Arrow's Impossibility Theorem Without Unanimity

A tight quantitative version of Arrow's impossibility theorem

The well-known Impossibility Theorem of Arrow asserts that any Generalized Social Welfare Function (GSWF) with at least three alternatives, which satisfies Independence of Irrelevant Alternatives (IIA) and Unanimity and is not a dictatorship, is necessarily nontransitive. In 2002, Kalai asked whether one can obtain the following quantitative version of the theorem: For any > 0, there exists δ =...

Welfarist-consequentialism, similarity of attitudes, and Arrow's general impossibility theorem

Arrow ' s Theorem with a Fixed Feasible Alternative *

Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if ...

Democracy and efficiency: A note on "Arrow's theorem is not a surprising result"

It has been shown that Arrow's impossibility result can be avoided when the notion of aggregation procedure is extended to include procedures leading to more than one relation on the set of alternatives. The purpose of this note is to study the structure of these aggregation procedures, generalizing previous results obtained by Phillipe Vincke. Under 'Arrowian' conditions, we prove that such pr...

Intradimensional Single-Peakedness and the Multidimensional Arrow Problem

Arrow's account (1951/1963) of the problem of social choice is based upon the assumption that the preferences of each individual in the relevant group are expressible by a single ordering. This paper lifts that assumption and develops a multidimensional generalization of Arrow's framework. I show that, like Arrow's original framework, the multidimensional generalization is affected by an imposs...