"The Bounded Wisdom"

Perfectly rational agents make the best individual decision given their information. But aggregating n imperfect decision-makers can outperform n perfect ones. The paper shows when and why.

Agents receive private signals about an unknown state and respond with quantal response — a model of bounded rationality where the probability of choosing each option increases with its expected utility but isn’t deterministic. The noise is calibrated by a rationality parameter: high rationality approaches optimal behavior, low rationality approaches random guessing.

The key result: when individual rationality falls below a threshold, majority voting is the optimal robust aggregator. Not weighted voting, not any exotic scheme — just counting heads. The simplicity of the aggregation rule is a consequence of the agents’ bounded rationality, not despite it. When agents are noisy enough, their errors are sufficiently uncorrelated that majority voting’s error-canceling property dominates any sophistication in weighting.

The striking finding: groups of moderately noisy agents can exceed the accuracy of perfectly rational agents. Noise introduces diversity — different agents make different errors — and the aggregation exploits this diversity. Perfect rationality produces correlated decisions (everyone reasons the same way from similar evidence), and correlated decisions aggregate poorly.

Validated on large language models: aggregating stochastic LLM outputs on complex reasoning tasks significantly improves accuracy, with the optimal randomness level being moderate, not minimal.

Imperfection as resource. Individual noise becomes collective signal when the aggregation mechanism can harvest the diversity that noise creates.