Convergence of Multi-Issue Iterative Voting under Uncertainty

TL;DR

This paper investigates how strategic voting in multi-issue iterative processes behaves under uncertainty, revealing conditions that ensure convergence and showing that uncertainty generally promotes stable outcomes.

Contribution

It introduces a new model combining multi-issue voting with local dominance theory and identifies conditions that guarantee convergence from any starting point.

Findings

Local dominance dynamics may fail to converge without restrictions.

Constraining preferences and reducing uncertainty ensure convergence.

Uncertainty significantly increases the likelihood of convergence in practice.

Abstract

We study the effect of strategic behavior in iterative voting for multiple issues under uncertainty. We introduce a model synthesizing simultaneous multi-issue voting with Meir, Lev, and Rosenschein (2014)'s local dominance theory and determine its convergence properties. After demonstrating that local dominance improvement dynamics may fail to converge, we present two sufficient model refinements that guarantee convergence from any initial vote profile for binary issues: constraining agents to have O-legal preferences and endowing agents with less uncertainty about issues they are modifying than others. Our empirical studies demonstrate that although cycles are common when agents have no uncertainty, introducing uncertainty makes convergence almost guaranteed in practice.