Odd or Even: Assembly Size and Majority Rule

This paper provides a probabilistic comparison of small assemblies with an even number of members versus an adjacent odd number of members. We show that assemblies with an odd number of members are more likely to pass proposals under absolute majority rule than assemblies with an adjacent even number of members. We also show they are more likely to attain quorum and to pass proposals under simple majority rule with a quorum. The first claim is supported by data on the U.S. appellate courts, 1940–84. Finally, we discover similar effects in the probability of making truthful judgements (Condorcet 1785) and the ability to satisfy common welfare criteria (Rae 1969). The results have important implications for institutional design.