Ignoring information in binary choice with continuous variables: When is less “more”?

By Robin M. Hogarth, Natalia Karelaia. 2005

97 citations recorded by the source corpus.

When can a single variable be more accurate in binary choice than multiple sources of information? We derive analytically the probability that a single variable (SV) will correctly predict one of two choices when both criterion and predictor are continuous variables. We further provide analogous derivations for multiple regression (MR) and equal weighting (EW) and specify the conditions under which the models differ in expected predictive ability. Key factors include variability in cue validities, intercorrelation between predictors, and the ratio of predictors to observations in MR. Theory and simulations are used to illustrate the differential effects of these factors. Results directly address why and when “one-reason” decision making can be more effective than analyses that use more information. We thus provide analytical backing to intriguing empirical results that, to date, have lacked theoretical justification. There are predictable conditions for which one should expect “less to be more.”

Subfields: Artificial Intelligence, General Decision Sciences, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/1268b0190e79fa427dc63d66d89fb6f96e2631ac

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Citations in the corpus

Heuristics made easy: an effort-reduction framework. (2008, methodology): “Variants of the lexicographic heuristic include the lexicographic semi-order heuristic (Tversky, 1969), the priority heuristic (Brandsta ¨tter, Gigerenzer, & Hertwig, 2006), the Take the Best heuristic (Gigerenzer et al., 1999), and the single variable heuristic ( Hogarth & Karelaia, 2005a, 2007 ).1”
The Priority Heuristic: Making Choices Without Trade-Offs (2006, background): “Correct predictions of the majority responses for the 56 certainty equivalence problems in Tversky and Kahneman (1992). The black parts of the bars represent correct predictions without guessing; the union of the black and white parts represents correct predictions with guessing (counting as 0.”
Why recognition is rational: Optimality results on single-variable decision rules (2010, methodology): “In contrast to the conditions identified in Hogarth and Karelaia (2005) and Fasolo et al. (2007), this over- 2Bothr andr′ are required to be non-negative (as described in Condition 1).”
Why Heuristics Work (2008, background): “Cue validities vary little, low redundancy (Hogarth & Karelaia, 2005, 2006).”
Rationality for Mortals: How People Cope with Uncertainty (2008, background): “Noncompensatory information is a special case of large variability in cue weights, which also favors take-the-best relative to linear models and is discussed in Hogarth and Karelaia 2005 and 2006.”
Homo Heuristicus: Why Biased Minds Make Better Inferences (2009, background): “The bias–variance dilemma is one of several principles that characterize the ecological rationality of heuristics (Gigerenzer et al., 1999; Hogarth & Karelaia, 2005, 2006; Katsikopoulos & Martignon, 2006; Todd et al., in press).”
Fast and frugal forecasting (2009, background): “& Goldstein, 1996) To infer which of two alternatives has the higher value: (a) search through cues in order of validity, (b) stop search as soon as a cue discriminates, (c) choose the alternative this cue favors Cue validities vary highly, moderate to high redundancy, scarce information ( Hogarth &”
"Take-the-best" and other simple strategies: Why and when they work "well" with binary cues (2006, background): “In a related paper (Hogarth and Karelaia, 2005), we have analyzed the performance of simple models for binary choice based on continuous cues.”