Reasoning about Social Choice Functions

TL;DR

This paper introduces a logic for reasoning about social choice functions, enabling formal analysis of their properties, including strategy-proofness, with proven expressiveness and decidability.

Contribution

It presents a novel logic that characterizes all social choice functions and supports reasoning about their strategic and preference-related properties.

Findings

Logic is expressively complete for social choice functions

The logic is decidable and has a complete axiomatization

Application demonstrated in verifying strategy-proofness

Abstract

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic is decidable, and give a complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof.