Condorcet Efficiency of Borda Rule under the Dual Culture Condition

Author: Gehrlein W.V.  

Publisher: Academic Press

ISSN: 0049-089X

Source: Social Science Research, Vol.28, Iss.1, 1999-03, pp. : 36-44

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Abstract

The Condorcet winner in an election is a candidate who could defeat each of the other available alternatives by majority rule in a series of pairwise votes. The Condorcet efficiency of a voting procedure is the conditional probability that it will elect the Condorcet winner, given that a Condorcet winner exists. The study considers the Condorcet efficiency of Borda Rule, which assigns weights of (1, ½, 0) respectively to each voter's first, second, and third ranked candidates, and elects the candidate with the most total points. A closed form representation is obtained for the Condorcet efficiency of Borda Rule with large electorates under the dual culture condition for three-candidate elections. Borda Rule is shown to perform very well over the range of dual culture probability vectors.