Does Decision Quality (Always) Increase with the Size of Information Samples? Some Vicissitudes in Applying the Law of Large Numbers

Adaptive decision-making requires that environmental contingencies between decision options and their relative advantages and disadvantages be assessed accurately and quickly. The research presented in this article addresses the challenging notion that contingencies may be more visible from small than large samples of observations. An algorithmic account for such a "less-is-more" effect is offered within a threshold-based decision framework. Accordingly, a choice between a pair of options is only made when the contingency in the sample that describes the relative utility of the two options exceeds a critical threshold. Small samples – due to their instability and the high dispersion of their sampling distribution – facilitate the generation of above-threshold contingencies. Across a broad range of parameter values, the resulting small-sample advantage in terms of hits is stronger than their disadvantage in terms of false alarms. Computer simulations and experimental findings support the predictions derived from the threshold model. In general, the relative advantage of small samples is most apparent when information loss is low, when decision thresholds are high, and when ecological contingencies are weak to moderate.