Naïve heuristics for paired comparisons: Some results on their relative accuracy

Abstract We study three heuristics for paired comparisons based on binary cues, which are all naive in that they ignore possible dependencies between cues, but take different approaches: linear (tallying) and lexicographic (Take The Best, Minimalist). There is empirical evidence on the heuristics’ descriptive adequacy and some first results on their accuracy. We present new analytical results on their relative accuracy. When cues are independent given the values of the objects on the criterion, there exists a linear decision rule, equivalent to naive Bayes, which is optimal; we use this result to characterize the optimality of Take The Best and tallying. Also, tallying and Take The Best are more accurate than Minimalist. When cues are dependent and the number of cues and objects is psychologically plausible, Take The Best tends to be more accurate than tallying, but it is also possible that tallying, and Minimalist, are more accurate than Take The Best.

[1]  G Gigerenzer,et al.  Reasoning the fast and frugal way: models of bounded rationality. , 1996, Psychological review.

[2]  R. Dawes,et al.  Linear models in decision making. , 1974 .

[3]  Ulrich Hoffrage,et al.  When do people use simple heuristics, and how can we tell? , 1999 .

[4]  Gregory F. Cooper,et al.  The Computational Complexity of Probabilistic Inference Using Bayesian Belief Networks , 1990, Artif. Intell..

[5]  D. Kahneman,et al.  Heuristics and Biases: The Psychology of Intuitive Judgment , 2002 .

[6]  Nir Friedman,et al.  Bayesian Network Classifiers , 1997, Machine Learning.

[7]  Pedro M. Domingos,et al.  On the Optimality of the Simple Bayesian Classifier under Zero-One Loss , 1997, Machine Learning.

[8]  Ruth Ben-Yashar,et al.  A nonasymptotic Condorcet jury theorem , 2000, Soc. Choice Welf..

[9]  Robin M. Hogarth,et al.  Simple Models for Multiattribute Choice with Many Alternatives: When It Does and Does Not Pay to Face Trade-offs with Binary Attributes , 2005, Manag. Sci..

[10]  Robin M. Hogarth,et al.  Ignoring information in binary choice with continuous variables: When is less “more”? , 2005 .

[11]  Tim Rakow,et al.  Simple heuristics from the Adaptive Toolbox: Can we perform the requisite learning? , 2004 .

[12]  R. Hogarth,et al.  Unit weighting schemes for decision making , 1975 .

[13]  P. Todd,et al.  Simple Heuristics That Make Us Smart , 1999 .

[14]  Laura Martignon,et al.  Can L'Homme Eclaire Be Fast and Frugal? Reconciling Bayesianism and Bounded Rationality , 2003 .

[15]  M. Lee,et al.  Evidence accumulation in decision making: Unifying the “take the best” and the “rational” models , 2004, Psychonomic bulletin & review.

[16]  Shmuel Nitzan,et al.  Optimal Decision Rules in Uncertain Dichotomous Choice Situations , 1982 .

[17]  J. Shanteau,et al.  Emerging Perspectives on Judgment and Decision Research: List of Contributors , 2003 .

[18]  B. Newell,et al.  Take the best or look at the rest? Factors influencing "one-reason" decision making. , 2003, Journal of experimental psychology. Learning, memory, and cognition.

[19]  L. Macchi,et al.  Thinking : psychological perspectives on reasoning, judgment and decision making , 2005 .

[20]  A. Bröder.  Assessing the empirical validity of the "take-the-best" heuristic as a model of human probabilistic inference. , 2000, Journal of experimental psychology. Learning, memory, and cognition.

[21]  Iver Mysterud,et al.  Take the best , 2000 .

[22]  Laura Martignon,et al.  Naive and Yet Enlightened: From Natural Frequencies to Fast and Frugal Decision Trees , 2003 .

[23]  A. Bröder,et al.  Take the best versus simultaneous feature matching: probabilistic inferences from memory and effects of representation format. , 2003, Journal of experimental psychology. General.

[24]  Eric J. Johnson,et al.  The adaptive decision maker , 1993 .

[25]  Juan A. Carrasco,et al.  Cumulative dominance and heuristic performance in binary multi-attribute choice , 2006 .

[26]  B. Newell,et al.  Empirical tests of a fast-and-frugal heuristic: Not everyone "takes-the-best" , 2003 .

[27]  Konstantinos V. Katsikopoulos,et al.  New tools for decision analysts , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[28]  H. Gulliksen.  Theory of mental tests , 1952 .

[29]  G. Gigerenzer,et al.  How good are fast and frugal heuristics , 1999 .

[30]  L Hasher,et al.  Automatic processing of fundamental information: the case of frequency of occurrence. , 1984, The American psychologist.

[31]  Bernard Grofman,et al.  Information pooling and group decision making : proceedings of the Second University of California, Irvine, Conference on Political Economy , 1986 .

[32]  A. Tversky.  Intransitivity of preferences. , 1969 .

[33]  U. Hoffrage,et al.  Fast, frugal, and fit: Simple heuristics for paired comparison , 2002 .