Wisdom of LLM Crowds: Aggregation and Contamination in Language Model Ensembles
The wisdom of crowds -- the finding that aggregating judgments across individuals often outperforms the best individual -- has been extensively studied with human forecasters. Whether the same phenomenon emerges when the ``crowd'' consists of large language models (LLMs) is an open question with both theoretical and practical implications. We elicited probability estimates from 15 LLMs on 254 binary prediction market questions and evaluated classical and learned aggregation methods. Learned aggregators -- a multilayer perceptron and a logistic regression -- outperformed all individual models and classical methods. The logistic regression was found to match the neural network, suggesting that the benefit of learned aggregation derives from learning a linear combination of diverse model outputs rather than from nonlinear interactions. Symbolic regression applied to the neural network's learned mapping recovered a pure model-disagreement signal as the lowest-complexity useful formula on the Pareto frontier, further supporting this interpretation. Training cutoff contamination proved a pervasive confound: the apparent capability gap between frontier cloud models and smaller local models collapsed from 35.8% to 8.9% on a clean subset of questions resolving after all models' training cutoffs, and individual model rankings showed only moderate stability. Even when the prediction market is evaluated at each model's training cutoff, LLMs remained substantially less accurate, indicating a genuine gap in collective information aggregation. These findings suggest that LLM crowds can exhibit wisdom-of-crowds effects, but that contamination-free evaluation is essential for reliable assessment.