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Performance of small group majorities in a single task

Aggregating decisions from larger groups typically results in outcomes with higher accuracy than decision outcomes from single individuals or smaller groups. Here I argue that it is important to consider not only overall proportion of correct decisions, but also individual competencies in terms of hits (h) and correct rejections (cr). I show that small groups can perform better than randomly selected individuals and larger groups in a single task when the average individual proportion correct is above .5, h and cr are asymmetric around .5, and h+cr>1. If the average individual proportion correct is below .5 and h+cr<1, small groups perform worse than individuals and larger groups. I also demonstrate that these two performance patterns can occur in empirical data from studies on violent recidivism, psychiatric morbidity, anxiety, and deception detection. I also show that the presence of correlations between decisions in a single task has both beneficial and detrimental effects when it comes to small group performance.