Unanimity and the Anscombe’s Paradox

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