An analysis of voting procedures with nonranked voting

Abstract

This paper analyzes decision making by simple voting procedures in organizational or societal systems. The simple voting procedures investigated are those that do not require voters to rank candidates when one of three or more candidates is to be elected to a single office or position. The procedures are compared on the basis of their propensities to elect the simple majority candidate when it exists. Propensity is measured in terms of efficiency of the procedure, which equals 100 times the probability that the candidate elected by the voting procedure is the simple majority candidate, given the latter exists. The procedures examined use either one or two ballots. On the first or only ballot they ask each voter either to vote for not more than so many candidates (variable procedures) or to vote for exactly so many candidates (constant procedures). Depending on assumptions about voter preferences and voting behavior, either the best variable procedure or the best constant procedure can have the higher efficiency. However, in both the one-stage and two-stage contexts, the difference in efficiency between the most efficient variable procedure and the most efficient constant procedure is usually negligible from a practical standpoint. On the other hand, efficiency can vary significantly depending on the number of stages and the number of candidates to be voted for, or up to, on the first ballot.