Condorcet's Jury Theorem with Abstention

TL;DR

This paper examines how abstention and voter overestimation of pivotality affect the classical Condorcet's Jury theorem, revealing conditions under which the theorem holds or fails in asymmetric voting scenarios.

Contribution

It introduces a boundedly rational model with overestimating voters, analyzing equilibrium outcomes and conditions where Condorcet's theorem is valid or broken.

Findings

Rational abstention leads to trivial equilibria with almost all voters abstaining.

Overestimation of pivotality results in non-trivial equilibria with bounded victory probabilities.

Victory certainty depends on how strongly pivotality estimates depend on the margin of victory.

Abstract

The well-known Condorcet's Jury theorem posits that the majority rule selects the best alternative among two available options with probability one, as the population size increases to infinity. We study this result under an asymmetric two-candidate setup, where supporters of both candidates may have different participation costs. When the decision to abstain is fully rational i.e., when the vote pivotality is the probability of a tie, the only equilibrium outcome is a trivial equilibrium where all voters except those with zero voting cost, abstain. We propose and analyze a more practical, boundedly rational model where voters overestimate their pivotality, and show that under this model, non-trivial equilibria emerge where the winning probability of both candidates is bounded away from one. We show that when the pivotality estimate strongly depends on the margin of victory, victory is not assured to any candidate in any non-trivial equilibrium, regardless of population size and in contrast to Condorcet's assertion. Whereas, under a weak dependence on margin, Condorcet's Jury theorem is restored.