Related papers: Between Arrow and Gibbard-Satterthwaite; A represe…
In Terao [24], Hiroaki Terao defined and studied "admissible map", which is a generalization of "social welfare function" in the context of hyperplane arrangements. Using this, he proved a generalized Arrow's Impossibility Theorem using…
This work deals with the implementation of social choice rules using dominant strategies for unrestricted preferences. The seminal Gibbard-Satterthwaite theorem shows that only few unappealing social choice rules can be implemented unless…
We characterize trees as median algebras and semilattices by relaxing conservativeness. Moreover, we describe median homomorphisms between products of median algebras and show that Arrow type impossibility theorems for mappings from a…
By the Gibbard--Satterthwaite theorem, every reasonable voting rule for three or more alternatives is susceptible to manipulation: there exist elections where one or more voters can change the election outcome in their favour by…
The traditional Arrow--Sen Social Choice Theory $\bf{TSCT}$ is a mathematical theory built apparently on higher--order formal language. In this paper, we propose a reformulation and reclassification of the $\bf{TSCT}$ axioms in order to…
The central problems in social sciences concern the social and psychological mechanisms and conditions required for the emergence and stability of human groups. The present article is dedicated to the problem of stability of human groups.…
We study a budget aggregation setting where voters express their preferred allocation of a fixed budget over a set of alternatives, and a mechanism aggregates these preferences into a single output allocation. Motivated by scenarios in…
We prove a quantitative version of the Gibbard-Satterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of $q \ge 4$ alternatives and n voters will be manipulable with probability at least…
This paper studies a general class of social choice problems in which agents' payoff functions (or types) are privately observable random variables, and monetary transfers are not available. We consider cardinal social choice functions…
Preference cycles are prevalent in problems of decision-making, and are contradictory when preferences are assumed to be transitive. This contradiction underlies Condorcet's Paradox, a pioneering result of Social Choice Theory, wherein…
We elucidate a close connection between the Theory of Judgment Aggregation (more generally, Evaluation Aggregation), and a relatively young but rapidly growing field of universal algebra, that was primarily developed to investigate…
The classic Gibbard-Satterthwaite theorem says that every strategy-proof voting rule with at least three possible candidates must be dictatorial. In \cite{McL11}, McLennan showed that a similar impossibility result holds even if we consider…
The purpose of this note is to prove the existence of a randomized mechanism, a social decision scheme (SDS), with desirable fairness, efficiency, and strategyproofness properties unmatched by all known SDSs. In particular, we disprove a…
We study private-good allocation under general constraints. Several prominent examples are special cases, including house allocation, roommate matching, social choice, and multiple assignment. Every individually strategy-proof and Pareto…
Arrow's celebrated Impossibility Theorem asserts that an election rule, or Social Welfare Function (SWF), between three or more candidates meeting a set of strict criteria cannot exist. Maskin suggests that Arrow's conditions for SWFs are…
Utility functions or their equivalents (value functions, objective functions, loss functions, reward functions, preference orderings) are a central tool in most current machine learning systems. These mechanisms for defining goals and…
In several decision-making problems, alternatives should be ranked on the basis of paired comparisons between them. We present an axiomatic approach for the universal ranking problem with arbitrary preference intensities, incomplete and…
One possible escape from the Gibbard-Satterthwaite theorem is computational complexity. For example, it is NP-hard to compute if the STV rule can be manipulated. However, there is increasing concern that such results may not re ect the…
The definition of preferences assigned to individuals is a concept that concerns many disciplines, from economics, with the search of an acceptable outcome for an ensemble of individuals, to decision making an analysis of vote systems. We…
We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when the outcome space is the convex hull of some finite set of alternatives. Individual and…