Essays in Microeconomic Theory

If the number of individuals is odd, Campbell and Kelly (2003) show that majority rule is the only non-dictatorial strategy-proof social choice rule on the domain of linear orders that admit a Condorcet winner, an alternative that is preferred to every other by a majority of individuals in pairwise majority voting. This paper shows that the claim is false when the number of individuals is even, and provides a characterization of non-dictatorial strategy-proof social choice rules on this domain. Two examples illustrate the primary reason that the result does not translate to the even case: when the number of individuals is even, no single individual can change her reported preference ordering in a manner that changes the Condorcet winner while remaining within the preference domain. Introducing two new definitions to account for this partitioning of the preference domain, the chapter concludes with a counterpart to the characterization of Campbell and Kelly (2003) for the even case.