An extension and an alternative characterization of May’s theorem

Josep Freixas () and Montserrat Pons ()
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Josep Freixas: Universitat Politècnica de Catalunya (Campus Manresa), UPC
Montserrat Pons: Universitat Politècnica de Catalunya (Campus Manresa), UPC

Annals of Operations Research, 2021, vol. 302, issue 1, No 6, 137-150

Abstract: Abstract The context of this work is a voting scenario in which each voter expresses his/her level of affinity about a proposal, by choosing a value in the set $${\mathcal {J}}=\{-j,\dots ,-1,0,1,\dots ,j\}$$ J = { - j , ⋯ , - 1 , 0 , 1 , ⋯ , j } , and these individual votes produce a collective result, in the same set $${\mathcal {J}}$$ J , through a decision function. The simple majority, defined for $$j=1$$ j = 1 , is a widely used example of such a decision function. In this paper, a set of independent axioms is proved to uniquely characterize the j-majority decision function. The j-majority decision is defined for any positive integer j, and it coincides with the simple majority decision when $$j=1$$ j = 1 . In this way, this axiomatic characterization meets two goals: it gives a new characterization of the simple majority decision when $$j=1$$ j = 1 and it extends May’s theorem to this broader context.

Keywords: Simple majority decision; May’s theorem; Multilevel decision functions; Extension of simple majority decision; Axiomatic characterization (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10479-021-03999-0

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