Probabilities of Voting Paradoxes

Abstract

A thorough discussion is presented for four basic models [Impartial Culture, Dual Culture, Uniform Culture and Impartial Anonymous Culture] that form the basis of the classical analysis for developing theoretical estimates of the likelihood that voting paradoxes might be observed. It is explained why each of these models is expected to produce exaggerated estimates of these probabilities. But, given that fact, relatively small estimates are still obtained for the probabilities that these paradoxical outcomes are observed. It is also shown that by comparing these models, we are able to determine the pure impact of varying specific characteristics for preferences of electorates without changing any other factors. For example, adding a degree of dependence among voters’ preferences will reduce the probability of observing paradoxes and changing the degree of homogeneity among voters’ preferences will also predictably alter their likelihoods.