A Computer Simulation of the Paradox of Voting*

David Klahr

American Political Science Review, 1966, vol. 60, issue 2, 384-390

Abstract: This paper presents estimates of the probability that the occurrence of the Paradox of Voting, commonly known as Arrow's Paradox, will prevent the selection of a majority issue when odd-sized committees of m judges vote upon n issues. The estimates, obtained through computer simulation of the voting process, indicate that the probability of such an intransitive social ordering is lower than the ratio of intransitive outcomes to all outcomes.Many of the arguments in political theory and welfare economics dealing with the paradox (e.g., Downs, 1957; Black, 1958; Schubert, 1960) seem to have implicitly assumed that since the paradox exists, its likelihood of occurrence is very close to 1. The results in this paper may call for a re-examination of these positions.

Date: 1966
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