Simple ways to construct search orders

Abstract

Simple Ways to Construct Search Orders Anja Dieckmann ([email protected]) Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany Peter M. Todd ([email protected]) Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany 3. Decision rule: Select the option to which the discriminating cue points, that is, the option that has the cue value associated with higher criterion values. Abstract Simple decision heuristics that process cues in a particular order and stop considering cues as soon as a decision can be made have been shown to be both accurate and quick. But one criticism of heuristics such as Take The Best is that these owe much of their simplicity and success to the not inconsiderable computations necessary for setting up the cue search order before the heuristic can be used. The criticism, though, can be countered in two ways: First, there are typically many cue orders possible that will achieve good performance in a given problem domain. And second, as we will show here, there are simple learning rules that can quickly converge on one of these useful cue orders through exposure to just a small number of decisions. We conclude by arguing for the need to take into account the computation necessary for not only the application but also the setup of a heuristic when talking about its simplicity. The performance of TTB has been tested on several real- world data sets, ranging from professors’ salaries to fish fertility (Czerlinski, Gigerenzer & Goldstein, 1999). Cross- validation comparisons have been made against other more complex strategies, such as multiple linear regression, by training on half of the items in each data set to get estimates of the relevant parameters (e.g., cue order based on validities for TTB, beta-weights for multiple linear regression) and testing on the other half of the data. Despite only using on average a third of the information employed by multiple linear regression, TTB outperformed regression in accuracy when generalizing to the test set (71% vs. 68%). The even simpler heuristic Minimalist was tested in the same way. It is another one-reason decision making heuristic that differs from TTB only in its search rule. Minimalist searches through cues randomly, and thus requires even less knowledge and precomputation than TTB – all it needs to know are the directions in which the cues point. Again it was surprising that this heuristic performed reasonably close to multiple regression (65%). But the fact that Minimalist lagged behind TTB by a noticeable margin of 6 percentage points indicates that part of the secret of TTB’s success lies in its ordered search. In this paper, we explore how such useful cue orders can be constructed in the first place, by testing a variety of simple order-learning rules in simulation. We find that simple mechanisms at the learning stage can enable simple mechanisms at the decision stage, such as one-reason decision heuristics, to perform well. One-Reason Decision Making and Ordered Search In the book Simple heuristics that make us smart, Gigerenzer and colleagues (1999) propose several decision making heuristics for predicting which of two objects or options, described by multiple binary cues, scores higher on some quantitative criterion. These heuristics have in common that information search is stopped once one cue is found that discriminates between the alternatives and thus allows an informed decision. No integration of information is involved, leading these heuristics to be termed “one- reason” decision mechanisms. These heuristics differ only in the search rule that determines the order in which information is searched. But where do these search orders come from? “Take the Best” (TTB; Gigerenzer & Goldstein, 1996, 1999) is the heuristic that has received most attention to date, both theoretically and empirically. TTB consists of three building blocks: Experimental Evidence for Ordered Search From an adaptive point of view, the combination of simplicity and accuracy makes one-reason decision making with ordered search, as in TTB, a plausible candidate for human decision processes. Consequently, TTB has been subjected to several empirical tests. Because TTB explicitly specifies information search as one aspect of decision making, it must be tested in situations in which cue information is not laid out all at once, but has to be searched for one cue at a time, either in the external environment or in memory (Gigerenzer & Todd, 1999). 1. Search rule: Search through cues in the order of their validity. Validity is the proportion of correct decisions made by a cue out of all the times that cue discriminates between pairs of options. 2. Stopping rule: Stop search as soon as one cue is found that discriminates between the two options.