Individuation, counting, and statistical inference: The role of frequency and whole-object representations in judgment under uncertainty

Evolutionary approaches to judgment under uncertainty have led to new data showing that untutored subject reliably produce judgments that conform to may principles of probability theory when (a) they are asked to compute a frequency instead of the probability of a single event, and (b) the relevant information is expressed as frequencies. But are the frequencycomputation systems implicated in these experiments better at operating over some kinds of input than others? Principles of object perception and principles of adaptive design led us to propose the individuation hypothesis : that these systems are designed to produce wellcalibrated statistical inferences when they operate over representations of “whole” objects, events, and locations. In a series of experiments on Bayesian reasoning, we show that human performance can be systematically improved or degraded by varying whether a correct solution requires one to compute hit and false-alarm rates over “natural” units, such as whole objects, as opposed to inseparable aspects, views, and other parsings that violate evolved principles of object construal. The ability to make well-calibrated probability judgments depends, at a very basic level, on the ability to count. The ability to count depends on the ability to individuate the world: to see it as composed of discrete entities. Research on how people individuate the world is, therefore, relevant to understanding the statistical inference mechanisms that govern how people make judgments under uncertainty. Computational machinery whose architecture is designed to parse the world and make inferences about it is under intensive study in many branches of psychology: perception, psychophysics, cognitive development, cognitive neurosci

[1]  S. Amano,et al.  Psychology of Reasoning , 1923 .

[2]  G. P. Baerends Fortpflanzungsverhalten und Orientierung der Grabwespe Ammophila campestris Jur , 1941 .

[3]  John Garcia,et al.  Relation of cue to consequence in avoidance learning , 1966 .

[4]  R. Rescorla Pavlovian conditioning and its proper control procedures. , 1967, Psychological review.

[5]  R. Rescorla Probability of shock in the presence and absence of CS in fear conditioning. , 1968, Journal of comparative and physiological psychology.

[6]  P. Johnson-Laird,et al.  Psychology of Reasoning: Structure and Content , 1972 .

[7]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[8]  John Aitchison,et al.  Statistical Prediction Analysis , 1975 .

[9]  Douglas L. Hintzman,et al.  Contextual variability and memory for frequency. , 1978 .

[10]  L. Hasher,et al.  Automatic and effortful processes in memory. , 1979 .

[11]  B. Fischhoff,et al.  Journal of Experimental Psychology: Human Learning and Memory , 1980 .

[12]  M. Bar-Hillel,et al.  Some teasers concerning conditional probabilities , 1982, Cognition.

[13]  L. Beach,et al.  Experience and the base-rate fallacy. , 1982, Organizational behavior and human performance.

[14]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[15]  Ray Jackendoff Semantics and Cognition , 1983 .

[16]  Ralph L. Rosnow,et al.  Essentials of Behavioral Research: Methods and Data Analysis , 1984 .

[17]  R. Shepard Ecological constraints on internal representation: resonant kinematics of perceiving, imagining, thinking, and dreaming. , 1984, Psychological review.

[18]  R. Dawkins The Blind Watchmaker , 1986 .

[19]  R. Baillargeon Representing the existence and the location of hidden objects: Object permanence in 6- and 8-month-old infants , 1986, Cognition.

[20]  J. Freyd Dynamic mental representations. , 1987, Psychological review.

[21]  G. Gigerenzer,et al.  Cognition as Intuitive Statistics , 1987 .

[22]  John Dupré,et al.  The Latest on the best : essays on evolution and optimality , 1987 .

[23]  Leonard Talmy,et al.  Force Dynamics in Language and Cognition , 1987, Cogn. Sci..

[24]  K. Fiedler The dependence of the conjunction fallacy on subtle linguistic factors , 1988 .

[25]  L. Weiskrantz,et al.  Thought Without Language , 1988 .

[26]  Robert C. Bolles,et al.  Evolution and learning , 1988 .

[27]  L. Cosmides The logic of social exchange: Has natural selection shaped how humans reason? Studies with the Wason selection task , 1989, Cognition.

[28]  John Tooby,et al.  Evolutionary psychology and the generation of culture, part I: Theoretical considerations , 1989 .

[29]  L. Cosmides,et al.  Evolutionary psychology and the generation of culture, part II: Case study: A computational theory of social exchange , 1989 .

[30]  Maya Bar-Hillel,et al.  How to Solve Probability Teasers , 1989, Philosophy of Science.

[31]  E. Spelke,et al.  Numerical abstraction by human infants , 1990, Cognition.

[32]  Elizabeth S. Spelke,et al.  Principles of Object Perception , 1990, Cogn. Sci..

[33]  Barbara A. Shepperson,et al.  Countable entities: Developmental changes , 1990, Cognition.

[34]  C. Gallistel The organization of learning , 1990 .

[35]  G. Gigerenzer,et al.  Probabilistic mental models: a Brunswikian theory of confidence. , 1991, Psychological review.

[36]  G. Gigerenzer How to Make Cognitive Illusions Disappear: Beyond “Heuristics and Biases” , 1991 .

[37]  Mark H. Johnson,et al.  Biology and Cognitive Development: The Case of Face Recognition , 1993 .

[38]  L A Real,et al.  Animal choice behavior and the evolution of cognitive architecture , 1991, Science.

[39]  L. Cosmides,et al.  Cognitive adaptations for social exchange. , 1992 .

[40]  L. Cosmides,et al.  The Adapted mind : evolutionary psychology and the generation of culture , 1992 .

[41]  G. Gigerenzer,et al.  Domain-specific reasoning: Social contracts, cheating, and perspective change , 1992, Cognition.

[42]  L. Cosmides,et al.  The Adapted Mind , 1992 .

[43]  Gerhard H. Fischer,et al.  "Contributions to Mathematical Psychology, Psychometrics, and Methodology" , 1993 .

[44]  A. Leslie Mapping the mind: ToMM, ToBY, and Agency: Core architecture and domain specificity , 1994 .

[45]  B. Cocroft,et al.  Book reviewStructures of social life: the four elementary forms of human relations: Alan Page Fiske New York: Macmillan Inc., 1991, 480 pp., $29.95 (cloth) , 1994 .

[46]  Gernot D. Kleiter,et al.  Natural Sampling: Rationality without Base Rates , 1994 .

[47]  S. Gelman,et al.  Mapping the Mind: Domain Specificity In Cognition And Culture , 1994 .

[48]  Karen Wynn,et al.  Origins of Numerical Knowledge. , 1995 .

[49]  Gerd Gigerenzer,et al.  How to Improve Bayesian Reasoning Without Instruction: Frequency Formats , 1995 .

[50]  L. Cosmides,et al.  Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty , 1996, Cognition.

[51]  John Tooby,et al.  Are humans good intuitive statisticians after all , 1996 .

[52]  S. Baron-Cohen Mindblindness: An Essay on Autism and Theory of Mind , 1997 .

[53]  C. Frith,et al.  Mapping the Mind , 1998 .