Abstract
Plurality rule is mostly criticized from being capable of choosing an alternative considered as worst by a strict majority. This paper considers elections in which the agenda consists of potential candidates strategically choosing whether or not to enter the election. In this context, we examine the ability of scoring rules to fulfil the Condorcet criterion. We show for the case of three potential candidates that Plurality rule is the only scoring rule that satisfies a version of the Condorcet criterion in two cases: 1) when preferences are single-peaked and, 2) when preferences are single-dipped.
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Notes
Unanimity requires that if all voters find the same candidate most preferred out of the entering candidates, then that candidate is selected.
Note that in two-candidate elections, all scoring rules coincide with Majority rule.
For n sufficiently large the voting numbers can be obtained as integer numbers.
Note that when either a or c are Condorcet winner, they indeed are strong Condorcet winner.
Furthermore, it can be shown that in an endogenous election involving three candidates no scoring rule elects a Condorcet loser. By contrast Lepelley et al. [10] show, in the classical three candidate election, that a Scoring rule can elect a Condorcet loser if and only if \(0 \leqslant w <\frac{1} {2}\).
Our conjecture is that the result in Theorem 3 can be extended to any number of candidates.
These preferences are separable since alternative a is never middle-ranked.
This Theorem was suggested by an anonymous referee.
Which is defined as the conditional probability that the rule selects the Condorcet winner.
See Lepelley [8] (Sections 4 and 5) for further comments on this point. This author also provides the example P=(3, 0, 2, 2) to illustrate that candidate a is a Condorcet loser selected by Plurality rule.
These authors show by means of experiments that, under Plurality rule, pre-election polls provide coordination signals which help voters to defeat Condorcet losers.
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Acknowledgements
We would like to thank Pablo Amorós, Carmen Beviá, Vincent Merlin and Matthias Messner for helpful comments and suggestions. We also thank two anonymous referees for their helpful comments. Financial support from Fundación Ramón Areces and the research project SEC2002-01926 are gratefully acknowledged.
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Moreno, B., Socorro Puy, M. The scoring rules in an endogenous election. Soc Choice Welfare 25, 115–125 (2005). https://doi.org/10.1007/s00355-005-0034-6
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DOI: https://doi.org/10.1007/s00355-005-0034-6