Integer Programming and Arrovian Social Welfare Functions

Integer Programming and Arrovian Social Welfare Functions

We characterize the class of Arrovian Social Welfare Functions (ASWFs) as integer solutions to a collection of linear inequalities. Many of the classical possibility, impossibility, and characterization results can be derived in a simple and unified way from this integer program. Among the new results we derive is a characterization of preference domains that admit a nondictatorial, neutral ASW...

Integer Programming and Nondictatorial Arrovian Social Welfare Functions

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, 12 , 1}. We show that there exists a one-to-one correspondence between the solutions of an integer program defi...

Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach∗

In the line opened by Kalai and Muller (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...

Integer Programming and Social Choice

We characterize the class of Arrovian Social Welfare Functions as integer solutions to a collection of linear inequalities. Many of the known results about impossibility, Arrovian Social Welfare Functions, properties of the majority rule etc., can be derived in a simple and unified way from this integer program. We characterize those preference domains that admit a non-dictatorial, neutral Arro...

Quadratic Social Welfare Functions