Decision Aggregation under Quantal Response

2026-03-14

AI Summary

This study addresses the design of robust collective decision-making mechanisms under the assumption that experts exhibit bounded rationality and stochastic choice behavior. Modeling expert decisions via a quantal response framework and assuming conditionally independent and identically distributed private signals, the authors formulate an aggregation mechanism within a minimax regret framework. Theoretical analysis reveals that moderate individual-level randomness can enhance the accuracy of group decisions, and that majority voting achieves optimal robustness under low rationality—suggesting that bounded rationality may serve as a feature rather than a flaw in collective intelligence. Empirical validation on complex reasoning tasks demonstrates that aggregating outputs from large language models with calibrated temperature-induced stochasticity significantly improves accuracy, corroborating the theoretical findings.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• collective decision-making
• bounded rationality
• quantal response
• decision aggregation
• minimax regret

Innovation

• quantal response
• bounded rationality
• majority voting
• minimax regret
• collective intelligence