Probabilities of voting paradoxes with three candidates

by Leslie M. McDonald

Institution: Oregon State University
Department: Mathematics
Degree: MS
Year: 2015
Keywords: voting; Voting  – Mathematical models
Record ID: 2062627
Full text PDF: http://hdl.handle.net/1957/55476


Pardoxes in voting has been an interest of voting theorists since the 1800's when Condorcet demonstrated the key example of a voting paradox: voters with individually transitive rankings produce an election outcome which is not transitive. With Arrow's Impossibility Theorem, the hope of finding a fair voting method which accurately reflected society's preferences seemed unworkable. Recent results, however, have shown that paradoxes are unlikely under certain assumptions. In this paper, we corroborate results found by Gehrelin for the probabilities of paradoxes, but also give results which indicate paradoxes are extremely likely under the right conditions. We use simulations to show there can be many situations where paradoxes can arise, dependent upon the variability of voters' preferences, which echo Saari's statements on the topic.