clarified. In this subsection, we introduce the background and basic logic of modern property rights theory, and in the subsection 4.2 explain how to integrate the ownership of DC.
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The modern propety rights theory. This theory identifies ownership with residual control rights and argues that, in setting with contracts that are incomplete and cannot mandate investment deci- sions, firm boundaries are determined by which ex ante investments are most valuable. It is worth noting that the concept of an incomplete contract was first introduced in the seminal work of modern property rights theory, which elaborated that a contract cannot be transformed into comprehensive and complete contract through meticulous enumeration. The author, Grosssan & Hart (I966) stated that the essence of ownership is the right to control the subject matter, with all exceptions except the contract's content. Since then, number of articles have expanded on this concept, gradually forming the modern theory of property rights (Hart & Moore, 1990; 1991] |Hart al.) 1996). The basic idea is that property rights created through collaboration should be assigned to the party who contributes the most to the post-cooperation output. comparison to the transaction cost theory (Coase 1960), this theory introduces a new concept for vertical integration and addresses the ques- tion of who integrates" during the integration process.
The necessity of integration. The modern property rights theory extends the definition of the property rights, which can be of two types: specific rights and residual rights. Data ownership refer to the control over the remaining property rights in addition to those specified in the contract. However, in the data marketplace, simply entrusting data property rights to them (such as individuals and small companies, etc.) is uneconomical. Externalities will greatly increase the operation cost of the data market and hinder its development. The externalities during different stages in a DC include but are not limited to:
Difficulties in data collection. The data collected from each original owner involves nego- tiation.
The high cost of model training. Both the time and space costs of data processing and the evaluation of data value increase exponentially with the volume of data. As we proposed the strategy network pre-training earlier in order to alleviate the time complexity with O(2*).
At this point, the advantages of ownership integration are obvious: On the one hand, the externalities stated above are internalized through vertical integration of property rights in DC, which will greatly reduce the costs and energize the data market. On the other hand, allowing particular agent to integrate property rights makes production decisions more uniform. At the same time, sub-optimal Nash equilibria resulting from each player's exclusive investment will no longer occur.
3.4 COMPENSATION ALLOCATION CRITERIA
After integrating the property rights of the DC, we hope to establish a stable allocation scheme, which can simultaneously satisfy the expectation of all agents. There are a number of allocation criteria proposed from the cooperative game. Shapley value, the most famous criterion we have in- troduced above, is more concerned with the fairness of the allocation instead of stability. Intuitively, should adopt a criterion with more concern about the stability of the distribution to make the consolidated DC more stable. What worse, it has been demonstrated that calculating approximate Shapley value in the context of big data fails obtain approximate from samples with uniform dis- tribution (Balkanski et al.) 2017). Therefore, we propose to use Core instead, which has not only an intuitive superiority over shapley value for solving compensation allocation in the context of prop- erty rights consolidation, but also a theoretical superiority in terms of the approximation algorithm's 's convergence guarantee. Furthermore, another cooperative game solution set that also involves the perspective of both parties should be concerned. The bargaining set (Aumann & Maschler 2016) is defined similarly to the core, while/Einy et al. (1999) demonstrated that both core and least-core are included in the bargaining solution set. However, the bargaining solution set only considers coalition deviations that are stable themselves compared the core, i.e. no inverse deviation permitted, which contradicts the complexity expected from actual compensation.
Core and the least-core. Consider the characteristic function game G = (N, and its outcome (CS,2) If the total payoff of a coalition S under is denoted by x(S), and xxS) < v(S) for some S C N, the agents in S might benefit more from departing the coalition structure CS and forming their own coalition. This gives each member of S an incentive deviate. As a result, the outcome (CS, æ) is unstable. The core of G is the set of stable outcomes, distributing the outcomes where no subset of agents has incentive deviate. Therefore, the core could be defined follow:
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Definition 2.
The core of characteristic function game G (N, is the set of all outcomes (CS,z) such that z(S) 2 v(S) for every S N.
However, the stable coalition structure may not exist. To assure non-emply solution urally request that the core notion be relaxed, requiring merely that no coalition gain considerably from deviations(if not, using Shapley value distribute compensation will also make Data chain (DC) unstable), i.e. no member deviations. We assume that each agent has an expected W; for their compensation, which is the bottom line when the a" allocates compensation. In this vein, adding an appropriate relaxation parameter d can alleviate the problem. This gives rise to the following definition:
nat-
Σ E FES
Σ W ES
CC
(1)
Then, any cooperative game would not has an empty core as long as the d large enough. When d is positíve, it means that there is gap of expected compensation between the integrated and the integrating agent. Then we hope to minimize this gap so that the property rights of DC can be integrated in the most stable way. Inversely, the negative d means that the integrating agent has paid compensation that exceeds the expected amount of the integrated. In this case, minimizing the additional compensation could reduce the costs while meeting the needs of the integrated agents. Therefore, we are interested in finding the smallest d, which would be defined as a set of solutions the following linear program:
min s.t.
E INN Φ1 = Lies Oi + W AA S DC
(3)
The the time complexity of exact solution of the least core is ((2*). Even calculating this scemingly simple linear programming equation faces the same amount computation as shapley value. But turns out be possible to find the least core solution with probability at least 1 1-8 (Yan & Procaceia 2021
Pr |d: + + wi22-1 S~CD
Since the Balkanski et al.] (2017) points out that the generalization error of the PAC-learnable function small when the number of samples is sufficient, and the solution under arbitrary pre- cision can be calculated from the number of samples related to the VC-dimension, we can give the - probable least core a probabilistic guarantee.
Theorem 1. Given 8, A > O, the linear program over O((n + log(1/A))/8* coalitions sam- pled from DC solved by the Monte Carlo algorithm would give payoff allocation the 8 probable least core with probability at least 1 A.
The proof theorem will be provided in the appendix A.
Compound interest How can the property rights consolidation process ensure that the property rights are not undervalued? The propose of this subsection is to estimate the payoff to each action (and its providers).
The compound interest considers the time value of the money. And the time value of money reflects that currently owned currency has greater value than the same amount of currency received in the future, thus the currency can be invested and compounded. Since the data is a special type of asset (Bodendorf al. 2022), naturally apply the compound interest estimate the time value of the data. According to this concept, the interest will be calculated based on the principal amount in addition the newly obtained interest can also generate interest. In the context of data trading market applications, the core theoretical basis of an agent's capital accumulation is the principle of compound interest, which allows one obtain desirable and significant time value by investing over a long period. Taking the initial moment of investment b9 of agent, as an example, the time value after times investments calculated as follows:
C 6/
(5)
with compound interest 7 (1+ investment, the principal amount is expected to increase to b/ (1 + 76)- It worth noting that
2d
As result, when a, completes the first phase of its

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after completing the second period of investment, agent, 's principal is expected to increase to b/ (1 + 1o rather than b/j (1 + % due to the subsequent discount in the nominal interest rate as the investment period increases. When the number of investments approaches infinity, the time value is calculated in a continuous form as follows:
lim (1+ + 70p= =e"6.
80000 t = e%6
(6)
4 METHOD
In this section, we will explain how to finish the data pricing task by compensation distribution. The framework proposes to integrate the ownership according to the contribution rate first, dividing the agents of the Data chain into integrator and integrated party. After that, it takes both the two parties' expectations into account allocate the compensation.
4.1 AGENT'S S CONTRIBUTION FOR DATA CHAIN
To evaluate the actions in data chain, we assume the payoff B, for the data chain at the time t is given. Then the problem is how to quantify the contribution to all the participating agents in DC. We then propose a revised version of Shapley Value. Specifically, we define a baseline provider az for A, which is the provider with no extra cost to serve the baseline function of a;- For example, for data providers, the baseline provider can the open data with no cost; and for data modeling, the baseline provider can be the open-soureed pre-trained model without extra cost for model training. Therefore, the coalition would prefer a low-cost baseline compared to the agent with negative contribution rate. Specifically, the contribution th; and the contribution rate % of a are defined as:
[S]((DCI -SS 1)! (v(Sua)) v(S)), 74 Σ, e DCI!
e
1/
Σ SCDC//
where U(SUa) - vSS) is actually about the difference of utilities of two data chain, one with a, and the other without a, but having baseline provider ot instead. We prefer softmax to the linear normalization for the following two characters: First, a negative marginal contribution can be normalized positive normalization cannot be calculated when the Shapley value of two agents is 0.5, -0.5 respectively. Secondly, when the number of agents is small, the difference in the marginal contribution can be huge. The linear normalization will cause the value of b to be close to 0 or 1, while the softmax normalization can alleviate this phenomenon. When the number of agents is large, the nor- malization methods are similar to each other. Our experiments on synthetic data sets illustrate the second feature of the softmax function.
by the softmax function. This avoids special case where linear
4.2 PROPERTY RIGHTS INTEGRATION
According to the modern propety rights theory, the goal of data ownership integration is to maxi- mize the value generated by the DC'. The ownership or residual control over data beyond the user agreement in the data integration process should be shifted to the agent that plays a key role, order to incentivize the agent to invest more resources in the data market's efficient operation. To realize the data property rights transaction the context modern property rights theory, the agent that contributes more significantly, i.e., the party that integrates user data, only needs to pay "compen- sation" to the user during the transaction process. Accordingly, we propose that a" Gargmazy
1
should integrate the other agents in the DC. This idea is inspired by modern property rights theory.
For example, if a² has the largest marginal contribution, he would have the largest unit input-output for DC. At this point, a* can integrate other agents obtain their control. It means that a" obtains the power to make the decision of all proprietary investment through integration, and guarantees output optimization through residual control. Then a" would gain the "income" of property rights. But correspondingly. other agents also lose investment motivation, resulting in insufficient invest- ment and distorting the final output. However, since the investment of a² is important to DC,
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the distortion will be much smaller than the efficiency loss of Nash equilibrium. The larger the difference of marginal contribution is, the closer the integration result will be to the optimal output.
Specifically, taking the DC with two agents preprocesses the data and 02 is the company that trains the model. Let q:(2 = 2) to be the sufficiently complex production decisions which cannot be specified completely in initial contract between the firms. d₁ and a2 represent the exclusive investments of a and 02, respectively. DP represents the output after integration, and here refers to the performance of modeling. To maximize the output of the DC, more accurate models that meeting the requirements of the order should be trained. As is mentioned above, the DP may not be ideal before integration. Meanwhile, 91 (data quality) and 92 (the cost of model training) cannot be reflected in advance (i.e., in the contract). Therefore, the noncontractibility q leads to the need to allocate residual control rights. Then the integration may occur in two situations: i) When to improve the training accuracy of the model. ii) When d2 integrates d1, it can exercise control over to increase the preprocessing input. If ag has greater marginal contribution, consolidated and its proprictary investment in period, will be controlled by a2 to optimize DP.
example. Suppose that aj is the company that
owns 02, it can exercise the control over
will be
4.3 COMPENSATION DISTRIBUTION
On the integrator perspective. The agent who contributes most to the DC' owns the property rights and therefore gains the income from now on. Since the compensation paid for the integrated party becomes the cost for him, it is naturally expected to be few possible. But matter how low the compensation is, it should be at least equal to the time value of the pre-integration capital at any time in the future, motivating the other agents willing to lose control. As a result, the total compensation paid by the consolidator to all other agents should satisfy the following condition:
Bu Σ B EN
with lim B 1.
On the integrated perspective. We define W; to be the compensation expected by the who loses residual control. In this paper, we argue that the rational expectation should consistent with the time value that can be calculated by Eqn(5). Inversely, irrational expectation may be either too large or too small in absolute value, or the relative expectation ranking among agents may not match the contribution ranking.
Allocation with least-core. Although our least-core scheme can provide a distribution scheme that is most conducive to the alliance's stability, it does not mean that disregard fairness entirely is reasonable. The aim of the distribution is to allocate the compensation based on the time value of DC at time far as possible to meet the expectations of each agent. We can still allocate according to the contribution rate in order to make the distribution in the irrational case. To achieve this goal, we adjust the deficit parameter under different coalitions by adding the coefficient c, which can be defintic as follow:
min d s.t.
(9)
LEEN Eies
à =Bo
(10)
Φ: + csd 2 Eies Wi, AS N,
with 65 = e
It should be noted that: i) when the marginal contribution rate of each agent is the same, the linear programming degenerates to the regular least-core solution ii) when W; is constant in different coalition S, the number of inequality constraints can be reduced to |N]. The calculation amount of equations (9) and (10) will mainly come from the marginal contribution rate 7 As we use tmc- Shapley (Ghorbani & Zou 2019) to estimate SV, the calculation amount is at most O according to Theorem We shall provide theoretical justification for the reasonableness of this change in the appendix.
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5 EMPIRICAL EXPERIMENT
Throughout the experiments, are trying to understand the following: i) Would the proposed Least-core be approximated by sampling according to Theorem 1? ii) Could the proposed Least- core gain benefits compared to the classical valuation criteria for valuation problems? iii) To what extent can least-core be competent for allocation under irrational expectations. The following ex- periments are conducted feature valuation and data valuation tasks. Although Yan & Procaccial (202)) has demonstrated the feasibility of core as a replacement for shapley value, our work adjusts the deficit parameter e and the inequality constraint functions train a logistic regression classifier on all possible subsets of large-sized datasets as well as get the exact Shapley values and least core, we verify Theorem in the context of the samll-sized prob- lem(such as feature valuation). For the other two experiments, we verify in the context of data valuation, because large-scale datasets are closer to real-world application.
random. Since it is infeasible to
5.1 EXPERIMENT ON FEATURE VALUATIONS
Since the assessment of the data full cycle involves fewer stages (such as data pre- model trainer, etc.). We hope experiment on larger datasets demonstrate the feasibility of our proposed method compared with the baseline. Therefore, we choose the feature selection and data valuation of the problem setting. We choose the wine datasets with 13-class classification and 178 samples (https: /aacch/arccieeee ics. uci eddu/ w wine/wine data). And the results of the same ex- periment on the bigger datasets including MNIST, CIFAR-10/10M would show in the appendix later. Let the agents to be the features and the define expected compensation To empirically verify Theorem 1, we sample the fraction of coalitions uniformly at random from all possible coalitions, and compute the least core by the Equation 2 to these coalitions. We then ex- constraints with respect to the exact deficit
ml/machinne ne wewe--leennnn-daaaaaaaaaa
coalition by equation] 7
ams what fraction of all coalitions satisfy the least These two kinds of fraction help us to get the accuracy 1 5 and thus lead to 5 - probable least core. As can be seen in Figure 2 left), even with restriction less than 10% could achieve prediction aceu- racy up to 80%.
100
70
95-
Prediction accuracy (9%)
Prediction accuracy (%)
65
90
85
60
80
75
55
TMC-Shapley
70
Core
65
50
Random
20
40
60
80
100
10
20
30
40
Fraction restrictions added (%)
Fraction train data removed (%)
Figure/ I: Least core accuracy (satisfaction of the core constraint) over coalitions(left). Data removal results of Synthetic data(right).
5.2
EXPERIMENT ON DATA VALUATIONS
First, We emulate the data removal experiments on Synthetic data as described in (Ghorbani & Zou 2019 to verify that the proposed least-core is up the task of valuation. Concretely, we conduct data removal: Sorting the data from most valuable to least valuable, eliminating the most valuable valuable 5% of the data at time. Intuitively, the best criteria would induce the fastest drop of performance. As we can see in Figure 2 right), the performance of least-core is as well as that of TMC-shapley.

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Furthermore, divide the irrational expectation into two cases: i) the expected compensation exceeds or falls below the time value the agent; ii) the order of the agent's 's expected compensation in the DC' does not match the order of its contribution. To verify the effect of revised Least-core case we use Gaussian random distribution noise (mean=0, standard deviation = 0.1, 1) injection strategy that perturbates the W; simulate irrational expectation of compensation. For another case, we randomly selected 10%, 30% of all the agents to disrupt the order of W,, while other variables remain unchanged. And this time, we add breast cancer datasets from the UCI Machine Learning repository ceatttoryytttpr https: :/ /o0 gl/ (2Uw22).. Figure Bleftt illustrates that the accuracy drops down while the deviation increase. And FigureBrrihht rright) shows that the revised version alleviates the impact of the irrational expectation while does not interfere with the solutions under rational expectations.
Prediction accuracy (%)
Prediction accuracy (%)
65
65
60
Core
60
Core
Core(n=0.1)
Core(r=0.1)
Core(n=1)
Core(r=0.3)
Core-cs
Core-cs
Co
Core-cs(r=0.1)
50
50
Core-cs(n=1)
Core-cs(r=0.3)
0
10
20
40
40 Fraction train data removed (%)
0
10
20
Fraction of train data removed (%)
Figure 2: Data remove result: Curves of logistic regression test performance after injecting Gaussian random distribution with standard deviation 0.1, 1(left) and disrupting the order of 0.1,0.3 agents (right). The best (Synthetic) data points ranked according to the least-core and the least-core with coefficient es are removed.
Prediction accuracy (%)
94
Prediction accuracy (%)
94
92
Core
92
Core
Core(n=
Core(r=0.1)
Core(n=1)
Core(r=0.3)
Core-cs
90
Core-cs
Core-cs(n=0.1)
Core-cs(r=0.1)
Core-cs(n=1)
Core-cs(r=0.3)
88
88
0
10
20
30
40
0
10
20
30
40
Fraction of train data removed (%)
Fraction of train data removed (%)
Figure 3: Data remove result: Curves of logistic regression test performance after injecting Gaussian random distribution with standard deviation 0.1, 1(left) and disrupting the order of 0.1, 0.3 agents (right). The best (Natural) data points ranked according to the least-core and the least-core with coefficient es removed.
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6 CONCLUSION AND FUTURE WORK
We have presented a data valuation mechanism based on modern property rights theory. The frame- work responds to the requirements of data rights confirmation in the data marketplace and provides scheme for quantifying property rights compensation. The theoretical and empirical results suggest the our framework a principled means of doing credit assignment in ML whether the demand of the integrated party is rational or not.
There are several exciting directions for future work. First, multiple agents can co-exist in practical applications, which form competitive relationship to maximize the revenue for themselves. Sec- ond, criteria to determine the most suitable adjustment coefficient while dealing with the irrational expectation of the integrated party should be given.
REFERENCES
Jad Asswad and Jorge Marx Gómez. Data ownership: A survey, Inf. 12(11))465, 2021. doi:
10.3390/info1211 10465. UtL.attss://eo.. org/1000.......... 3390/nnfo12110465
Jad Asswad and Jorge Marx Gómez. Data ownership: A survey, Information, 12(11), 2021, ISSN
2078-2489
doi: 10.3390/info1211046 URL https: /twp://wwwwww..... www.
ccm/2078-22899
12/11/465
Robert J. Aumann and Michael Maschler. THE BARGAINING SET FOR COOPERATIVE GAMES, volume 52 of Advances in Game Theory. (AM-52), pp. 443-476. Princeton University Press, Princcton, 2016. ISBN 069 0891079021197880991779000
Eric Balkanski, Umar Syed, and Sergei Vassilvitskii. Statistical cost sharing. I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus. S. Vishwanathan, and R. Gar- nett (eds.), Advances in Neural Information Processing Systems, volume 30. Curran Asso- ciates, Inc., 2017. URL https: http::s:s///ccoeeddeioe F86f766 Paper .ddf
neuriess /cc//paper/201//f1le
32b3eee0272955bb33
Frank Bodendorf, Klaus Dehmel, and Jörg Franke. Scientific approaches and methodology to deter- mine the value of data asset and use case in the automotive industry. In 55th Hawaii Interna- tional Conference on System Sciences, HICSS 2022, Virtual Event / Maui, Hawaii, USA, January 4-7, 2022, pp. 1-10. ScholarSpace, 2022. URL http: //hpl//hlllam handle pwwpeeee///eeeeeee. 80023 WRL
Lingjiao Chen, Paraschos Koutris, and Arun Kumar. Towards model-based pricing for machine learning in a data marketplace. Proceedings the 2019 International Conference on Management of Data, 2019.
Ronald H. Coase. The problem of social cost. The Journal of Law and Economies, 3:1 -44, 1960.
Harold Demsetz. Toward a theory of property rights. The American Economic Review, pp. 163-177, 1967.
Ezra Einy, Ron Holzman, and Dov Monderer. On the least core and the mas-colell bargaining set. Games and Economic Behavior, 28: 181-188, 1999.
Amirata Ghorbani and James Zou. Data shapley: Equitable valuation of data for machine learn- ing. In Kamalika Chaudhuri and Ruslan Salakhutdinov (eds.), Proceedings of the 36th Interna- tional Conference on Machine Learning, ICML 2019, 9-15 June 2019, Long Beach, California, USA, volume 97 of Proceedings of Machine Learning Research, pp. 2242 2251. PMLR, 2019. htt.://ccccccccaappeee////////aa
URL httppp//wpppeeeen..n....eeeessss
mir wtwpppp9t///ppp.p hwtp://///ooooaaoo.oo html
Sanford J. Grossman and Oliver Hart. The costs and benefits of ownership: A theory of vertical and lateral integration. Journal of Political Economy, 94:691-719, 1986.
Oliver Hart and John. Moore. Property rights and the nature of the firm. Journal of Political Economy, 98: 119 1158, 1990.
Oliver Hart and John. Moore. A theory of debt based on the inalienability of human capital. NBER Working Paper Series, 1991.
11

---

Under review as a conference paper at ICLR 2023
Oliver Hart, Andrei Shleifer, and Robert W. Vishny. The proper scope of govermment: Theory and an application to prisons. Microeconomic Theory eJournal, 1996.
Ibrahim Abaker Targio Hashem, Ibrar Yaqoob, Nor Badrul Anuar, Salimah Mokhtar, Abdullah Gani, and Samee Ullah Khan. The rise of "big data" cloud computing: Review and open research issues. Inf Syst. 47:98 115, 2015. doi: 00.1016fj.s.2014..00 .006.
10. 10.61116/7 is. 201 07. 006
Ruoxi Jia, David Dao, Boxin Wang. Frances Ann Hubis, Nick Hynes, Nezihe Merve Gürel, Bo Li, Ce Zhang, Dawn Song, and Costas J. Spanos. Towards efficient data valuation based on the shapley value. In Kamalika Chaudhuri and Masashi Sugiyama (eds.), The 22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019, 16-18 April 2019, Naha, Oki- nawa, Japan, volume 89 of Proceedings of Machine Learning Research, pp. 1167-1176. PMLR, 2019. URL ARLL:ttp//rroeee.nngss mlr press / v89 wiwllaalll........ html
JiChu Jiang, Burak Kantarci, Sema Fatma Oktug, and Tolga Soyata. Federated learning in smart city sensing: Challenges and opportunities. Sensors (Basel, Switzerland), 20, 2020.
Heather Kelly. Facebook says cambridge analytica may have had data on 87 mil-
lion people. [Online].
Paraschos Koutris, Prasang Upadhyaya, Magdalena Balazinska, Bill Howe, and Dan Suciu. Toward practical query pricing with querymarket. In SIGMOD '13, 2013.
Paraschos Koutris, Prasang Upadhyaya, Magdalena Balazinska, Bill Howe, and Dan Suciu. Query- based data pricing. Journal of the ACM (JACM). 62:1 44, 2015.
Yongchan Kwon and James Zou. Beta shapley: unified and noise-reduced data valuation frame- work for machine learning. In Gustau Camps- Valls, Francisco J. R. Ruiz, and Isabel Valera (eds.), International Conference on Artificial Intelligence and Statistics, AISTATS 2022, 28-30 March 2022, Virtual Event, volume 151 of Proceedings of Machine Learning Research, pp. 8780-8802. PMLR, 2022. URL (ttts:::: http:///ooceedeeeeeeeooooo ngs wwwpiig.......rrr..m.m /ttptttss/////ooeeeeeeeeti
html
Yongchan Kwon, Manuel A. Rivas, and James Zou. Efficient computation and analysis of distribu- tional shapley values. In Arindam Banerjee and Kenji Fukumizu (eds.). The 24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021, April 13-15, 2021, Virtual Event, volume 130 of Proceedings of Machine Learning Research, pp. 793-801. PMLR, 2021. html
URL httl:tttpppoceeee//ee http:eeewiiinnne...eeeeseeesssee
Chao Li, Daniel Yang Li, Gerome Miklau, and Dan Suciu. A theory of pricing private data. In ICDT '13, 2013.
He Li, Lu Yu, and Wu He. The impact of gdpr global technology development. Journal of Global Information Technology Management, pp. 1-6, 2019.
Tian Li, Anit Kumar Sahu, Ameet Talwalkar, and Virginia Smith. Federated learning: Challenges, methods, and future directions. IEEE Signal Processing Magazine, 37:50 60, 2020.
Jinfei Liu. Dealer: End-to-end data marketplace with model-based pricing. ArXiv, abs/2003.13103, 2020.
Pratyush Maini, Mohammad Yaghini, and Nicolas Papernot. Dataset inference: Ownership res- olution in machine learning. In 9th International Conference Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net, 2021. URL https:
//openzeview.co www.:/teet.tn.m.ioooo fow..uummm.....ck.vvyy.....
Yod Samuel Martín and Antonio Kung. Methods and tools for gdpr compliance through privacy and data protection engincering. 2018 IEEE European Symposium on Security and Privacy Workshops (EaroS&PW), pp. 108-111, 2018
L. S. Shapley. A VALUE FOR n-PERSON GAMES, volume 2 of Contributions to the Theory of Games (AM-28), Volume II, pp. 307-318. Princeton University Press, Princeton, 1953. ISBN 9691079338,978869 1079356:.
12

---

Under review as a conference paper at ICLR 2023
Shuai Wang, Yong Yuan, Xiao Wang, Juanjuan Li, Rui Qin, and Feiyue Wang. An overview of smart contract: Architecture. applications, and future trends. 2018 IEEE Intelligent Vehicles Symposium (IV), pp. 108-113,20) 2018.
Chris Dede Wirth and Michael Kolain. Privacy by blockchain design: A blockchain-enabled gdpr- compliant approach for handling personal data. 2018.
Jie Xu and Fei Wang. Federated learning for healthcare informatics. Journal of Healthcare Infor-
matics Research, 5:1 19, 2021.
Tom Yan and Ariel D. Procaccia. If you like shapley then you'll love the core. In Thirty- Fifth AAAI Conference on Artificial Intelligence, AAAI 2021, Thirty-Thinn Third Conference on In- novative Applications of Artificial Intelligence, IAAI 2021, The Eleventh Symposium ucational Advances in Artificial Intelligence, EAAI 2021, Virtual Event, February 2-9, 2021, pp. 5751-5759. AAAI Press, 2021. URL https: aaai. wwaai.orr/aaaeaeoooaaaaaaaae perg/indees wi///nddexx.//// php/ AAAI/ axticle/view/16721
Ed-
Tal Z. Zarsky. Incompatible: The gdpr in the age of big data. Social Science Research Network, 2017.
A
THE PROOF OF THEOREM 1
We employ the following known lemmas (Balkanski al. 2017 to prove that the least-core could be approximated by sampling.
Lemma 1. Denote H X {-1, 1} with VC-dimension. If function f is the groundtruth and the number of samples O [n-togg( +1)) Then,
P [h(x) + f(x)] - Σ l10e) * f(x)) 8 S-DC
where x², 22 ..... xtth DC.
Lemma 2. The function class {x ( sign(w x) =>| E R") has VC-dimension n.
According to the lemma 2. we denote h E H is the class of function that satisfies: H = {h + sign((Ø 1 ee)- (Lies WW 1)), o; E E² e subset with n + 2 VC-dimension containing the least-core. We then define that o f''speeccllyy represent the compensation allocation in the least core, the subsidy and the classifier accordingly.
E Φ; B). This allows H be
Let vector yd = (lies WW; 1). then h(y*) ) = 1, for all i E S, and f" (yy) 1 for S E 2
P l 0; v(S) + e" 2 0] > P SDDC
6; - v(S) + 2 0]
(11)
SwDC iES
iES
dh v((S) +220
(12)
SDDC ieS
P 11('")
(13)
SDDC
P (((('))) f0() - Σ )f
(14)
S-DC
8
(15)
B COMPUTATION OF THE LEAST-CORE
Actually, the equation ? may be an overdetermined linear equations. Thus, the exact distribution & = (oi.... .... 2N) is least square solution from the following equation:
min |1
(16)
s.t.
EiEN iss
Φ Bo.
(17)
@ t e 2 Eies Wi, CS
with calculated from equation
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C INTERPRETATION OF ADJUSTMENT PARAMETER
To proof that the solution set least-core with adjusted parameter e is still stable, we empoly the boundedness principle to prove that perturbation error is controllable well as the Proposition from Kwon & Zou (2022). For the benefit of modifying e, we give a formal proof in an easy-to-understand graphical way.
C.I ERROR ANALYSIS
Studying the influence of adding coefficients on linear programming problems is actually a pertur- bation error problem.
Lemma 3.
When the cardinality |S] is large enough, the performance change U(SU=*) - USSis near zero, and thus the marginal contribution [=S](=";U, D) becomes negligible for any =².
Therefore, the marginal contribution of Agents is bounded for coalition under any cooperative combination, the same is true as the contribution ratd7] We then denote the supremum of marginal contribution rate to be "maz. To distinguish between the natural index and the deficit parameter, we define the latter as è. The coefficient ey of any inequality constrained deficit parameter é satisfies cs S ElS1-Tmax, and el +
At this point, the matrix form of inequality constraints for linear programming problems:
Φ
58
W W2
d2
C82
E.
>
ON
02
W2*
Among them, E is sparse matrix with 2 X N, Edg = if and only if aj Sj, the coefficient matrix of the parameter is the diagonal matrix T. Then,
é W E.
(18)
W E- $b
|ē|
(19)
[|'ll
IW
E Ebl
lim A |e
W
E +1
(20)
+0000
[[]
|||
IW
E
(21)
|T
0
(22)
We use the I--norm of matrix during the proof. Since the product of a bounded number and number that converges still converges O, the Equation 21 holds.
C.2 MITIGATING THE EFFECTS OF IRRATIONALITY
The smaller the non-negative coefficient of e in the inequality constraint is, the more extent the constraint considered. In this section, we examined the impact of the implementation of the allegations above by the Number Shape Union Method. Taking the DC' with two agents for example, the solution of linear programming equation 9 alwaays lies in the line of equality constraint (or the equation will have no solution).
Supposed that the least-core has already been computed, we then examined the impact on the allocation of Φ = (Φ1, Φ2). As is shown in three figures, the Red dotted line represent the restriction
B. Φ; + 2 W,, and the blue solid line represents the equality constraint Φ1 42 2
Case 1. Concretely, the Figure shows an ideal situation of the solution, since computing the
1q 16 brings the solution that Φ2 Ba
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When the adjusted coefficients apply the inequality constraint, which can be seen as the red solid lines figures, the optimal solution of equation may change. If not, the coefficients should satisfy (1-4) the new inequality constraint becoming "closer to the optimal solution" but not overpass it. And the idea can be descrihed
I & e, equivalent to c; 2 2/
B 2. The assertion comes from the idea that
- = (W; C. e) (W; c) = B c. 1=
(23)
with of be denoted the distribution solution.It means that the new inequality constraint would not overpass the original optimal solution, twisting the original allocation. Inversely, when comes the irrational expectation before compensating, the coefficient satisfies c; S change the irrational solution instead.
B 2 would
Case 2. In this case, the optimal solution without applying coefficients is located at the intersection of the constraint line formed by the expectation of one of the agents and the equality constraint line. Assume that the vertical axis is compensation for plig and the horizontal axis is compensation for p, then the phi is more than phig before adjusting the coefficient parameter e.
When this situation is caused by irrational expectations, that is, in fact, the contribution of a2 is greater than that of 01 but the final compensation is less because of the less expected compensation.
obviously that the inequality constraint boundary will be close the parallel coordinate axis while the coefficient is greater than 1, otherwise away from the coordinate axis. Additionally, the new solution set merely influenced by the constraint line formed by the expectation of a1 and the equality constraint line in this case. Therefore, C1. the coefficient of parameter e in a1 's inequality constraint, is expected to have larger coefficient while the equality constraint fixed. This causes the new optimal solution to move closer to the axis perpendicular to Φ2, increasing the compensation of it and decreasing the compensation ofæ1.
Case 3. The case is the symmetric form of Case 2, and the same conclusion can be obtained by similar proofs.
Overall, the function of the coefficient should satisfy the following properties:
Non-negativity. The Non-negative coefficient avoids changing the sign parameter e, which in turn affects the allocation.
Monotonicity. Monotonically decreasing coefficients with increasing contribution rate can alleviate distorted distribution
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equality constraint adjustng after adjustin [|+]2=+
Figure 4: case
equality constraint before adjustng
adjustig
[||[2=
Figure case2
equality constraint adjustin
after adusting
Figure 6: case3
16


Reviews:
[{"review_id": "nDrO0vTK7eh", "reviewer": "Reviewer_V9Lr", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper discusses the data ownership problem from an economic perspective. The authors propose to use a compensation mechanism in the Modern Property Right Theory for solving data pricing problems in machine learning. Transferring the property right or ownership requires compensation, which is calculated by a modified least-core calculation. The formulation also incorporates fairness notions by introducing a parameter related to the contribution rate calculated through Shapley values. The paper also shows empirical experiments on data removal to demonstrate the usefulness of the proposed mechanism.", "summary_of_the_review": "This paper is a nice addition to the machine learning data pricing and ownership literature from an economist’s perspective. It is new to me that an agent contributing the most could perform integration through compensation, and subsequently gain income from all integrated data property rights. This process could be efficient from a societal point of view. However, careless writing and the lack of clarity in the presentation affects the readability of the paper.", "strength_and_weaknesses": "Strength:\n1. Provides data ownership from an economist’s perspective. It is an insightful contribution to formulate data ownership and pricing problem in the property right theory.\n2. The time value introduction to contribution calculation is interesting.\n\nWeakness:\n1. The writing of the paper needs major improvement. Proofread to make the paper flow consistently. Also, providing brief explanations for concepts used as well as intuitive interpretations of the theoretical results could significantly improve the readability of the paper.\n2. Some details of the method are not clearly described, partially due to the flow of the paper.\n3. The experiments are lacking.\n\nI have provided more detailed explanations of the weaknesses below.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "GsqIpP-UBcD", "reviewer": "Reviewer_WvJ5", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a data valuation mechanism based on modern property rights theory aiming to address the problem of data rights and data integration. The framework gives the power of integrating data and allocating compensations to the agent that contributes most significantly. Their framework uses a contribution evaluation method based on the Data Shapley to decide who has the power to integrate the data and give compensation. And they assign the compensation using the Least-core method. Finally, they demonstrate experimentally that the compensation mechanism is feasible in solving the data pricing problem.", "summary_of_the_review": "The main contribution of the paper is the conceptual contribution of using the modern property right theory in the problem of data valuation. The methodological contribution is not super strong based on the previous work. The motivation and the practicability of their method are not clear.", "strength_and_weaknesses": "Strength:\nThe paper tries to address an important problem through a new lens. The main contribution is the conceptual contribution of adopting the property rights theory in the problem of data valuation. Basically, they adopt the theory to give the agent with the highest contribution the power of integrating user data and allocating payments. \n\nWeakness:\n1. The main techniques come from previous literature. The method of deciding the contribution is basically the Data Shapley method from (Ghorbani & Zou, 2019), and the method of allocating compensations is just the least-core method from (Yan & Procaccia, 2021).\n2. The motivation for using property rights theory to assign integration power is not clear. How is this method fundamentally different from having a trusted central planner? It seems to me that the method is basically choosing a central planner among the agents based on their contributions. Furthermore, it is not clear how to prevent the integrator from malicious behaviors of giving non-truthful payments. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "8bwUbvpJa1", "reviewer": "Reviewer_ELSX", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a data valuation framework based on property right theory. ", "summary_of_the_review": "The paper takes an interdisciplinary approach to address an important question in data market. However, the experiment part does not sufficiently validate the key contributions of the paper.", "strength_and_weaknesses": "Strength:\n\n- The paper takes an inter-disciplinary approach and couples property right theory, cooperative game theory, machine learning to address the problem of data valuation\n\n- The questions examined by the paper are crucial: how to address the ownership problem on a data chain? How to compensate each agent?\n\nWeaknesses:\n-Section 4.3: it’s not clear how to determine $B_0^i$ in Eqn (8)\n- The efficiency aspect of the pricing mechanism in (9)-(10) needs to be further discussed. Specifically, to determine $\\gamma$, one needs to solve Shapley value, which has exponential complexity in the number of agents. The optimization in (9)-(10) per se is also combinatorial in the number of agents. \n- One of the most intriguing part of the proposed framework is the ability to deal with data chain (i.e., different agents take different roles in a data pipeline line: some are data pre-processor, some are model trainer). However, this part is not empirically validated in the experiment \n- Section 5.1 aims at validating Theorem 1. However, this theorem was not the contribution of this paper but proposed in Yan et al. It’ll be great if the paper can focus on evaluating the differentiating factors of the paper.\n- The writing of the paper can be significantly improved. This manuscript contains a lot of typos and grammar issues. \n- If the paper’s final target venue is ML conference, I would suggest the authors to significantly revise Section 3 “Preliminaries and Background” to contextualize the property right theory and other economic concepts in the machine learning and data analytics setup. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject