  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.
