The Impossibility of Extending Random Dictatorship to Weak Preferences

TL;DR

This paper proves that it is impossible to extend the random dictatorship mechanism to handle weak preferences while maintaining efficiency and strategyproofness, highlighting fundamental limitations in social decision schemes.

Contribution

It demonstrates the fundamental impossibility of extending random dictatorship to weak preferences under key desirable properties.

Findings

No extension of random dictatorship to weak preferences satisfies efficiency and strategyproofness.

Weakening strategyproofness does not enable such an extension.

Highlights inherent limitations in social choice mechanisms.

Abstract

Random dictatorship has been characterized as the only social decision scheme that satisfies efficiency and strategyproofness when individual preferences are strict. We show that no extension of random dictatorship to weak preferences satisfies these properties, even when significantly weakening the required degree of strategyproofness.