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Abstract: We study claims problems in which agents may also have reference points. We show first that many classical rules satisfy an egalitarian property in this setting; namely, the differences between each agents’ payoff and the corresponding reference value are as equal as possible. We also introduce a broad class of rules that satisfy a generalized condition, dubbed egalitarian-in-deviation relative to a reference system. For each problem, the system proposes a reference vector which is a function of the claims. We show that these rules allocate the nearest efficient point to the reference vector. Our findings generalize previous results in the literature, such as the one stating that the CEA rule minimizes the squared distance to the equal division point. Concede-and-divide, a focal rule to solve two-agent claims problems, does not satisfy the egalitarian-in-deviation condition relative to any reference system. But, under certain conditions, it can be reinterpreted as the limit of a weighted egalitarian-in-deviation rule. Finally, we explore the behavior of egalitarian-in-deviation rules with respect to the important notions of consistency and duality. PubDate: 2025-07-01
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Abstract: We discuss sequential vote-buying games, wherein an outsider, called the “principal,” sequentially attempts to influence committee members with opposite preferences regarding a project implementation before they make a decision through generalized majority voting. To characterize the equilibria, we introduce the affordably bribable groups within the members of the generalized majority, which are sets of members from whom the principal can buy votes at a cost below his gain from the project implementation. It is shown that the bribe amount and the committee decision are uniquely determined, given a sequential vote-buying game. In addition, we provide the conditions under which the principal successfully buys votes, and does so at a negligible cost, by comparing the number of affordably bribable groups with the number of members who do not belong to the generalized majority. Based on our characterization of equilibrium, we discuss the effects of committee size, derivations of simple and supermajority rules, whom to bribe, and the order of bribing. PubDate: 2025-06-28
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Abstract: We compare two alternative procedures for decomposing the Lorenz curve and the Gini coefficient into within-groups and between-groups contributions: the standard additive decomposition (Bhattacharya and Mahalanobis in J Am Stat Assoc 62(317):143–161, 1967) and another inspired by the path-independent decomposition (Foster and Shneyerov in J Econ Theory 91(2):199–222, 2000). We show that the former approach offers a clean measure of the between-group inequality, which is insensitive to changes in the distribution that do not alter the relative difference between the groups’ averages. On the other hand, the latter approach offers an unbiased measure of the within-group inequality, which is independent of the between-group component. Hence, we propose and interpret a new decomposition of the Gini index that is based on the path-independent approach. Finally, we explore the implications of Lorenz between-group dominance combined with Lorenz within-group dominance. We show the difficulty of defining sufficient conditions for two Lorenz curves not to intersect and suggest an alternative partial order based on concentration curves which does not account for the overlap between groups. PubDate: 2025-06-17
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Abstract: We consider network formation, where some locations can be connected. Every network has a cost and every agent has an individual value of every network. A planner aims at implementing a welfare maximizing network and allocating the resulting cost, but information is asymmetric: agents are fully informed and the planner is ignorant. Full implementation in Nash and strong Nash equilibria is studied. We show the correspondence consisting of welfare maximizing networks and individually rational cost allocations is implementable. We construct a minimal Nash implementable, welfare maximizing, and individually rational solution in the set of upper hemi-continuous and Nash implementable solutions. It is not possible to implement solutions such as the Shapley value unless we settle for partial implementation. PubDate: 2025-06-16
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Abstract: We provide an axiomatic approach to the allocation of responsibility for GHG emissions in supply chains. Considering a set of axioms standardly used in networks and decision theory, and consistent with legal principles underlying responsibility, we show that responsibility measures shall be based on exponential discounting of upstream and downstream emissions. From a network theory perspective, the proposed responsibility measure corresponds to a convex combination of the Bonacich centralities for the upstream and downstream weighted adjacency matrices. Scope 1 emissions, consumption-based accounting and income-based accounting are obtained as particular cases of our approach, which also gives a precise meaning to scope 3 emissions while avoiding double-counting. We apply our approach to the assessment of country-level responsibility for global GHG emissions and to sector-level responsibility in the USA. We examine how the responsibility of countries/sectors varies with the discounting of indirect emissions. We identify three groups of countries/sectors: producers of emissions whose responsibility decreases with the discounting factor, consumers of emissions whose responsibility increases with the discounting factor, and an intermediary group whose responsibility mostly depends on the network position and varies non-monotonically with the discounting factor. Overall, our axiomatic approach provides strong normative foundations for the definition of reporting requirements for indirect emissions and for the allocation of responsibility in claims for climate-related loss and damage. PubDate: 2025-06-16
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Abstract: May’s Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May’s axioms, we can uniquely determine how to vote on three alternatives (setting aside tiebreaking). In particular, we add two axioms stating that the voting method should mitigate spoiler effects and the so-called strong no show paradox. We prove a theorem stating that any preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, must choose from among the Minimax winners in all three-alternative elections. When applied to more than three alternatives, our axioms also distinguish Minimax from other known voting methods that coincide with or refine Minimax for three alternatives. PubDate: 2025-06-13
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Abstract: Baryshnikov presented a remarkable algebraic topology proof of Arrow’s impossibility theorem trying to understand the underlying reason behind the numerous proofs of this fundamental result of social choice theory. We continue this program, but focusing on combinatorial topology arguments that do not use advanced mathematics, providing a very intuitive geometric reason for Arrow’s impossibility under domain restrictions. We present a geometric proof for the basis case of two voters, $$n=2$$, and three alternatives, $$ X =3$$, based on the index lemma, that counts the absolute number of times that a closed curve in the plane travels around a point. This yields a characterization of the domain restrictions that allow non-dictatorial aggregation functions and, as a consequence, Baryshnikov’s conjecture relating such domains with contractible spaces is revealed as untrue. It also exposes the geometry behind prior pivotal arguments to Arrow’s impossibility. We explain why the basis case of two voters, is where this interesting geometry happens, by giving a simple proof that this case implies Arrow’s impossibility for any $$ X \ge 3$$ and any finite $$n\ge 2$$. PubDate: 2025-06-04
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Abstract: Tournament solutions play an important role within social choice theory and the mathematical social sciences at large. We construct a tournament of order 36 that can be partitioned into the Banks set and the bipartisan set. As a consequence, the Banks set, as well as its refinements, such as the minimal extending set and the tournament equilibrium set, can be disjoint from the bipartisan set. PubDate: 2025-06-02
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Abstract: This paper proposes a multi-region fiscal bargaining model where country border stability depends on preference heterogeneity, income inequality and scale economies in public policy. It demonstrates how increasing preference heterogeneity can increase border stability by increasing political disagreements over government expenditures, reducing the willingness to pay taxes and better aligning them with the fiscal preferences of the discontented and the wealthy. Hence, stable and efficient country borders may require a minimal degree of preference heterogeneity or, lacking that, stabilization through a credible tax ceiling, compensating transfers or fiscal decentralization. PubDate: 2025-05-30
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Abstract: This paper presents a novel welfare approach that focuses on and prioritizes the worst-off. It bridges the gap between social welfare functions and poverty measures to provide a new tool for policy analysis. In contrast to social welfare functions, individuals are compared in terms of their lack of opportunities for a decent standard of living. In contrast to poverty measures, the assessment of individuals is non-paternalistic and respects individuals’ views of what constitutes a good life. The characterized social deprivation function is also generalized to differences in household needs. PubDate: 2025-05-30
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Abstract: We study the optimal voting franchise for a decision which affects different persons with different intensities. When the agents’ opinions are ex ante permutation invariant, we show that it is optimal to restrict the franchise to the agents with the highest stakes, with a smaller franchise when the stakes are more concentrated. When they are i.i.d. (all voters independently favour Yes with the same probability p), we further show that two forces are at work: on the one hand, the imperative to restrict voting rights to those most affected; on the other, when and only when $$p \ne 1/2$$, the Condorcet jury effect according to which allowing more voters to participate increases the probability of making the right decision. This helps to shed light on the problem in large populations. PubDate: 2025-05-26
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Abstract: Standard spatial models of political competition predict that competing candidates would converge to the same policy position. In this paper, we present a novel mechanism of policy divergence in a model of campaign finance, where campaign contributions from ideologically extreme donors can be used to boost the turnout of impressionable voters. In our model, the exact location of the median voter is unknown to the candidates. Together with donors’ contributions, this generates policy divergence even when the candidates are ex-ante identical and purely office-motivated. We characterize the unique equilibrium of the model in mixed strategies and provide closed form expression for the expected level of policy polarization. We further show that polarization is higher when only the incumbent can benefit from campaign contributions. PubDate: 2025-05-24
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Abstract: We introduce a new framework to study the group dynamics and game-theoretic considerations when voters are allowed to trade votes. This model advances prior work by considering vote-for-vote trades in a low-information environment where voters do not know the preferences of their trading partners and do not abstain from voting. All voters draw their preference intensities on two issues from a common probability distribution and then consider offering to trade with an anonymous partner. The result is a strategic game between two voters that can be studied analytically. We compute the Nash equilibria for this game and derive several interesting results involving symmetry, group heterogeneity, and more. This framework allows us to determine that trades are typically detrimental to the welfare of the group as a whole, but there are exceptions. We also expand our model to allow all voters to trade votes and derive approximate results for this more general scenario. Finally, we emulate vote trading in real groups by forming simulated committees using real voter preference intensity data and computing the resulting equilibria and associated welfare gains or losses. PubDate: 2025-05-21
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Abstract: Empirical welfare analyses often impose stringent parametric assumptions on individuals’ preferences and neglect unobserved preference heterogeneity. We develop a framework to conduct individual and social welfare analysis for discrete choice that does not suffer from these drawbacks. We first adapt the class of individual welfare measures introduced by Fleurbaey (J Econ Lit 47(4):1029–1075, 2009) to settings where individual choice is discrete. Allowing for unrestricted, unobserved preference heterogeneity, these measures become random variables. We then demonstrate that their distribution can be derived from choice probabilities, which can be estimated nonparametrically from cross-sectional data. Additionally, we derive nonparametric results for the joint distribution of welfare and welfare differences, and for social welfare. The former is an important tool in determining whether the winners of a price change belong disproportionately to those groups who were initially well-off. PubDate: 2025-05-21
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Abstract: This paper studies how the cost of cooperation affects the effectiveness of community enforcement in a society of strangers, as in Kandori (Rev Econ Stud 59:63–80, 1992) and Ellison (Rev Econ Stud 61:567–588, 1994). We identify a critical threshold for the cost of cooperation, beyond which community punishment becomes a credible sanction to defectors, regardless of the population size and discount factor. Furthermore, we demonstrate that for any population size and discount factor, there exists a target cost of cooperation that makes community enforcement effective in supporting cooperation. This target cost can be used as a coordination device to sustain cooperation as an equilibrium outcome when the cost of cooperation is endogenous. PubDate: 2025-05-13
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Abstract: This paper examines how the structure of communication networks influences learning and social welfare when participants have different prior opinions and face uncertainty about an external state. We analyze a game in which players form links to exchange opinions on the state and reduce their uncertainty. The players hold imperfectly correlated subjective priors on the state. Therefore, their opinions transmit their private signals with frictions, termed interpretation noise. Network clustering facilitates learning by eliminating this interpretation noise. Therefore, the egalitarian efficient network is: a complete component if the interpretation noise is sufficiently high, and a flower otherwise. This network constitutes a Nash equilibrium. These findings establish a link between a key feature of social networks (clustering) and the quality of learning through network communication, offering a potential explanation for the prevalence of clustering in real-world social networks. PubDate: 2025-05-12
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Abstract: There are two dominant criteria for evaluating social welfare, the utilitarian and maximin criteria. Both exhibit extreme properties: the utilitarian criterion focuses exclusively on efficiency, while the maximin criterion is highly concerned with the utility level of the least advantaged individuals. To consider more moderate criteria, this paper modifies the axioms postulating their extreme attitudes. More specifically, we relax Hammond equity of the maximin criterion and the additivity property of the utilitarian criterion. We show that together with standard axioms, these modified axioms characterize the convex combinations of these two welfare criteria, which we call the mixed utilitarian-maximin social welfare orderings. PubDate: 2025-05-12
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Abstract: Interest groups (IGs) can potentially influence policy making process or policy outcomes in their favor by using different lobbying tactics. In this paper, we study how and under what circumstances IGs exert influence on policy outcomes when they can use Micro-targeting (MT) as a lobbying strategy, i.e. the IGs can send group specific messages to a subset of voters. In the absence of IGs, the political candidate does not have means to privately commit a policy to a group of voters, who might vote for her after observing such policy commitment. Recognizing this, IGs can get policy favours from the political candidate in exchange for facilitating candidate’s private commitment. We identify conditions in which MT is influential, in the sense of leading to a different policy outcome in the presence of IGs. The analysis fully characterizes the set of influential MT equilibria. The like minded IG does not have any direct influence, but its presence could severely impact the direct influence of unlike minded IGs given that the competing candidates are ideologically motivated. Moreover, this may also lead to polarisation between the two competing candidates. PubDate: 2025-05-07
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Abstract: Suppose voters are asked to submit approval ballots for a certain set of alternatives, with approval voting applied to determine a winning alternative. The same voters are then asked to report rankings over these alternatives, and some voting rule intended for ranked ballots is applied. If voters are sincere, can an approval winner possibly win this second election' Can an approval loser lose that election, or all approval co-winners be co-winners of the election' These questions give rise to three notions of approval compatibility for voting rules: positive, negative, and uniform positive approval compatibility (PAC, NAC, and UPAC). We find that NAC is a very weak notion and UPAC is a very strong one. Moreover, PAC, a stronger variant of it called OPAC, and a weaker variant of UPAC called FUPAC divide usual voting rules into four families: Condorcet-consistent rules satisfy all of them; K-approval rules for $$K\ge 2$$ satisfy none; plurality, plurality with runoff and STV satisfy OPAC but fail FUPAC; and Borda satisfies FUPAC and PAC but fails OPAC. PubDate: 2025-04-30
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Abstract: We investigate the implementation of social choice functions with asymmetric information concerning the state from an epistemological perspective. Although agents are either selfish or honest, they do not expect other participants to be honest. However, an honest agent may exist not among participants but in their higher-order beliefs. We assume that “all agents are selfish” never happens to be common knowledge. We show a positive result in general asymmetric information environments, demonstrating that with a minor restriction on signal correlation called information diversity, any incentive-compatible social choice function, whether ethical or nonethical, is uniquely implementable in the Bayesian Nash equilibrium. PubDate: 2025-04-21
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