Abstract
The property of participation is satisfied by a voting rule if under no circumstances it is to the benefit of a voter to abstain rather than vote according to his/her preferences. By Moulin’s result of 1988 all voting rules that always elect a Condorcet winner when one exists fail on the property of participation [16]. Focusing on preference profiles that are restricted to those having a Condorcet winner we ask whether Moulin’s result holds under these preference profiles. It turns out that while some types of monotonicity paradoxes vanish in the Condorcet domains, others persist.
H. Nurmi—The author is indebted to the late Dan S. Felsenthal for numerous conversations in which the problems touched upon in this article were discussed. Those conversations culminated in the joint monograph [5] which this article largely draws upon. The constructive comments of the referees on an earlier version are gratefully acknowledged.
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Notes
- 1.
A Condorcet winner is a candidate that would defeat all others in pairwise majority votes.
- 2.
This division is not a partition as some rules, notably the Borda count, can be implemented in both binary and positional manner. Moreover, there are voting rules that are based on neither binary nor positional principles, e.g. a randomized dictatorship.
- 3.
- 4.
This is not an accident, but happens every time a Condorcet paradox profile is added to another profile. This is because the Borda scores of each candidate in a Condorcet paradox profile are equal and, thus, the Borda score of each candidate in the original profile is added by the same number keeping the score differences unchanged.
- 5.
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Nurmi, H. (2020). Pairwise Voting Rules in Restricted Domains: The Disappearance and Persistence of Some Monotonicity Paradoxes. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds) Transactions on Computational Collective Intelligence XXXV. Lecture Notes in Computer Science(), vol 12330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-62245-2_3
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