Abstract
Approval Voting is known to possess many good properties when voters have dichotomous preferences. But, when attention was restricted to the limiting case for large electorates with three candidates in an early study, Approval Voting was found to have the same Condorcet Efficiency as both Plurality Rule and Negative Plurality rule when no voter indifference is allowed in voters’ preferences with the assumption of the impartial culture condition (IC). However, a later study by Diss et al. (Handbook on approval voting, 2010) shows that the introduction of any degree of indifference in an extended impartial culture condition leads to a dominance of Approval Voting over both Plurality Rule and Negative Plurality Rule on the basis of Condorcet Efficiency. Scenarios were also found for which Approval Voting had greater Condorcet Efficiency than Borda Rule. The assumptions of that study are analyzed here, and an arguably more reasonable set of assumptions leads to the conclusion that Borda Rule will dominate Approval Voting on the basis of Condorcet Efficiency for all degrees of voter indifference, except for the case of completely dichotomous preferences. The same outcome is found to result in the current study for an extended version of the Impartial Anonymous Culture Condition.
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Of course, the methodological choices in this Section are also made for the sake of simplicity: if the number of voter preference types is too high, the desired representations become either impossible to derive or too complex to be useful.
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The authors are grateful to Mostapha Diss for his comments on an early draft of this paper. They also thank an anonymous referee for helpful remarks and suggestions.
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Gehrlein, W.V., Lepelley, D. The Condorcet Efficiency Advantage that Voter Indifference Gives to Approval Voting Over Some Other Voting Rules. Group Decis Negot 24, 243–269 (2015). https://doi.org/10.1007/s10726-014-9388-4
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DOI: https://doi.org/10.1007/s10726-014-9388-4