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Theoretical results underpinning the Wisdom of Crowds, such as the CondorcetJury Theorem, point to substantial accuracy gains through aggregation ofdecisions or opinions, but the foundations of this theorem are routinelyundermined in circumstances where individuals are able to adapt their ownchoices based after observing what other agents have chosen. In sequentialdecision-making, rational agents use the choices of others as a source ofinformation about the correct decision, creating powerful correlations betweendifferent agents' choices that violate the assumptions of independence on whichthe Condorcet Jury Theorem depends. In this paper I show how such correlationsemerge when agents are rewarded solely based on their individual accuracy, andthe impact of this on collective accuracy. I then demonstrate how a simplecompetitive reward scheme, where agents' rewards are greater if they correctlychoose options that few have already chosen, can induce rational agents to makeindependent choices, returning the group to optimal levels of collectiveaccuracy. I further show that this reward scheme is robust, offeringimprovements to collective accuracy across of wide range of competitionstrengths, suggesting that such schemes could be effectively implemented inreal-world contexts to improve collective wisdom.

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