Decision Aggregation under Quantal Response

TL;DR

This paper explores how bounded rationality modeled by quantal response affects decision aggregation, showing that majority voting can be optimal and that stochasticity in models like LLMs can enhance collective decision accuracy.

Contribution

It introduces a decision aggregation framework using quantal response models and demonstrates the potential benefits of stochasticity in collective decision-making, validated with large language models.

Findings

Majority voting is optimal under certain bounded rationality conditions.

Stochastic outputs from LLMs improve decision accuracy.

Bounded rationality can be an advantage in collective intelligence.

Abstract

The effectiveness of collective decision-making is often challenged by the bounded rationality and inherent stochasticity of individual agents. We investigate this by analyzing how to aggregate decisions from n experts, each receiving a private signal about an unknown state. Assuming signals are conditionally independent and identically distributed, we depart from the fully rational paradigm and model expert behavior using quantal response, a stochastic choice model capturing bounded rationality. Within a minimax regret framework, we show that majority voting is the optimal robust aggregator when individual rationality falls below a certain threshold. Interestingly, such groups can outperform perfectly rational agents, as their decision randomness encodes weak but informative signals lost in deterministic behavior. We validate these findings using large language models (LLMs), which naturally exhibit quantal response via their temperature parameter. Aggregating moderately stochastic LLM outputs significantly improves accuracy on complex reasoning tasks, highlighting bounded rationality not as a limitation, but as a potential strength in collective intelligence.