Using elections to represent preferences

This paper takes voting theory out of the realm of mechanism design and studies elections as tools for representing preferences: every preference relation on a set of n elements is the outcome of pairwise voting by approximately 2 log₂ n voters with transitive preferences. Results like this one provide representation for preference relations not representable by utility functions. They also motivate definitions of the levels of intransitivity, nonlinearity and nonrepresentability (by utility function) of a preference relation. Received: 25 March 1999/Accepted: 19 June 2000