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.

翻译：集体决策的有效性常常受到个体智能体的有限理性与内在随机性的挑战。我们通过分析如何聚合来自n位专家的决策来研究此问题，每位专家接收一个关于未知状态的私有信号。假设信号在给定状态下条件独立且同分布，我们偏离完全理性范式，采用量化响应（一种捕捉有限理性的随机选择模型）来建模专家行为。在极小化极大遗憾框架内，我们证明当个体理性低于特定阈值时，多数投票是最优的鲁棒聚合器。有趣的是，此类群体可以超越完全理性的智能体，因为其决策随机性编码了在确定性行为中丢失的微弱但信息丰富的信号。我们使用大型语言模型（LLMs）验证了这些发现，LLMs通过其温度参数自然地表现出量化响应。聚合中等随机性的LLM输出能显著提升复杂推理任务的准确性，这表明有限理性并非一种局限，而是集体智能中潜在的优势。