Econometrica: Mar, 1974, Volume 42, Issue 2

Voting Anomalies, the Number of Voters, and the Number of Alternatives

https://doi.org/0012-9682(197403)42:2<239:VATNOV>2.0.CO;2-2
p. 239-252

Jerry S. Kelly

Assuming each assignment of strong preference orderings to individuals is equally likely, we examine how the probability of social intransitivity (under asimple majority vote decision rule) changes with changes in the number of alternatives and the number of voters. A similar study is made of violation of quasi-transitivity and failure of existence of a maximal alternative.