Voting with Coarse Beliefs

TL;DR

This paper explores voting rules under coarse beliefs, showing that by relaxing assumptions, it is possible to design strategy-proof voting mechanisms that avoid classical impossibility results.

Contribution

It introduces a bounded-rationality framework with coarse beliefs, enabling the construction of strategy-proof voting rules that bypass traditional impossibility theorems.

Findings

Good voting rules satisfying strategy-proofness with coarse beliefs

Circumvents Gibbard-Satterthwaite impossibility under new assumptions

Provides a behavioral economics perspective on voting mechanisms

Abstract

The classic Gibbard-Satterthwaite theorem says that every strategy-proof voting rule with at least three possible candidates must be dictatorial. Similar impossibility results hold even if we consider a weaker notion of strategy-proofness where voters believe that the other voters' preferences are i.i.d.~(independent and identically distributed). In this paper, we take a bounded-rationality approach to this problem and consider a setting where voters have "coarse" beliefs (a notion that has gained popularity in the behavioral economics literature). In particular, we construct good voting rules that satisfy a notion of strategy-proofness with respect to coarse i.i.d.~beliefs, thus circumventing the above impossibility results.