Optimising collective accuracy among rational individuals in sequential decision-making with competition

Theoretical results underpinning the Wisdom of Crowds, such as the Condorcet Jury Theorem, point to substantial accuracy gains through aggregation of decisions or opinions, but the foundations of this theorem are routinely undermined in circumstances where individuals are able to adapt their own choices based after observing what other agents have chosen. In sequential decision-making, rational agents use the choices of others as a source of information about the correct decision, creating powerful correlations between different agents' choices that violate the assumptions of independence on which the Condorcet Jury Theorem depends. In this paper I show how such correlations emerge when agents are rewarded solely based on their individual accuracy, and the impact of this on collective accuracy. I then demonstrate how a simple competitive reward scheme, where agents' rewards are greater if they correctly choose options that few have already chosen, can induce rational agents to make independent choices, returning the group to optimal levels of collective accuracy. I further show that this reward scheme is robust, offering improvements to collective accuracy across of wide range of competition strengths, suggesting that such schemes could be effectively implemented in real-world contexts to improve collective wisdom.