Effects of abstentions on voting procedures in three-candidate elections

Abstract

This article deals with decision making in living systems at the levels of the organization, society, or supranational system. Abstention rates have a significant effect on the propensities of different voting procedures to elect the global Condorcet majority candidate in a three-candidate election when it exists. Hence any comparison of voting procedures that is concerned about the election of a global Condorcet candidate should reckon with abstention rates that may obtain for different procedures. Precise and approximate Condorcet propensities as functions of abstention rates are derived for the following voting rules for large electorates: Condorcet rules, including Black's rule; weighted scoring rules, including plurality and Borda rules; approval voting; and runoff elections in which a weighted scoring rule is used to eliminate one of the three candidates after the first ballot.