Averting the quorum paradox

Abstract

The quorum paradox is a phenomenon whereby the probability that a voting body which is not fully assembled will reach the same decision that would have been reached if it were fully assembled may not be monotonically increasing with the number of voters present. To avert this paradox, it is suggested that regardless of the size of the quorum needed to conduct a vote: (1) if the decision rule for passing issues is a simple majority of the members present and the number of members present is even, a tie should be broken randomly if it occurs; (2) if a special majority is deemed appropriate for passing an issue, one must always require that the issue should be supported by a special majority of the entire electorate. With such revisions in voting rules, there would be ample legitimacy to using the quorum as a criterion for holding votes. Moreover, by adopting these revisions, the distinction between odd- and even-sized voting bodies would lose much of its significance.