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Abstract: Abstract The search for a compromise between marginalism and egalitarianism has given rise to many discussions. In the context of cooperative games, this compromise can be understood as a trade-off between the Shapley value and the Equal division value. We investigate this compromise in the context of multi-choice games in which players have several activity levels. To do so, we propose new extensions of the Shapley value and of the Equal division value to multi-choice games. Contrary to the existing solution concepts for multi-choice games, each one of these values satisfies a Core condition introduced by Grabisch and Xie (Math Methods Oper Res 66(3):491–512, 2007), namely Multi-Efficiency. We compromise between marginalism and egalitarianism by introducing the multi-choice Egalitarian Shapley values, computed as the convex combination of our extensions. To conduct this study, we introduce new axioms for multi-choice games. This allows us to provide an axiomatic foundation for each of these values. PubDate: 2022-05-20
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Abstract: Abstract We report the results of a vignette study with an online sample of the German adult population in which we analyze the interplay between need, equity, and accountability in third-party distribution decisions. We asked participants to divide firewood between two hypothetical persons who either differ in their need for heat or in their productivity in terms of their ability to chop wood. The study systematically varies the persons’ accountability for their neediness as well as for their productivity. We find that participants distribute significantly fewer logs of wood to persons who are held accountable for their disadvantage. Independently of being held accountable or not, the needier person is partially compensated with a share of logs that exceeds her contribution, while the person who contributes less is given a share of logs smaller than her need share. Moreover, there is a domain effect in terms of participants being more sensitive to lower contributions than to greater need. PubDate: 2022-05-17
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Abstract: Abstract The paper presents a coalitional bargaining model, the Burning Coalition Bargaining Model, having a peculiar type of partial breakdown. In fact, in this model, the rejection of a proposal causes the possibility of the proposed coalition to vanish, rather than triggering the end of all negotiations or the exclusion of some players from the game, as already proposed in the literature. Under this type of partial breakdown and adopting a standard rejecter-proposes protocol, 0-normalized, 3-players games are examined for extreme values of the breakdown probability. When such probability is equal to one, efficiency is more difficult to obtain than in models adopting discounting and the first mover advantage is strongly diminished. Furthermore, when an efficient outcome is attained, the final distribution of payoffs reflects the strength of players in the game, with strength being represented by belonging to more valuable coalitions. The same feature is retained when considering a probability of breakdown approaching zero. PubDate: 2022-05-16
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Abstract: Abstract The purpose of this paper is to illustrate, formally, an ambiguity in the exercise of political influence. To wit: A voter might exert influence with an eye toward maximizing the probability that the political system (1) obtains the correct (e.g. just) outcome, or (2) obtains the outcome that he judges to be correct (just). And these are two very different things. A variant of Condorcet’s Jury Theorem which incorporates the effect of influence on group competence and interdependence is developed. Analytic and numerical results are obtained, the most important of which is that it is never optimal—from the point-of-view of collective accuracy—for a voter to exert influence without limit. He ought to either refrain from influencing other voters or else exert a finite amount of influence, depending on circumstance. Philosophical lessons are drawn from the model, to include a solution to Wollheim’s “paradox in the theory of democracy”. PubDate: 2022-05-13
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Abstract: Abstract In college admission, financial aid plays an important role in students’ enrollment decision as well as their preparation for college application. We analyze how different types of financial aid affect these decisions and admission outcomes. We consider two financial aid regimes—need-based and merit-based—in a simple college admission model and characterize respective equilibria. We find that a more competitive college has a higher admission cutoff under a need-based regime than under a merit-based regime. A less competitive college, on the other hand, benefits from a merit-based regime as it admits students with a higher average ability than it does under no aid. We next allow colleges to choose their own financial aid system so as to account for a stylized fact in the US college admissions. We show that when one college is ranked above the other, it is a dominant strategy for the higher-ranked college to offer need-based aid and for the lower-ranked college to offer merit-based aid. PubDate: 2022-05-09
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Abstract: Abstract We use a model of impressionable voters to study multi-candidate elections under different electoral rules. Instead of maximizing expected utility, voters cast their ballots based on impressions. We show that, under each rule, there is a monotone relationship between voter preferences and vote measures. The nature of this relationship, however, varies by electoral rule. Vote measures are biased upwards for socially preferred candidates under plurality rule, but biased downwards under negative plurality. There is no such bias under approval voting or Borda count. Voters always elect the socially preferred candidate in two-way races for any electoral rule. In multi-candidate elections, however, the ability to elect a Condorcet winner varies by rule. The results show that multi-candidate elections can perform well even if voters follow simple behavioral rules. The relative performance of specific electoral institutions, however, depends on the assumed behavioral model of voting. PubDate: 2022-05-07
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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We investigate cases of preference change in the context of cake-cutting problems. In some circumstances, believing that some other player can be credited with a particular preference structure triggers a preference shift by imitation. As a result of this, players may experience regret. However, in typical examples the extent of the change (and the ensuing regret) cannot be anticipated, so players cannot adjust their behavior beforehand. Our goal is to describe the phenomenon, provide a formal model for it, and explore circumstances and allocation procedures that may alleviate some of its negative consequences. In the face of utility shifts we propose a new criterion for fairness, which we dub Ratifiability; in a ratifiable allocation rational players are happy to stick to their choices, in spite of the changes in utilities they may experience. We argue that this embodies a sense of fairness that is not captured by other properties of fair allocation. PubDate: 2022-05-01
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Abstract: Abstract Consider two principles for social evaluation. The first, “laissez-faire”, says that mean-preserving redistribution away from laissez-faire incomes should be regarded as a social worsening. This principle captures a key aspect of libertarian political philosophy. The second, weak Pareto, states that an increase in the disposable income of each individual should be regarded as a social improvement. We show that the combination of the two principles implies that total disposable income ought to be maximized. Strikingly, the relationship between disposable incomes and laissez-faire incomes must therefore be ignored, leaving little room for libertarian values. PubDate: 2022-05-01
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Abstract: Abstract We study criteria that compare mechanisms according to a property (e.g., Pareto efficiency or stability) in the presence of multiple equilibria. The multiplicity of equilibria complicates such comparisons when some equilibria satisfy the property while others do not. We axiomatically characterize three criteria. The first criterion is intuitive and based on highly compelling axioms, but is also very incomplete and not very workable. The other two criteria extend the comparisons made by the first and are more workable. Our results reveal the additional robustness axiom characterizing each of these two criteria. PubDate: 2022-05-01
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Abstract: Abstract The problem of no hands concerns the existence of so-called responsibility voids: cases where a group makes a certain decision, yet no individual member of the group can be held responsible for this decision. Criteria-based collective decision procedures play a central role in philosophical debates on responsibility voids. In particular, the well-known discursive dilemma has been used to argue for the existence of these voids. But there is no consensus: others argue that no such voids exist in the discursive dilemma under the assumption that casting an untruthful opinion is eligible. We argue that, under this assumption, the procedure used in the discursive dilemma is indeed immune to responsibility voids, yet such voids can still arise for other criteria-based procedures. We provide two general characterizations of the conditions under which criteria-based collective decision procedures are immune to these voids. Our general characterizations are used to prove that responsibility voids are ruled out by criteria-based procedures involving an atomistic or monotonic decision function. In addition, we show that our results imply various other insights concerning the logic of responsibility voids. PubDate: 2022-05-01
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Abstract: Abstract When including outside pressure on voters as individual costs, sequential voting (as in roll call votes) is theoretically preferable to simultaneous voting (as in recorded ballots). Under complete information, sequential voting has a unique subgame perfect equilibrium with a simple equilibrium strategy guaranteeing true majority results. Simultaneous voting suffers from a plethora of equilibria, often contradicting true majorities. Experimental results, however, show severe deviations from the equilibrium strategy in sequential voting with not significantly more true majority results than in simultaneous voting. Social considerations under sequential voting—based on emotional reactions toward the behaviors of the previous players—seem to distort subgame perfect equilibria. PubDate: 2022-05-01
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Abstract: Abstract We consider the strategy-proof rules for reallocating individual endowments of an infinitely divisible good when agents’ preferences are single-peaked. In social endowment setting, the seminal work established by Sprumont (Econometrica 59:509–519, 1991) proves that the uniform rule is the unique one which satisfies strategy-proofness, efficiency, and envy-freeness. However, the uniform rule is not so appealing in our model since it disregards the differences in individual endowments. In other words, the uniform rule is not individually rational. In this paper, we propose a new rule named the uniform proportion rule. First, we prove that it is the unique rule which satisfies strategy-proofness, efficiency, and envy-freeness on proportion and we show that it is individually rational. Then, we show that our rule is indeed a member of the class of sequential allotment rules characterized by Barberà et al. (Games Econ Behav 18:1–21, 1997). PubDate: 2022-05-01
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Abstract: Abstract Policymakers are generally most concerned about improving the lives of the worst-off members of society. Identifying these people can be challenging. We take various measures of subjective wellbeing (SWB) as indicators of the how well people are doing in life and employ Latent Class Analysis to identify those with greatest propensity to be among the worst-off in a nationally representative sample of over 215,000 people in the United Kingdom. Our results have important implications for how best to analyse data on SWB and who to target when looking to improve the lives of those with the lowest SWB (The authors owe a massive debt of gratitude to the Office for National Statistics for their support throughout this research. We are particularly grateful to Dawn Snape and Eleanor Rees for their valuable comments on earlier drafts of this paper, to Salah Mehad for the thorough review of methodology, and to Vahe Nafilyan for advice on clustering analysis. We also thank the anonymous reviewers for the very helpful comments. Thank you all very much.). PubDate: 2022-05-01
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Abstract: Abstract The doctrinal paradox is analysed from a probabilistic point of view assuming a simple parametric model for the committee’s behaviour. The well known premise-based and conclusion-based majority rules are compared in this model, by means of the concepts of false positive rate (FPR), false negative rate (FNR) and Receiver Operating Characteristics (ROC) space. We introduce also a new rule that we call path-based, which is somehow halfway between the other two. Under our model assumptions, the premise-based rule is shown to be the best of the three according to an optimality criterion based in ROC maps, for all values of the model parameters (committee size and competence of its members), when equal weight is given to FPR and FNR. We extend this result to prove that, for unequal weights of FNR and FPR, the relative goodness of the rules depends on the values of the competence and the weights, in a way which is precisely described. The results are illustrated with some numerical examples. PubDate: 2022-05-01
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Abstract: Abstract This paper explores the possibility, in case of belief and taste heterogeneity, to aggregate individual preferences through a deliberation process enabling society to reach a consensus. However, we show that the same deliberation process, even characterized by a convergent matrix, may lead to different consensus depending on the updating rule which is chosen by individuals, i.e., deliberation is sufficient to determine social preferences but not univocally. Then, we prove that the Pareto condition allows to choose from possible consensus the one whereby social deliberated beliefs and tastes are of a utilitarian shape. PubDate: 2022-04-26
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Abstract: Abstract This paper examines the implications of habit formation in private and public goods consumption for the Pareto-efficient provision of public goods, based on a two-period model with nonlinear taxation. Under weak leisure separability, and if the public good is a flow-variable such that the government directly decides on the level of the public good in each period, habit formation leads to a modification of the policy rule for public good provision if, and only if, the degrees of habituation differ for private and public good consumption. By contrast, if the public good supply is time-invariant, the presence of habit formation generally alters the policy rule for public good provision. PubDate: 2022-04-20
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Abstract: Abstract We propose new axiomatizations of the core and three related solution concepts that also provide predictions for (classes of) games in which the core itself is empty. Our results showcase the importance of the reduced game formulation and identify the corresponding converse consistency property as the differentiating characteristic between the core and its various extensions. Existing axiomatizations of the core and similar concepts include the required form of feasibility in the generic definition of a solution concept and/or are restricted to the domain of games for which existence is guaranteed. We dispense of both practices, thus opening up the possibility of comparing, via basic axioms, solution concepts that have different feasibility constraints and domains. PubDate: 2022-04-19
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Abstract: Abstract Natural resources such as water, for which the availability to users is random, are often shared according to predefined rules. What determines users’ choice of a sharing rule' To answer this question, we designed an experiment in which subjects: (1) vote on sharing rules; (2) choose the technology that transforms the resource into payoffs; and (3) respond to a survey on their adhesion to principles of fairness. We find that although subjects tend to vote for the sharing rule that is aligned with their self-interest, they become more egalitarian if they report their views on the fairness principles before voting. Furthermore, the adhesion to fairness principles affects the subjects’ votes not directly but rather indirectly through the choice of technology. PubDate: 2022-04-04
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