QRE vs Nash equilibrium: Evaluating the Jury Paradox in Voting Games

Abstract

In traditional game theory, Nash Equilibrium (NE) has been the dominant framework for predicting and explaining behaviour in strategic settings, including voting games. However, NE assumes fully rational decision-making in the sense that it assumes individuals make choices which are free of error. Yet, this often fails to capture real-world behaviour. This limitation is particularly evident in the jury paradox, where rational jurors, following their strategic incentives, may systematically convict innocent defendants or fail to convict the guilty. Empirical evidence suggests that, in reality, jurors do not strictly adhere to Nash equilibrium predictions, particularly when uncertainty and asymmetric payoffs come into play.

This dissertation examines the prevalence and persistence of the jury paradox under both a Nash Equilibrium and Quantal Response Equilibrium (QRE) framework. QRE introduces bounded rationality by allowing for probabilistic decision-making, which better reflects real-world uncertainty and its impact on voting behaviour. Using computational simulations, we analyse how equilibrium outcomes shift as decision noise, payoff asymmetry, and uncertainty increase. Our findings suggest that QRE not only captures deviations from Nash equilibrium behaviour but also provides a more accurate representation of jury voting dynamics, particularly in cases where Nash equilibrium predictions exhibit a jury paradox.

The results highlight the importance of incorporating bounded rationality into equilibrium models to accurately reflect real-world decision-making. This research deepens our understanding of how the jury paradox emerges and persists across different equilibrium models, offering insights relevant to both theoretical and applied game theory.