Unanimity and the Anscombe's paradox

Abstract

We establish a new sufficient condition for avoiding a generalized Anscombe's paradox. In a situation where votes describe positions regarding finitely many yes-or-no issues, the Anscombe's alpha-paradox holds if more than alpha% of the voters disagree on a majority of issues with the outcome of issue-wise majority voting. We define the level of unanimity of a set of votes as the number of issues minus the maximal Hamming distance between two votes. We compute for the case of large electorates the exact level of unanimity above which the Anscombe's alpha-paradox never holds, whatever the distribution of individuals among votes.