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Integer Programming and Nondictatorial Arrovian Social Welfare Functions

Francesca Busetto, Giulio Codognato and Simone Tonin

No 2012-36, EconomiX Working Papers from University of Paris Nanterre, EconomiX

Abstract: Following Sethuraman, Teo and Vohra ((2003), (2006)), we apply integer programming tools to the analysis of fundamental issues in social choice theory. We generalize Sethuraman et al.'s approach specifying integer programs in which variables are allowed to assume values in the set {0; 1/2 ; 1}. We show that there exists a one-to-one correspondence between the solutions of an integer program defined on this set and the set of the Arrovian social welfare functions with ties (i.e. admitting indifference in the range). We use our generalized integer programs to analyze nondictatorial Arrovian social welfare functions, in the line opened by Kalai and Muller (1977). Our main theorem provides a complete characterization of the domains admitting non- dictatorial Arrovian social welfare functions with ties by introducing a notion of strict decomposability.

JEL-codes: D71 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-mic
Date: 2012
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