Categorical decision making by people, committees, and crowds

Choosing among alternatives is a basic decision problem faced by people in all aspects of life, whether individually or collectively. Results in cognitive science suggest that people perform approximately Bayes-optimal decision making but that cognitive limitations require the coarse categorization of ensembles of problems rather than the application of optimal decision rules on a problem-by-problem basis. These observations motivate the development of a mathematical theory for Bayesian hypothesis testing with quantized prior information. This paper reviews recent results in minimum Bayes risk quantizer design and its economic implications. In the context of individual decision making, the theory explains differentials in false alarm and missed detection error rates for majority and minority subpopulations without appealing to a taste for discrimination. In group decision making by majority vote, quantizer design becomes a strategic form game. Nash equilibria are guaranteed to exist but often are not Pareto optimal. The analysis reveals precise senses in which a team of agents performs best when it is diverse and shares common goals. Finally, the implications of the theory for crowdsourcing are discussed.