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Soc Choice Welf (2009) 33:159171
DOI 10.1007/s00355-008-0352-6
ORIGINAL PAPER
Received: 4 July 2007 / Accepted: 12 November 2008 / Published online: 29 November 2008 Springer-Verlag 2008
Abstract Dening regularity as the conjunction of unanimity, anonymity, neutrality and monotonicity, we show that every regular social choice rule can be expressed as a function of vote differences and the maximal number of canceling couples. This equivalence not only identies the class of regular social choice rules but also allows a unied conception of various majority characterizations.
1 Introduction
In a society confronted to make a collective choice from a given pair of alternatives, two distinct conceptions of majoritarianism arise. For one of these, it is the relative support of the alternatives, which matters, while for the other, the collective decision depends on whether the alternatives receive some absolute support. We refer to the former approach as relative and to the latter as absolute major-itarianism. Relative majoritarianism dates back to the seminal majority characterization of May (1952) where a majority winner is dened as an alternative whose support exceeds the support of its rival.1 Requiring that this excess goes beyond some given threshold leads to the class of relative majority rules, which have been considered by Fishburn (1973), Saari (1990), and Garca-Lapresta and Llamazares (2001),
1 Asan and Sanver (2002), Woeginger (2003), Miroiu (2004) and Woeginger (2005) characterize the same rule in societies of variable size.
I acknowledge the support of the Turkish Academy of Sciences Distinguished Young Scientist Award Program (TUBA-GEBIP).
M. R. Sanver (B)
Department of Economics, Istanbul Bilgi University, Istanbul, Turkey e-mail: [email protected]
Characterizations of majoritarianism: a unied approach
M. Remzi Sanver
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160 M. R. Sanver
and characterized by Llamazares (2006) and Houy (2007).2 As for absolute majority rules, a majority winner is an alternative that receives the support of a (possibly qualied) majority. An early characterization of this class of rules is made by Fishburn (1973), which has been followed by Austen-Smith and Banks (1999), Yi (2005), and Asan and Sanver (2006).
Relativism and absolutism are essentially incompatible conceptions of majoritarianism.3 On the other hand, they share the following four central axioms of social choice theory as common denominator: Unanimity, which requires that a unanimously supported alternative must be the social outcome; anonymity,...