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In this paper, we take a statistical decision-theoretic viewpoint on social choice, putting a focus on the decision to be made on behalf of a system of agents. In our framework, we are given a statistical ranking model, a decision space,…
Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on…
Condorcet's jury theorem states that the correct outcome is reached in direct majority voting systems with sufficiently large electorates as long as each voter's independent probability of voting for that outcome is greater than 0.5. Yet,…
Recovering and distinguishing between the strict-preference, indifference and/or indecisiveness parts of a decision maker's preferences is a challenging task but also important for testing theory and conducting welfare analysis. This paper…
Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections' outcomes, no matter how paradoxical it may appear. On this purpose…
One of the central economic paradigms in multi-agent systems is that agents should not be better off by acting dishonestly. In the context of collective decision-making, this axiom is known as strategyproofness and turns out to be rather…
We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles…
Incomputability results in Formal Logic and the Theory of Computation (i.e., incompleteness and undecidability) have deep implications for the foundations of mathematics and computer science. Likewise, Social Choice Theory, a branch of…
We consider a social choice problem where only a small number of people out of a large population are sufficiently available or motivated to vote. A common solution to increase participation is to allow voters use a proxy, that is, transfer…
Voting is a very general method of preference aggregation. A voting rule takes as input every voter's vote (typically, a ranking of the alternatives), and produces as output either just the winning alternative or a ranking of the…
To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings,…
An important -- but very demanding -- property in collective decision-making is strategyproofness, which requires that voters cannot benefit from submitting insincere preferences. Gibbard (1977) has shown that only rather unattractive rules…
We develop an approach to choice principles and their contrapositive bar-induction principles as extensionality schemes connecting an ''intensional'' or ''effective'' view of respectively ill-and well-foundedness properties to an…
We consider the social welfare function a la Arrow, where some voters are not qualified to evaluate some alternatives. Thus, the inputs of the social welfare function are the preferences of voters on the alternatives that they are qualified…
We consider voting rules in settings where voters' identities are difficult to verify. Voters can manipulate the process by casting multiple votes under different identities or abstaining from voting. Immunities to such manipulations are…
Journal ranking is becoming more important in assessing the quality of academic research. Several indices have been suggested for this purpose, typically on the basis of a citation graph between the journals. We follow an axiomatic approach…
The quantile admission process with veto power is a stochastic processes suggested by Alon, Feldman, Mansour, Oren and Tennenholtz as a model for the evolution of an exclusive social group. The model itself consists of a growing multiset of…
May's Theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that…
Preference aggregation is a fundamental problem in voting theory, in which public input rankings of a set of alternatives (called preferences) must be aggregated into a single preference that satisfies certain soundness properties. The…
Social decision schemes (SDSs) map the ordinal preferences of individual voters over multiple alternatives to a probability distribution over the alternatives. In order to study the axiomatic properties of SDSs, we lift preferences over…