An Axiomatic Decomposition of Strategyproofness for Ordinal Mechanism with Indifferences

TL;DR

This paper introduces an axiomatic decomposition of strategyproofness for mechanisms operating on ordinal preferences with indifferences, extending previous strict preference results to weak preferences.

Contribution

It presents a novel decomposition of strategyproofness into three natural axioms applicable to mechanisms with weak preferences, broadening the theoretical understanding of strategyproof mechanisms.

Findings

Decomposition of strategyproofness into three axioms.

Extension of previous strict preference results to weak preferences.

Provides a framework for analyzing mechanisms with indifferences.

Abstract

We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three axioms: separation monotonic, separation upper invariant, and separation lower invariant. Each axiom is a natural restriction on how mechanisms can react when agents change their opinion about the relative ranking of any two adjacently ranked groups of alternatives. Our result extends a result from (Mennle and Seuken, 2017), a decomposition of strategyproofness for strict preferences, to the full domain that includes weak preferences.