Nondictatorial Arrovian Social Welfare Functions An Integer Programming Approach

In the line opened by Kalai and Muller (1977), we explore new con- ditions on preference domains which make it possible to avoid Arrow's impossibility result. In our main theorem, we provide a complete char- acterization of the domains admitting nondictatorial Arrovian social welfare functions with ties (i.e. including indi erence in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach rst applied to so- cial choice theory by Sethuraman, Teo and Vohra ((2003), (2006)). In order to obtain a representation of Arrovian social welfare functions whose range can include indi erence, we generalize Sethuraman et al.'s work and specify integer programs in which variables are allowed to assume values in the set indeed, we show that there exists a one-to-one correspondence between the solutions of an integer program de ned on this set and the set of all Arrovian social welfare functions - without restrictions on the range