Let $V$ be society whose members express preferences about two alternatives, indifference included. Identifying anonymous binary social choice functions with binary functions $f=f(k,m)$ defined over the integer triangular grid $G=\{(k,m)\in \mathbb{N}_0\times\mathbb{N}_0 : k+m\le |V|\} $, we show that every strategy-proof, anonymous social choice function can be described geometrically by listing, in a sequential manner, groups of segments of G, of equal (maximum possible) length, alternately horizontal and vertical, representative of preference profiles that determine the collective choice of one of the two alternatives. Indeed, we show that every function which is anonymous and strategy-proof can be described in terms of a sequence of nonnegative integers $(q_1, q_2, \cdots, q_s)$ corresponding to the cardinalities of the mentioned groups of segments. We also analyze the connections between our present representation with another of our earlier representations involving sequences of majority quotas.
A Python code is available with the authors for the implementation of any such social choice function.
Let V be a finite society whose members express weak orderings (hence also indifference, possibly) about two alternatives. We show a simple representation formula that is valid for all, and only, anonymous, non-manipulable, binary social choice functions on V . The number of such functions is $2^{n+1}$ if V contains $n$ agents.
Coalition strategy-proof anonymous binary social choice in a countably infinite society
Dipartimento di Scienze Economiche e Statistiche, Università Federico II（那不勒斯费德里科二世大学）；Department of Computer Information Systems, Indiana University Northwest（印第安纳大学西北分校）；School of Business and Economics, Indiana University Northwest（印第安纳大学西北分校）
We provide a necessary and sufficient condition for rationalizable implementation of social choice functions, i.e., we offer a complete answer regarding what social choice functions can be rationalizably implemented.
Social decision schemes (SDSs) map the preferences of a group of voters over some set of $m$ alternatives to a probability distribution over the alternatives. A seminal characterization of strategyproof SDSs by Gibbard implies that there are no strategyproof Condorcet extensions and that only random dictatorships satisfy ex post efficiency and strategyproofness. The latter is known as the random dictatorship theorem. We relax Condorcet-consistency and ex post efficiency by introducing a lower bound on the probability of Condorcet winners and an upper bound on the probability of Pareto-dominate…
Keeping up with "The Joneses" matters. This paper examines a model of reference dependent choice where reference points are determined by social comparisons. An increase in the strength of social comparisons, even by only a few agents, increases consumption and decreases welfare for everyone. Strikingly, a higher marginal cost of consumption can increase welfare. In a labour market, social comparisons with co-workers create a big fish in a small pond effect, inducing incomplete labour market sorting. Further, it is the skilled workers with the weakest social networks who are induced to give up…
We give a structure theorem for all coalitionally strategy-proof social choice functions whose range is a subset of cardinality two of a given larger set of alternatives. We provide this in the case where the voters/agents are allowed to express indifference and the domain consists of profiles of preferences over a society of arbitrary cardinality. The theorem, that takes the form of a representation formula, can be used to construct all functions under consideration.
I present an example in which the individuals' preferences are strict orderings, and under the majority rule, a transitive social ordering can be obtained and thus a non-empty choice set can also be obtained. However, the individuals' preferences in that example do not satisfy any conditions (restrictions) of which at least one is required by Inada (1969) for social preference transitivity under the majority rule. Moreover, the considered individuals' preferences satisfy none of the conditions of value restriction (VR), extremal restriction (ER) or limited agreement (LA), some of which is requ…
We study efficiency in general collective choice problems where agents have ordinal preferences and randomization is allowed. We explore the structure of preference profiles where ex-ante and ex-post efficiency coincide, offer a unifying perspective on the known results, and give several new characterizations. The results have implications for well-studied mechanisms including random serial dictatorship and a number of specific environments, including the dichotomous, single-peaked, and social choice domains.
The notion of distortion in social choice problems has been defined to measure the loss in efficiency -- typically measured by the utilitarian social welfare, the sum of utilities of the participating agents -- due to having access only to limited information about the preferences of the agents. We survey the most significant results of the literature on distortion from the past 15 years, and highlight important open problems and the most promising avenues of ongoing and future work.
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Indian Institute of Science（印度科学学院）；IIT, Kanpur（坎普尔印度理工学院）；ISI, Kolkata（加尔各答印度统计研究所）
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Social choice functions (SCFs) map the preferences of a group of agents over some set of alternatives to a non-empty subset of alternatives. The Gibbard-Satterthwaite theorem has shown that only extremely restrictive SCFs are strategyproof when there are more than two alternatives. For set-valued SCFs, or so-called social choice correspondences, the situation is less clear. There are miscellaneous - mostly negative - results using a variety of strategyproofness notions and additional requirements. The simple and intuitive notion of Kelly-strategyproofness has turned out to be particularly comp…
