Abstract
This chapter concludes the analysis of the 20 voting procedures in terms of 5 voting paradoxes in restricted domains characterized by the existence of a Condorcet winner which at the same time is elected by the procedure under investigation. The restricted domain provides a perspective to how much difference various profile types make in terms of the possibility of encountering a voting paradox. In this analysis we contrast the general (unrestricted) domain with one where the initial outcome is stable. We illustrate the problems involved in the choice of an appropriate procedure by discussing the recent proposal for electoral reform suggested by Maskin and Sen.
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Notes
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- 2.
There are various estimates as to the relative frequency of finding cyclical majorities in the social preference ordering as a function of the number of voters and competing alternatives. These estimates are based on various theoretical assumptions and computer simulations, as well as on some laboratory experiments and limited actual election results conducted under some voting procedures. These estimates, in general, seem to be quite low.
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This article can be viewed in the following website: https://www.nytimes.com/2016/05/01/opinion/sunday/how-majority-rule-might-have-stopped-donald-trump.html.
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In contrast, note that the Plurality with Runoff procedure is invulnerable to two of the five paradoxes analyzed in this booklet, i.e., to the No-Show and to the Preference Inversion paradoxes.
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The only Condorcet-consistent procedure in Table 8.1 which seems to have an advantage over the Plurality Voting procedure is Minimax, which is vulnerable to only the Preference Inversion paradox.
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The Condorcet loser is a candidate that would be defeated by all the others if pairwise majority comparisons were conducted and the voters voted according to their preferences.
Reference
Felsenthal, D. S., & Nurmi, H. (2018). Voting procedures for electing a single candidate: Proving their (in)vulnerability to various voting paradoxes. Cham, Switzerland: Springer.
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Felsenthal, D.S., Nurmi, H. (2019). Summary. In: Voting Procedures Under a Restricted Domain. SpringerBriefs in Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-12627-8_8
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DOI: https://doi.org/10.1007/978-3-030-12627-8_8
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