Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

Francesca Busetto (), Giulio Codognato () and Simone Tonin ()
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Francesca Busetto: Università degli Studi di Udine
Giulio Codognato: Università degli Studi di Udine
Simone Tonin: University of Glasgow

A chapter in Individual and Collective Choice and Social Welfare, 2015, pp 149-169 from Springer

Abstract: Abstract In the line opened by Kalai and Muller (J Econ Theory 16:457–469, 1977), we explore new conditions on preference domains which make it possible to avoid Arrow’s impossibility result. In our main theorem, we provide a complete characterization of the domains admitting nondictatorial Arrovian social welfare functions with ties (i.e. including indifference in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach first applied to social choice theory by Sethuraman et al. (Math Oper Res 28:309–326, 2003; J Econ Theory 128:232–254, 2006). In order to obtain a representation of Arrovian social welfare functions whose range can include indifference, we generalize Sethuraman et al.’s work and specify integer programs in which variables are allowed to assume values in the set $$\{0, \frac{1} {2},1\}$$ : indeed, 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 all Arrovian social welfare functions—without restrictions on the range.

Keywords: Arrovian social welfare function; Integer programming; Nondictatorial domain (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-662-46439-7_10

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