Several studies published during the past five years have attempted to assess the propensities of different voting procedures to elect the simple majority candidate when one exists in a multicandidate election. The present paper provides a summary of what we believe to be the most salient results of this research. The data are first discussed within the context of the assumptions used in our simulations. We then extend our interpretations to account for potential political realities that were not incorporated in the simulations.
Large-scale elections to elect one of three or more candidates are usually conducted either by plurality voting -each voter can vote for one candidate, and the candidate who receives the most votes wins -or by a plurality ballot, followed by a runoff between the top two candidates when no candidate gets at least 40 (or sometimes 50) percent of the total votes cast.
Since the late eighteenth century, and probably earlier, a huge variety of other multicandidate voting procedures have been proposed (Borda, 1781; Condorcet, 1785;Hoag and Hallett, 1926;Black, 1958;Fishburn, 1977) but seldom used, due to numerous theoretical, practical and political factors. The latter realities, plus the belief that other simple procedures may be superior to plurality or plurality-with-runoff voting in important ways, have recently led to more thorough analyses of practical alternatives to the common procedures. One example concerns 'approval voting' (Brams and Fishburn, 1978; Fishburn and Brains, 1979;Merrill, 1979;Weber, 1978) under which each voter can vote for as many candidates as he wishes. Each candidate a voter votes for receives a full vote from the voter, and the winner is the candidate who receives the most votes.
Beginning in the early 1970's, the present authors conducted a series of simulation studies (Fishburn, 1974a(Fishburn, , 1974b;; Fishburn and Gerhlein, 1976, 1977) on one especially important aspect of voting procedures, namely their propensities to elect the simple majority candidate when it exists: candidate x