Power in voting rules with abstention: an axiomatization of a two components power index

Josep Freixas () and Roberto Lucchetti ()
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Josep Freixas: Technical University of Catalonia (Campus of Manresa)
Roberto Lucchetti: Politecnico di Milano

Annals of Operations Research, 2016, vol. 244, issue 2, No 9, 455-474

Abstract: Abstract In order to study voting situations when voters can also abstain and the output is binary, i.e., either approval or rejection, a new extended model of voting rule was defined. Accordingly, indices of power, in particular Banzhaf’s index, were considered. In this paper we argue that in this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We also provide an axiomatization for both indices, and from this a characterization as well of the standard Banzhaf index (the sum of the former two) is obtained. Some examples are provided to show how the indices behave.

Keywords: Decision making process; Voting systems in democratic organizations; Abstention; Power; Axioms; 91A12; 90B50; 91A35; 05C65; 94C10 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10479-016-2124-5

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