Anonymous voting in a heterogeneous society

TL;DR

This paper investigates how anonymous voting mechanisms perform in diverse societies, showing that while majority rules are optimal for two agents, cardinal mechanisms can outperform ordinal ones with three or more agents in certain environments.

Contribution

It demonstrates the conditions under which cardinal preference-based mechanisms outperform ordinal majority rules in anonymous voting settings with multiple agents.

Findings

Majority rule maximizes welfare for two agents.

Cardinal mechanisms can outperform ordinal rules with three or more agents.

Performance depends on agents' valuation distributions.

Abstract

We study the design of voting mechanisms in a binary social choice environment where agents' cardinal valuations are independent but not necessarily identically distributed. The mechanism must be anonymous -- the outcome is invariant to permutations of the reported values. We show that if there are two agents then expected welfare is always maximized by an ordinal majority rule, but with three or more agents there are environments in which cardinal mechanisms that take into account preference intensities outperform any ordinal mechanism.