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Nondictatorial Arrovian social welfare functions : an integer programming approach.

Busetto, F. and Codognato, G. and Tonin, S. (2015) 'Nondictatorial Arrovian social welfare functions : an integer programming approach.', in Individual and collective choice and social welfare : essays in honor of Nick Baigent. Berlin, Heidelberg: Springer, pp. 149-169. Studies in choice and welfare.


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 {0,12,1}: 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.

Item Type:Book chapter
Keywords:Arrovian social welfare function, Integer programming, Nondictatorial domain.
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
File format - PDF (Copyright agreement prohibits open access to the full-text)
Publisher Web site:
Date accepted:No date available
Date deposited:07 October 2015
Date of first online publication:May 2015
Date first made open access:No date available

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