Partition-edit-count: naive extensional reasoning in judgment of conditional probability.

The authors provide evidence that people typically evaluate conditional probabilities by subjectively partitioning the sample space into n interchangeable events, editing out events that can be eliminated on the basis of conditioning information, counting remaining events, then reporting probabilities as a ratio of the number of focal to total events. Participants' responses to conditional probability problems were influenced by irrelevant information (Study 1), small variations in problem wording (Study 2), and grouping of events (Study 3), as predicted by the partition-edit-count model. Informal protocol analysis also supports the authors' interpretation. A 4th study extends this account from situations where events are treated as interchangeable (chance and ignorance) to situations where participants have information they can use to distinguish among events (uncertainty).

[1]  B. Finetti.  Sul significato soggettivo della probabilità , 1931 .

[2]  B. D. Finetti.  La prévision : ses lois logiques, ses sources subjectives , 1937 .

[3]  A. Bakst,et al.  The Second Scientific American Book of Mathematical Puzzles and Diversions. , 1962 .

[4]  Henry E. Kyburg,et al.  Studies in Subjective Probability , 1965 .

[5]  M. Stone,et al.  Studies in Subjective Probability , 1965 .

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

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

[8]  D. Krantz,et al.  The use of statistical heuristics in everyday inductive reasoning , 1983 .

[9]  H. Simon,et al.  Why are some problems hard? Evidence from Tower of Hanoi , 1985, Cognitive Psychology.

[10]  D. R. Lehman,et al.  Teaching reasoning. , 1987, Science.

[11]  R. Fildes.  Journal of business: Lupoletti, William M. and Roy H. Webb, 1986, Defining and improving the accuracy of macroeconomic forecasts; contributions from a VAR model, 59, 263-284 , 1988 .

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

[13]  Shinsuke Shimojo,et al.  Intuitive reasoning about probability: Theoretical and experimental analyses of the “problem of three prisoners” , 1989, Cognition.

[14]  H. Simon,et al.  What makes some problems really hard: Explorations in the problem space of difficulty , 1990, Cognitive Psychology.

[15]  Ram C. Dahiya,et al.  Let's Make a Deal: The Player's Dilemma , 1991 .

[16]  N. Sanders,et al.  Journal of behavioral decision making: "The need for contextual and technical knowledge in judgmental forecasting", 5 (1992) 39-52 , 1992 .

[17]  R. Falk.  A closer look at the probabilities of the notorious three prisoners , 1992, Cognition.

[18]  A. Garnham,et al.  Thinking and Reasoning , 1994 .

[19]  A. Tversky,et al.  Support theory: A nonextensional representation of subjective probability. , 1994 .

[20]  Thad A. Brown.  The Monty Hall Dilemma Donald Granberg , 1995 .

[21]  Thomas Gilovich,et al.  Commission, Omission, and Dissonance Reduction: Coping with Regret in the "Monty Hall" Problem , 1995 .

[22]  Raymond S. Nickerson,et al.  AMBIGUITIES AND UNSTATED ASSUMPTIONS IN PROBABILISTIC REASONING , 1996 .

[23]  A. Tversky,et al.  Heuristics and Biases: Unpacking, Repacking, and Anchoring: Advances in Support Theory , 2002 .

[24]  F. Wilkening,et al.  Children's construction of fair chances: adjusting probabilities. , 1998, Developmental psychology.

[25]  Daniel Friedman,et al.  Monty Hall's Three Doors: Construction and Deconstruction of a Choice Anomaly , 1998 .

[26]  Gary L. Brase,et al.  Individuation , Counting , and Statistical Inference : The Role of Frequency and Whole-Object Representations in Judgment Under Uncertainty , 1998 .

[27]  Maria Sonino Legrenzi,et al.  Naive probability: a mental model theory of extensional reasoning. , 1999, Psychological review.

[28]  Baruch Fischhoff,et al.  Fifty–fifty = 50%? , 1999 .

[29]  G. Gigerenzer,et al.  Teaching Bayesian reasoning in less than two hours. , 2001, Journal of experimental psychology. General.

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

[31]  Craig R. Fox,et al.  Partition Priming in Judgment Under Uncertainty , 2003, Psychological science.

[32]  S. Krauss,et al.  The psychology of the Monty Hall problem: discovering psychological mechanisms for solving a tenacious brain teaser. , 2003, Journal of experimental psychology. General.

[33]  M. Bazerman,et al.  Focusing Failures in Competitive Environments: Explaining Decision Errors in the Monty Hall Game, the Acquiring a Company Problem, and Multiparty Ultimatums , 2003 .

[34]  Michael R. Dougherty,et al.  Reasoning in the Monty Hall problem: Examining choice behaviour and probability judgements , 2003 .

[35]  Nigel Harvey,et al.  Blackwell Handbook of Judgment and Decision Making , 2004 .

[36]  Steven A. Sloman,et al.  Inside and Outside Probability Judgment , 2008 .

[37]  Philip N. Johnson-Laird,et al.  The Shape of Reason : Essays in Honour of Paolo Legrenzi , 2005 .

[38]  No Value,et al.  The Monty Hall Dilemma , 2006 .