Showing papers in "Social Choice and Welfare in 2017"
TL;DR: In this paper, the authors consider a generalization of single-winner scoring rules, including SNTV, Bloc, k-Borda, STV, and several variants of the Chamberlin-Courant rule and the Monroe rule.
Abstract: A committee selection rule (or, multiwinner voting rule) is a mapping that takes a collection of strict preference rankings and a positive integer k as input, and outputs one or more subsets of candidates of size k. In this paper we consider committee selection rules that can be viewed as generalizations of single-winner scoring rules, including SNTV, Bloc, k-Borda, STV, as well as several variants of the Chamberlin–Courant rule and the Monroe rule and their approximations. We identify two natural broad classes of committee selection rules, and show that many of the existing rules belong to one or both of these classes. We then formulate a number of desirable properties of committee selection rules, and evaluate the rules we consider with respect to these properties.
146 citations
TL;DR: In this article, the authors argue that all behaviors and accomplishments of children should be considered the consequence of circumstances: that is, an individual should not be considered to be responsible for her choices before an age of consent is reached.
Abstract: Many studies have estimated the effect of circumstances on income acquisition. Perhaps surprisingly, the fraction of inequality attributable to circumstances is usually quite small—in the advanced democracies, approximately 20%. One reason for this is the lack of data on circumstance variables in empirical research. Here, we argue that all behaviors and accomplishments of children should be considered the consequence of circumstances: that is, an individual should not be considered to be responsible for her choices before an age of consent is reached. Using two data sets that contain data on childhood accomplishments, other environmental circumstances and the income as an adult, we calculate that the fraction of income inequality due to circumstances in the US rises from 27 to 43% when accounting for childhood circumstances. In the UK it rises from 18 to 27%.
33 citations
TL;DR: In this paper, the authors characterize the subgame perfect equilibrium and show that each player's expected payoff and probability of winning is maximized when he competes in the first and the last rounds.
Abstract: We study round-robin tournaments with either three or four symmetric players whose values of winning are common knowledge. With three players there are three rounds, each of which includes one pair-wise game such that each player competes in two rounds only. The player who wins two games wins the tournament. We characterize the subgame perfect equilibrium and show that each player’s expected payoff and probability of winning is maximized when he competes in the first and the last rounds. With four players there are three rounds, each of which includes two sequential pair-wise games where each player plays against a different opponent in every round. We again characterize the subgame perfect equilibrium and show that a player who plays in the first game of each of the first two rounds has a first-mover advantage as reflected by a significantly higher winning probability as well as by a significantly higher expected payoff than his opponents.
33 citations
TL;DR: It is found that donations to poverty relief charities are inversely related to the perceived transfers made to the poorest quintile, and there is little correlation between giving and political beliefs.
Abstract: Many Americans hold erroneous beliefs regarding the level of inequality in the United States and the efforts by the federal government to alleviate poverty. In general, they overestimate the extent of poverty relief undertaken by government. Given that poverty relief programs are a public good and likely underprovided, overestimation of the level of income redistribution is likely to exacerbate this under-provision by reducing giving to private charities. This paper considers if this misperception affects giving to poverty-relief charities. We report a real-donation experiment investigating links between contributions to poverty-relief charities and perceptions of federal transfers to low income households. We also ask participants to self-identify political affiliation, religiosity, race, and gender. We find that donations to our poverty relief charities are inversely related to the perceived transfers made to the poorest quintile. Donations are approximately $0.20 less for each $1000 of perceived transfers. Interestingly, we find little correlation between giving and political beliefs.
29 citations
TL;DR: It is shown that the same kinds of axioms have radically different implications for different aggregation problems: linearity for probability aggregation and dictatorship for binary judgment or preference aggregation.
Abstract: How can several individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events – the agenda – is a-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain or an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we unify our results with existing results on binary judgment aggregation and Arrovian preference aggregation. We show that the same kinds of axioms (independence and consensus preservation) have radically different implications for different aggregation problems: linearity for probability aggregation and dictatorship for binary judgment or preference aggregation.
24 citations
TL;DR: A model where families consist of one parent and one child, with children differing in income and all agents having the same probability of becoming dependent when old is developed, which provides several reasons for the stylized fact that there are little social LTC transfers in most countries.
Abstract: We develop a model where families consist of one parent and one child, with children differing in income and all agents having the same probability of becoming dependent when old. Young and old individuals vote over the size of a social long term care transfer program, which children complement with help in time or money to their dependent parent. Dependent parents have an intrinsic preference for help in time by family members. We first show that low (resp., high) income children provide help in time (resp. in money), whose amount is decreasing (resp. increasing) with the child's income. The middle income class may give no family help at all, and its elderly members would be the main beneficiaries of the introduction of social LTC transfers. We then provide several reasons for the stylized fact that there are little social LTC transfers in most countries. First, social transfers are dominated by help in time by the family when the intrinsic preference of dependent parents for the latter is large enough. Second, when the probability of becoming dependent is lower than one third, the children of autonomous parents are numerous enough to oppose democratically the introduction of social LTC transfers. Third, even when none of the first two conditions is satisfied, the majority voting equilibrium may entail no social transfers, especially if the probability of becoming dependent when old is not far above one third. This equilibrium may be local (meaning that it would be defeated by the introduction of a sufficiently large social program). This local majority equilibrium may be empirically relevant whenever new programs have to be introduced at a low scale before being eventually ramped up.
21 citations
TL;DR: In this article, it was shown that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures, in contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature.
Abstract: We show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature.
21 citations
TL;DR: It is argued that a redistribution mechanism based on this principle would eliminate unfair inequalities and preserve fair inequalities, and when the generalized proportionality principle is equivalent to the simple proportionalities principle is discussed.
Abstract: How should income be distributed in a way that respects both the egalitarian ideal that inequalities due to differences in opportunities should be eliminated and the liberal ideal that people should be free to pursue their own idea of the good life without interference from society? We show that reasonable interpretations of the egalitarian and the liberal ideal characterize what we refer to as the generalized proportionality principle. This principle states that an individual should have the share of total income that he or she would have had if everyone had the same opportunities and these opportunities were given by the average of the pre-tax income functions of all individuals in society. We argue that a redistribution mechanism based on this principle would eliminate unfair inequalities and preserve fair inequalities, and discuss when the generalized proportionality principle is equivalent to the simple proportionality principle.
21 citations
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TL;DR: The implications of four natural axioms in taxation are explored: continuity, equal treatment of equals, consistency, composition down and composition down (an increase in the tax burden is handled according to agents’ current post-tax incomes).
Abstract: We explore the implications of four natural axioms in taxation: continuity (small changes in the data of a taxation problem should not lead to large changes in the tax allocation), equal treatment of equals (agents with the same pre-tax incomes pay equal taxes), consistency (the way in which a group allocates a tax burden is immune to secessions of taxpayers) and composition down (an increase in the tax burden is handled according to agents’ current post-tax incomes). The combination of the four axioms characterizes a large family of rules, which we call generalized equal-sacrifice rules, encompassing the so-called equal-sacrifice rules (such as the flat tax), as well as constrained equal-sacrifice rules (such as the head tax), and exogenous poverty-line rules (such as the leveling tax, and some of its possible compromises with the previous ones).
20 citations
TL;DR: A structured list of most rules that have been proposed and studied recently in the literature, together with various properties of such rules, focusing on the majority-preservation property, which generalizes Condorcet-consistency, and which of the rules satisfy it.
Abstract: The literature on judgment aggregation is moving from studying impossibility results regarding aggregation rules towards studying specific judgment aggregation rules. Here we give a structured list of most rules that have been proposed and studied recently in the literature, together with various properties of such rules. We first focus on the majority-preservation property, which generalizes Condorcet-consistency, and identify which of the rules satisfy it. We study the inclusion relationships that hold between the rules. Finally, we consider two forms of unanimity, monotonicity, homogeneity, and reinforcement, and we identify which ofthe rules satisfy these properties.
19 citations
TL;DR: It is proved that efficiency, symmetry and a monotonicity axiom characterize (i) four linear solutions in the literature, namely, the Shapley value, the equal divisionvalue, the CIS value and the ENSC value, and (ii) a class of solutions obtained by taking a convex combination of the above solutions.
Abstract: The purpose of this study is to provide a comprehensive characterization of linear solutions to cooperative games by using monotonicity. A monotonicity axiom states an increase in certain parameters of a game as a hypothesis and states an increase in a player’s payoff as a conclusion. We focus on various parameters of a game and introduce new axioms. Combined with previous results, we prove that efficiency, symmetry and a monotonicity axiom characterize (i) four linear solutions in the literature, namely, the Shapley value, the equal division value, the CIS value and the ENSC value, and (ii) a class of solutions obtained by taking a convex combination of the above solutions. Our methodological contribution is to provide a new linear algebraic approach for characterizing solutions by monotonicity. Using a new basis of the linear space of TU games, we identify a class of games in which a solution that satisfies monotonicity is linear. Our approach provides some intuition for why monotonicity implies linearity.
TL;DR: It is concluded that there is greater equality of opportunity among women than among men, with gender the single most important circumstance in accounting for inequality in long-run income in Sweden.
Abstract: This paper considers the role of gender in generating inequality of opportunity. Using data on long-run income for Swedish men and women, we explore to what extent income inequality is due to circumstances beyond individuals’ control, such as gender and parental income, rather than to differences in individuals’ choices. The key idea is that a society has achieved equality of opportunity if there is no income inequality that is due to circumstances. Analyzing men and women separately, we find that circumstances account for up to 31% of income inequality among men and up to 25% among women. We conclude that there is greater equality of opportunity among women than among men. When we analyze men and women together, treating gender as a circumstance, at most 38% of income inequality can be attributed to circumstances. Gender accounts for up to 13% of income inequality, making gender the single most important circumstance in accounting for inequality in long-run income in Sweden.
TL;DR: In this paper, an extensive combinatorial analysis of the single-peaked domain restriction and the likelihood that an election is single-peak is presented, and exact results for elections with few voters or candidates are given.
Abstract: This paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can be defined by certain forbidden configurations. This upper bound implies that many domain restrictions (including the single-peaked restriction) are very unlikely to appear in a random election chosen according to the Impartial Culture assumption. For single-peaked elections, this upper bound can be refined and complemented by a lower bound that is asymptotically tight. In addition, we provide exact results for elections with few voters or candidates. Moreover, we consider the Polya urn model and the Mallows model and obtain lower bounds showing that single-peakedness is considerably more likely to appear for certain parameterizations.
TL;DR: It is shown that equal treatment of equals, efficiency, and strategy-proofness are incompatible, and anonymity, neutrality, efficiency and weak group strategy-Proofness become incompatible when agents have single-unit demands.
Abstract: We consider the problem of assigning objects probabilistically among a group of agents who may have multi-unit demands Each agent has linear preferences over the (set of) objects The most commonly used extension of preferences to compare probabilistic assignments is by means of stochastic dominance, which leads to corresponding notions of envy-freeness, efficiency, and strategy-proofness We show that equal treatment of equals, efficiency, and strategy-proofness are incompatible Moreover, anonymity, neutrality, efficiency, and weak strategy-proofness are incompatible If we strengthen weak strategy-proofness to weak group strategy-proofness, then when agents have single-unit demands, anonymity, neutrality, efficiency, and weak group strategy-proofness become incompatible
TL;DR: A new version of the reward principle is proposed based on the idea that effort deserves reward for it is costly, and it is shown that luck can be introduced in two ways in the definition of these principles.
Abstract: Equality of opportunity is usually defined as a situation where the effect of circumstances on outcome is nullified (compensation principle) and effort is rewarded (reward principle). We propose a new version of the reward principle based on the idea that effort deserves reward for it is costly. We show that luck can be introduced in two ways in the definition of these principles, depending on whether the correlation between luck and circumstances should be nullified and whether the correlation between luck and effort should be rewarded. In this regard, the timing of luck with respect to effort decisions is crucial, as is exemplified by moral hazard where effort choice influences the lottery of future uncertain events.
TL;DR: Analysis of participants’ need judgments using a latent-class, rank-ordered conditional logit model reveals that most individuals draw on all three definitions of need when assessing need, and that here is heterogeneity in interpretations of need among the public.
Abstract: The concept of need is central to the non-market allocation of many public resources, although the definition of need to serve as a basis for such resource allocation often remains contested. This study uses a discrete-choice experiment to investigate the general public’s interpretation of need in the context of health care resource allocation, focusing on three commonly cited definitions of need: need as a person’s baseline health status; need as a person’s ability-to-benefit; and need as the amount of resources required to exhaust a person’s ability-to-benefit. Analysis of participants’ need judgments using a latent-class, rank-ordered conditional logit model reveals that most individuals draw on all three definitions when assessing need, and that here is heterogeneity in interpretations of need among the public. Baseline health status is the most influential and consistent determinant of need, while ability-to-benefit and resources-required-to-exhaust-benefit are considered jointly. However, while some assign greater need to those who are worse off in the sense that they have little ability-to-benefit and require large amounts of resources to achieve that benefit, others assign greater need to those who have greater ability-to-benefit and whose benefit can be achieved with small amounts of resources. The public’s reasoning about need contrasts sharply in a number of ways with the types of arguments offered in the literature on needs-based resource allocation.
TL;DR: The paper addresses John Roemer’s recent work on Kantian optimization and Kantian equilibria, and discusses critically his argument that his findings can be explained by assuming that agents are conditional Kantians.
Abstract: The paper addresses John Roemer’s recent work on Kantian optimization and Kantian equilibria. Roemer argues that the standard economic theory of Nash equilibria is incapable of accounting for cooperative behavior such as recycling, reporting one’s income honestly, and voting in national elections. Instead we should assume that a cooperator is motivated to do what would most benefit her if all did the same. In commenting on this proposal, the first section of the paper summarizes Kant’s original formulation of the categorical imperative and relates it to psychological and historical studies of magical thinking. The next section distinguishes between unconditional and conditional norms of behavior and, within the latter, between the social norms of cooperation that can be triggered when what the agent does is being observed by others and the quasi-moral norms of cooperation that can be triggered when an agent observes what others do. To illustrate these ideas, the paper cites many experiments and historical case studies, the most important being the non-consumption, non-importation, and non-exportation movements in the American revolution. The concluding section summarizes Roemer’s own empirical work, and discusses critically his argument that his findings can be explained by assuming that agents are conditional Kantians.
TL;DR: There are a number of single-profile impossibility theorems in social choice theory and welfare economics that demonstrate the incompatibility of unanimity/dominance criteria with various nonconsequentialist principles given some rationality restrictions on the rankings being considered.
Abstract: There are a number of single-profile impossibility theorems in social choice theory and welfare economics that demonstrate the incompatibility of unanimity/dominance criteria with various nonconsequentialist principles given some rationality restrictions on the rankings being considered. This article is concerned with examining what they have in common and how they differ. Groups of results are identified that have similar formal structures and are established using similar proof strategies.
TL;DR: An axiomatic analysis of the concept of unequal exchange (UE) between countries is developed in a dynamic general equilibrium model that generalises John Roemer's (Central Planning and the Soviet Economy, MIT Press, Cambridge, 1983) economy with a global capital market.
Abstract: An axiomatic analysis of the concept of unequal exchange (UE) between countries is developed in a dynamic general equilibrium model that generalises John Roemer’s (Central Planning and the Soviet Economy, MIT Press, Cambridge, 1983) economy with a global capital market. The class of UE definitions that satisfy three fundamental properties—including a correspondence between wealth, class and UE exploitation status—is completely characterised. It is shown that this class is nonempty and a definition of UE exploitation between countries is proposed, which is theoretically robust and firmly anchored to empirically observable data. The full class and UE exploitation structure of the international economy is derived in equilibrium.
TL;DR: This work model inter-individual differences in preferences for redistribution as a function of self-interest, ideas about the deservingness of income differences due to luck, effort and talent, and the consequences for redistributive preferences of homophilous reference group formation based on talent.
Abstract: We model inter-individual differences in preferences for redistribution as a function of (a) self-interest; (b) ideas about the deservingness of income differences due to luck, effort and talent; (c) subjective perceptions of the relative importance of these determinants for explaining the actual income distribution Individuals base the latter on information obtained from their reference group We analyse the consequences for redistributive preferences of homophilous reference group formation based on talent Our model makes it possible to understand and integrate some of the main insights from the empirical literature We illustrate with GSS data from 1987 how our model may help in structuring empirical work
TL;DR: Responses suggest that population size is not neutral to social welfare, and many participants reported that a larger population of people living good lives could be strictly preferable, at small or no costs to average well-being.
Abstract: Is a larger population of people living good lives a better population, all else equal? This question is central to population issues in social welfare, ethics, and policy. Many answers in the philosophical literature argue that if a policy choice results in the birth of additional people living good lives, these extra lives are irrelevant to any evaluation of the policy. This paper applies the questionnaire-experimental method of empirical studies of social choice to investigate participants’ policy choices and social orderings with respect to population size and average well-being. In general, heterogeneous responses depended on the quantitative and qualitative properties of the question. In particular, an experimentally manipulated increase in population size caused an option to be more likely to be selected, on average. Overall, responses suggest that population size is not neutral to social welfare. Many participants, although not all, reported that a larger population of people living good lives could be strictly preferable, at small or no costs to average well-being.
TL;DR: In this article, the authors study the strategy-proofness properties of the randomized Condorcet voting system (RCVS) and show that the RCVS is group-strategy-proof.
Abstract: In this paper, we study the strategy-proofness properties of the randomized Condorcet voting system (RCVS). Discovered at several occasions independently, the RCVS is arguably the natural extension of the Condorcet method to cases where a deterministic Condorcet winner does not exists. Indeed, it selects the always-existing and essentially unique Condorcet winner of lotteries over alternatives. Our main result is that, in a certain class of voting systems based on pairwise comparisons of alternatives, the RCVS is the only one to be Condorcet-proof. By Condorcet-proof, we mean that, when a Condorcet winner exists, it must be selected and no voter has incentives to misreport his preferences. We also prove two theorems about group-strategy-proofness. On one hand, we prove that there is no group-strategy-proof voting system that always selects existing Condorcet winners. On the other hand, we prove that, when preferences have a one-dimensional structure, the RCVS is group-strategy-proof.
TL;DR: New tools for obtaining stochastic improvements in lotteries are provided to help facilitate the design of practical lottery mechanisms that improve upon the widely used random serial dictatorship mechanism and a lottery representation of its competitor, the probabilistic serial mechanism.
Abstract: There has been a surge of interest in stochastic assignment mechanisms that have proven to be theoretically compelling thanks to their prominent welfare properties. Contrary to stochastic mechanisms, however, lottery mechanisms are commonly used in real life for indivisible goods allocation. To help facilitate the design of practical lottery mechanisms, we provide new tools for obtaining stochastic improvements in lotteries. As applications, we propose lottery mechanisms that improve upon the widely used random serial dictatorship mechanism and a lottery representation of its competitor, the probabilistic serial mechanism. The tools we provide here can be useful in developing welfare-enhanced new lottery mechanisms for practical applications such as school choice.
TL;DR: A characterization of the family of non-contestable budget-monotone rules for the allocation of objects and money as those obtained by maximizing a maxmin social welfare function among all non-Contestable allocations and shows that one can “rectify” any non- Contestable rule without losing non- Contestability.
Abstract: We characterize the family of non-contestable budget-monotone rules for the allocation of objects and money as those obtained by maximizing a maxmin social welfare function among all non-contestable allocations. We provide three additional seemingly independent approaches to construct these rules. We present three applications of this characterization. First, we show that one can “rectify” any non-contestable rule without losing non-contestability. Second, we characterize the preferences that admit, for each budget, a non-contestable allocation satisfying a minimal or maximal individual consumption of money constraint. Third, we study continuity properties of the non-contestable correspondence.
TL;DR: In this paper, the authors formalize this idea by introducing a "premise-based" approach to probabilistic opinion pooling, and show that it leads to linear or neutral pooling on the "premises" under a variety of assumptions.
Abstract: How can several individuals’ probability functions on a given $$\sigma $$
-algebra of events be aggregated into a collective probability function? Classic approaches to this problem usually require ‘event-wise independence’: the collective probability for each event should depend only on the individuals’ probabilities for that event. In practice, however, some events may be ‘basic’ and others ‘derivative’, so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize this idea by introducing a ‘premise-based’ approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the ‘premises’.
TL;DR: The problem of allocating heterogeneous indivisible tasks in a multi-object-demand model where monetary transfers are allowed and the class of envy-free and egalitarian-equivalent Groves mechanisms when costs are subadditive is studied.
Abstract: We study the problem of allocating heterogeneous indivisible tasks in a multi-object-demand model (i.e., each agent can be assigned multiple objects) where monetary transfers are allowed. Agents’ costs for performing tasks are their private information and depend on what other tasks they are obtained with. First, we show that when costs are unrestricted or superadditive, then there is no envy-free and egalitarian-equivalent mechanism that assigns the tasks efficiently. Then, we characterize the class of envy-free and egalitarian-equivalent Groves mechanisms when costs are subadditive. Finally, within this class, under a bounded-deficit condition, we identify the Pareto-dominant subclass. We show that the mechanisms in this subclass are not Pareto-dominated by any other Groves mechanism satisfying the same bounded-deficit condition.
TL;DR: On the domain of cooperative games with transferable utility, it is investigated if there are single-valued solutions that reconcile individual rationality, core selection, consistency and monotonicity (with respect to the worth of the grand coalition).
Abstract: On the domain of cooperative games with transferable utility, we investigate if there are single-valued solutions that reconcile individual rationality, core selection, consistency and monotonicity (with respect to the worth of the grand coalition). This paper states some impossibility results for the combination of core selection with either complement consistency (Moulin, J Econ Theory 36:120–148, 1985) or projected consistency (Funaki, Dual axiomatizations of solutions of cooperative games. Mimeo, Tokyo, 1998), and core selection, max consistency (Davis and Maschler, Naval Res Logist Q 12:223–259, 1965) and monotonicity. By contrast, possibility results are manifest when combining individual rationality, projected consistency and monotonicity.
TL;DR: The study shows the evidence of partial stickiness rather than complete stickiness of default options as indicated in empirical studies, which is robust to the variation of the game employed, but the effect on contribution is sensitive to it.
Abstract: It is well documented that people are reluctant to switch from a default option. We experimentally test the robustness of this behavioral inertia in a collective decision-making setting by varying the default option type and the decision-making environment. We examine the impacts of automatic-participation and no-participation default options on subjects’ participation in a public goods provision and their contributions. Two variants of public goods game are employed: the linear and the threshold public goods games. The study shows the evidence of partial stickiness rather than complete stickiness of default options as indicated in empirical studies. Our experimental results square with the evidence of behavioral inertia only when the automatic-participation default is used. This default boosts contributions in the linear public goods game but not in the threshold public goods game. The evidence of partial stickiness is robust to the variation of the game employed, but the effect on contribution is sensitive to it.
TL;DR: This paper considers how Roemer's General Theory of Exploitation and Class and related work has engaged and reframed the historical materialist critique of capitalism initiated by Marx’s Capital project, and how imperfect contracting conditions and capital accumulation might figure in a coherent materialist theory of profit and exploitation.
Abstract: This paper considers how Roemer’s General Theory of Exploitation and Class and related work has engaged and reframed the historical materialist critique of capitalism initiated by Marx’s Capital project, and in turn how aspects of Marx’s account of capitalist profit and exploitation not addressed in the General Theory might be analyzed within Roemer’s framework of rationally optimizing agents and equilibrating markets. In particular, the paper discusses how imperfect contracting conditions and capital accumulation might figure in a coherent materialist theory of profit and exploitation.
TL;DR: This paper provides four characterizations of the agent-proposing deferred acceptance allocation rule for all acceptant substitutable choice functions and suggested that two new axioms: rank monotonicity and weak consistency, deserve further attention.
Abstract: We study the problem of allocating a set of indivisible objects to a set of agents based on agents’ preferences over objects and objects’ “choice functions” over agents, when monetary transfers are not allowed. Following Kojima and Manea (Econometrica 78(2):633–653, 2010) and Morrill (Int J Game Theory 42(1):19–28, 2013a), this paper provides four characterizations of the agent-proposing deferred acceptance allocation rule for all acceptant substitutable choice functions. It is the only rule satisfying any one of the following groups of axioms: (1) stability, rank monotonicity; (2) non-wastefulness, top best, weak consistency, rank monotonicity; (3) non-wastefulness, strong top best, weak Maskin monotonicity; (4) non-wastefulness, strong group rationality, rank monotonicity. These results suggested that two new axioms: rank monotonicity and weak consistency, deserve further attention. They also shed light on what distinguishes the agent-proposing deferred acceptance rule from the other rules.