The (In)Vulnerability of 20 Voting Procedures to Lack of Monotonicity in a Restricted Domain
This chapter focuses on the possibility that some well-known voting procedures lead to specific types of monotonicity paradoxes in preference profiles that are characterized by the presence and election of a Condorcet winner. Moulin’s (Journal of Economic Theory 45:53–64, 1988) theorem establishes the incompatibility of Condorcet-consistency and invulnerability to the No-Show paradox in voting procedures when there are more than three alternatives to be chosen from. We ask whether this conclusion would also hold in the proper subset of profiles distinguished by the property that a Condorcet winner exists and is elected in the initial profile. Our focus is on 20 voting procedures designed to elect a single candidate. These procedures include both Condorcet-consistent and non-consistent rules. The former are, however, only briefly touched upon because their invulnerability to most types of monotonicity violations in the restricted domain is obvious.
KeywordsElections Non-monotonicity No-show paradox Condorcet-consistency Fixed electorates Variable electorates
- Felsenthal, D. S., & Machover, M. (2008). The majority judgment voting procedure: A critical evaluation. Homo Oeconomicus, 25, 319–333.Google Scholar
- Felsenthal, D. S., & Tideman, N. (2014). Interacting double monotonicity failure with direction of impact under five voting methods. Mathematical Social Sciences, 67, 57–66.Google Scholar
- Meredith, J. C. (1913). Proportional representation in Ireland. Dublin: Edward Ponsonby, Ltd. (Reprint from the collection of the University of California Libraries).Google Scholar