The Vulnerability of Majority Rule to Anscombe's and Ostrogorkski's Paradoxes : a Comparative Analysis

Abstract

The aim of this paper is to study the circumstances at which the Anscombe and Ostrogorski paradoxes are susceptible to arise when individual votes are dichotomous, that is, in the context of yes-no voting. Our main results provide an answer to the question of the likelihood of those paradoxes under two classical probabilistic models: the impartial culture (IC) and the impartial anonymous culture (IAC) assumptions. More precisely, we determine the exact frequencies of occurrence of these phenomena in the three-issue case, under simple majority rule; we also provide estimates - obtained by means of the Monte Carlo technique - for more than three issues.(original abstract)