Why recognition is rational: Optimality results on single-variable decision rules

The Recognition Heuristic (Gigerenzer \& Goldstein, 1996; Goldstein \& Gigerenzer, 2002) makes the counter-intuitive prediction that a decision maker utilizing less information may do as well as, or outperform, an idealized decision maker utilizing more information. We lay a theoretical foundation for the use of single-variable heuristics such as the Recognition Heuristic as an optimal decision strategy within a linear modeling framework. We identify conditions under which over-weighting a single predictor is a mini-max strategy among a class of a priori chosen weights based on decision heuristics with respect to a measure of statistical lack of fit we call ``risk''. These strategies, in turn, outperform standard multiple regression as long as the amount of data available is limited. We also show that, under related conditions, weighting only one variable and ignoring all others produces the same risk as ignoring the single variable and weighting all others. This approach has the advantage of generalizing beyond the original environment of the Recognition Heuristic to situations with more than two choice options, binary or continuous representations of recognition, and to other single variable heuristics. We analyze the structure of data used in some prior recognition tasks and find that it matches the sufficient conditions for optimality in our results. Rather than being a poor or adequate substitute for a compensatory model, the Recognition Heuristic closely approximates an optimal strategy when a decision maker has finite data about the world.