The risk to breach vote privacy by unanimous voting

Abstract

The paper studies the risk that all members of a set of voters give their votes unanimously and thereby breach the privacy of the voting procedure. This problem becomes relevant in the situation that the voting behavior of a small (sub)set of voters can be identified by the way they transmit their votes, e. g., when at least two possible ways to give votes (like voting with ballot boxes, postal voting, and electronic voting) are admitted in theory but one of them is used by only a small minority of voters in practice.For the situation of a simple alternative between “yes” and “no” it turns out that as long as the probability of approval lies between 25% and 75% the probability of a breach of vote privacy by unanimous voting is smaller than 1% if there are at least 17 voters and even smaller than 0.1% if there are at least 25 voters. If, however, the rate of approval or disapproval increases, even to values already observed in reality, then the probability of such a breach of vote privacy can no longer be neglected. And even small values for the probability of a breach of vote privacy sum up when several thousands of these situations appear in parallel.Furthermore, if there is a three valued situation “yes” – “no” – “abstention” present, then, depending on the concept of vote privacy, a breach of it becomes considerably more probable even if the probability of approval remains within the boundaries mentioned above.