Categorical decision making by people, committees, and crowds

Abstract

Abstract-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.

Distributed inference in wireless sensor networks

“…Another challenging open problem in distributed inference is when heterogeneous sensors, e. g. of different modalities, are observing the same phenomenon. Finally, when humans are part of the inference process along with physical sensors, many new problems arise owing to the nature of their information (soft versus hard information) and human limitations on information acquisition and processing such as their categorization of priors [136]. Such distributed inference problems become important with the ever-increasing role that social networking is playing in our lives.…”

Quantization of Prior Probabilities for Collaborative Distributed Hypothesis Testing

“…Asymptotically, decays inversely with ; more precisely [33] ( 22) If the agents could share their observations rather than their local hard decisions, the team would base its decision on the sample mean of the observations. The resulting performance is governed by the variance of the sample mean of the noise variables .…”

Bayes Risk Error is a Bregman Divergence

“…Similarly, it seems possible to transfer ideas of intermediate levels of minimax robustness for Bayes risk error [18] to general Bregman divergences. The concept of "price of segregation" developed in [19] and [20] might be applicable in non-Bayesian hypothesis testing scenarios. It may or may not be possible to generalize game-theoretic quantization of prior probabilities for distributed Bayesian hypothesis testing [21] because game-theoretic considerations arise in that context due to differences in Bayes costs c ij , which have no direct analogue in other Bregman divergences.…”