The logical meaning of Expansion

TL;DR

This paper explores the connection between the Expansion property in Social Choice theory and a logical property of nonmonotonic consequence relations, revealing a logical perspective on a known rationality condition.

Contribution

It establishes a formal correspondence between the Expansion property and a pure logical property of nonmonotonic consequence relations, clarifying their theoretical relationship.

Findings

Expansion corresponds to a logical property of consequence relations

Union of definable sets being definable is crucial for soundness

Provides a logical interpretation of a social choice rationality condition

Abstract

The Expansion property considered by researchers in Social Choice is shown to correspond to a logical property of nonmonotonic consequence relations that is the {\em pure}, i.e., not involving connectives, version of a previously known weak rationality condition. The assumption that the union of two definable sets of models is definable is needed for the soundness part of the result.