Related papers: A Phase Transition in Arrow's Theorem

We introduce the threshold $q$-voter opinion dynamics where an agent, facing a binary choice, can change its mind when at least $q_0$ amongst $q$ neighbors share the opposite opinion. Otherwise, the agent can still change its mind with a…

Social choice theory is the study of preference aggregation across a population, used both in mechanism design for human agents and in the democratic alignment of language models. In this study, we propose the representative social choice…

To the best of our knowledge, a complete characterization of the domains that escape the famous Arrow's impossibility theorem remains an open question. We believe that different ways of proving Arrovian theorems illuminate this problem.…

The traditional axiomatic approach to voting is motivated by the problem of reconciling differences in subjective preferences. In contrast, a dominant line of work in the theory of voting over the past 15 years has considered a different…

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…

Voting is the aggregation of individual preferences in order to select a winning alternative. Selection of a winner is accomplished via a voting rule, e.g., rank-order voting, majority rule, plurality rule, approval voting. Which voting…

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…

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…

We extend Approval voting to the settings where voters may have intransitive preferences. The major obstacle to applying Approval voting in these settings is that voters are not able to clearly determine who they should approve or…

Problems with majority voting over pairs as represented by Arrow's Theoremand those of finding the lengths of closed paths as captured by the Traveling Salesperson Problem (TSP) appear to have nothing in common. In fact, they are connected.…

We introduce a non-linear variant of the voter model, the q-voter model, in which q neighbors (with possible repetition) are consulted for a voter to change opinion. If the q neighbors agree, the voter takes their opinion; if they do not…

May's classical theorem states that in a single-winner choose-one voting system with just two candidates, majority rule is the only social choice function satisfying anonimity, neutrality and positive responsiveness axiom. Anonimity and…

Collective decision-making is a process by which a group of individuals determines a shared outcome that shapes societal dynamics; from innovation diffusion to organizational choices. A common approach to model these processes is using…

The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. However, its original formulation is not, in general, thermodynamically consistent,…

Understanding the nature of strategic voting is the holy grail of social choice theory, where game-theory, social science and recently computational approaches are all applied in order to model the incentives and behavior of voters. In a…

Voting is a game with a no-go theorem. New proofs of Arrow's impossibility theorem are given based on quantum information theory. We show that the Arrowian dictator is equivalent to the perfect cloning circuit. We present…

We study the voting problem with two alternatives where voters' preferences depend on a not-directly-observable state variable. While equilibria in the one-round voting mechanisms lead to a good decision, they are usually hard to compute…

The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…

The statistical properties of pairwise majority voting over S alternatives is analyzed in an infinite random population. We first compute the probability that the majority is transitive (i.e. that if it prefers A to B to C, then it prefers…

The well-known Condorcet's Jury theorem posits that the majority rule selects the best alternative among two available options with probability one, as the population size increases to infinity. We study this result under an asymmetric…