Borda’s Paradox with weighted scoring rules |
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Authors: | Mostapha Diss William V Gehrlein |
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Institution: | 1. CREM and University of Caen Basse-Normandie, Caen, France 2. University of Delaware, Newark, DE, USA
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Abstract: | Representations are obtained for the probabilities that a Strict Borda Paradox and a Strong Borda Paradox are observed for
large electorates with three candidates under the standard assumptions of Impartial Culture and Impartial Anonymous Culture.
These representations are obtained for general weighted scoring rules (WSRs), and the probabilities are found to be maximized
for voting rules like plurality rule and negative plurality rule. It is found that these paradox probabilities are not reduced
for every scoring rule with the introduction of some degree of dependence among voters’ preferences with IAC. It is concluded
that actual observances of a Strict Borda Paradox should be extremely rare, and that while observances of a Strong Borda Paradox
should also be rare, they might occasionally be witnessed. |
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