Anonymous and neutral social choice: a unified framework for existence results, maximal domains and tie-breaking

Abstract

We present a group-theoretical method to analyze and compare necessary and sufficient conditions on the size of the social choice problem for the existence of anonymous, neutral and resolute social choice and social welfare rules in a unified framework. We define the largest domain of preference profiles that would allow for the existence of such aggregation rules when said conditions are not met. We propose a tie-breaking procedure to obtain resolute refinements of social choice rules, which preserves anonymity and neutrality. Compatibility of this refinement procedure with simple monotonicity is compared with that of conventional tie-breaking mechanisms. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.