Symmetric majority rules

TL;DR

This paper investigates symmetric majority rules within the Arrovian framework, establishing conditions for their existence when preferences and alternatives are partitioned, and providing methods to construct and count such rules.

Contribution

It introduces necessary and sufficient conditions for reversal symmetric majority rules that are anonymous and neutral relative to partitions, expanding the understanding of symmetry in social choice rules.

Findings

Characterization of conditions for symmetric majority rules

A general method for constructing and counting these rules

Explicit applications to specific partition cases

Abstract

In the standard arrovian framework and under the assumption that individual preferences and social outcomes are linear orders on the set of alternatives, we study the rules which satisfy suitable symmetries and obey the majority principle. In particular, supposing that individuals and alternatives are exogenously partitioned into subcommittees and subclasses, we provide necessary and sufficient conditions for the existence of reversal symmetric majority rules that are anonymous and neutral with respect to the considered partitions. We also determine a general method for constructing and counting those rules and we explicitly apply it to some simple cases.