Recognizing Linked Domain in Polynomial Time

TL;DR

This paper demonstrates that identifying whether an election domain is linked can be efficiently decided in polynomial time, extending the Gibbard-Satterthwaite theorem's applicability to linked domains.

Contribution

It provides a polynomial-time algorithm to recognize linked domains, broadening the understanding of strategy-proof social choice functions.

Findings

Linked domain recognition is polynomial-time computable.

The Gibbard-Satterthwaite theorem extends to linked domains.

Efficient algorithms facilitate analysis of strategy-proofness in complex domains.

Abstract

The celebrated Gibbard-Satterthwaite Theorem states that any surjective social choice function which is defined over the universal domain of preferences and is strategy-proof must be dictatorial. Aswal, Chatterji and Sen generalize the Gibbard-Satterthwaite theorem by showing that the Gibbard-Satterthwaite theorem still holds if the universal domain is replaced with the linked domain. In this note, we show that determining whether an election is linked can be done in polynomial time.