Two Theorems on the Range of Strategy-proof Rules on a Restricted Domain

TL;DR

This paper extends the Gibbard-Satterthwaite theorem by proving that strategy-proof rules with more than two outcomes are dictatorial on certain restricted preference domains.

Contribution

It completes the proof of a classic result by establishing full range theorems on specific subdomains of preferences.

Findings

Strategy-proof rules with more than two outcomes are dictatorial on the domain NP.

Full range results are established on two subdomains of NP.

The work completes the proof of a key theorem in social choice theory.

Abstract

Let g be a strategy-proof rule on the domain NP of profiles where no alternative Pareto-dominates any other and let g have range S on NP. We complete the proof of a Gibbard-Satterthwaite result - if S contains more than two elements, then g is dictatorial - by establishing a full range result on two subdomains of NP.