In this paper we provide a sufficient condition for a social welfare relation to be a social decision relation (i.e. an acyclic social welfare relation) when the profile of individual preferences is given.

This note presents a simple proof of Arrow's impossibility theorem using Saari's [3, 4] "geometry of voting".

Arrow's theorem is proved on a domain consisting of two types of preference profiles. Those in the first type are "almost unanimous": for every profile some alternative x is such that the preferences of any two individuals merely differ in the ranking of x, which is in one of the first three...

An extension of Condorcet's paradox by McGarvey (1953) asserts that for every asymmetric relation R on a finite set of candidates there is a strict-preferences voter profile that has the relation R as its strict simple majority relation. We prove that McGarvey's theorem can be extended to...

In this paper, we prove a fuzzy version of Arrow's Theorem that contains the crisp version. We show that under our definitions, Arrow's Theorem remains intact even if levels of intensities of the players and levels of membership in the set of alternatives are considered.

Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341--375, 2011) have recently proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean (MBA) preference orderings. This paper investigates the...

In a paper published in 1952, the French mathematician Georges-Théodule Guilbaud has generalized Arrow's impossibility result to the "logical problem of aggregation", thus anticipating the literature on abstract aggregation theory and judgment aggregation. We reconstruct the proof of Guilbaud's...

We present a straightforward proof of Arrow's Theorem. Our approach avoids some of the complexities of existing proofs and is meant to be transparent and easily followed.