The Bayesian logic of frequency-based conjunction fallacies

Journal of Mathematical Psychology

Volumn 55, Issue 2, 2011, Pages 119-139

  von Sydow, Momme ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Bayesian models; Conjunction fallacy; Inductive logic; Paradoxes of predication; Probability judgments; Rationality

Indexed keywords

EID: 79952818280     PISSN: 00222496     EISSN: 10960880     Source Type: Journal    
DOI: 10.1016/j.jmp.2010.12.001     Document Type: Article

References (130)

1. Adams E.W. On the logic of high probability. Journal of Philosophical Logic 1986, 1:255-279.
2. Agnoli F., Krantz D. Suppressing natural heuristics by formal instruction: the case of the conjunction fallacy. Cognitive Psychology 1989, 21:515-550.
3. Anderson J.R. The adaptive character of thought 1990, Erlbaum, Hillsdale.
4. Barbey A.K., Sloman St.A. Base-rate respect: from ecological rationality to dual processes. Behavioral and Brain Sciences 2007, 30:241-297.
5. Bar-Hillel M. Commentary on Wolford, Taylor, and Beck: the conjunction fallacy. Memory & Cognition 1991, 19:412-414.
6. Betsch T., Fiedler K. Understanding conjunction effects: the role of implicit mental models. European Journal of Social Psychology 1999, 29:75-93.
7. Bonini N., Tentori K., Osherson D. A different conjunction fallacy. Mind & Language 2004, 19:199-210.
8. Busemeyer J.R., Wang Z., Townsend J.T. Quantum dynamics of human decision-making. Journal of Mathematical Psychology 2006, 50:220-241.
9. Carbonetto, P., Kisyński, J., de Freitas, N., & Poole, D. (2005). Nonparametric Bayesian logic. In Proc. 21st UAI (pp. 1-9).
10. Carnap R. The continuum of inductive methods 1952, Chicago University Press.
11. Chater N., Oaksford M. The rational analysis of mind and behavior. Synthese 2000, 122:93-131.
12. The probabilistic mind: prospects for Bayesian cognitive science 2008, Oxford University Press. N. Chater, M. Oaksford (Eds.).
13. Chater N., Tenenbaum J., Yuille A. Probabilistic models of cognition: conceptual foundations. Trends in Cognitive Sciences 2006, 10:287-291.
14. Cheng P.W. From covariation to causation: a causal power theory. Psychological Review 1997, 104:367-405.
15. Cosmides L., Tooby J. Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition 1996, 58:1-73.
16. Costello F.J. A unified account of conjunction and disjunction fallacies in people's judgments of likelihood. Proceedings of the twenty-seventh annual conference of the cognitive science society 2005, 494-499. Erlbaum, Mahwah, NJ.
17. Crupi V., Fitelson B., Tentori K. Probability, confirmation, and the conjunction fallacy-theoretical note. Thinking & Reasoning 2008, 14:182-199.
18. De Houwer J., Beckers T. A review of recent developments in research and theories on human contingency learning. The Quarterly Journal of Experimental Psychology, Section B 2002, 55:289-310.
19. De Neys W. Automatic-heuristic and executive-analytic processing during reasoning: chronometric and dual-task considerations. Quarterly Journal of Experimental Psychology 2006, 59:1070-1100.
20. De Raedt L., Kersting K. Probabilistic logic learning. SIGKDD Exploitations 2003, 5(1):31-48.
21. Erdfelder, E., Bröder, A., & Brandt, M. (1998). Zur bedeutung des antwortformats für die Häufigkeit von konjunktionsfehlern. The relevance of response format for the frequency of conjunction errors. In Talk presented at the 40th TEAP in Marburg. Germany.
22. Evans J.St.B.T., Handley S.H., Perham N., Over D.E., Thompson V.A. Frequency versus probability formats in statistical word problems. Cognition 2000, 77:197-213.
23. Evans St.B.T., Over D.E. If 2004, Oxford University Press.
24. Fantino E., Kulik J., Stolarz-Fantino St., Wright W. The conjunction fallacy: a test of averaging hypotheses. Psychonomic Bulletin & Review 1997, 4:96-101.
25. Fiedler K. The dependence of the conjunction fallacy on subtle linguistic factors. Psychological Research 1988, 50:123-129.
26. Fiedler K. Beware of samples! a cognitive-ecological sampling approach to judgment biases. Psychological Review 2000, 107:659-676.
27. Fisk J.E. The conjunction effect: fallacy or Bayesian inference?. Organizational Behavior and Human Decision Processes 1996, 67:76-90.
28. Fisk J.E., Slattery R. Reasoning about conjunctive probabilistic concepts in childhood. Canadian Journal of Experimental Psychology 2005, 59:168-178.
29. Fitelson B. Inductive logic. Philosophy of science: an encyclopedia 2006, Routledge, London. J. Pfeifer, S. Sarkar (Eds.).
30. Frege G. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens 1879, Verlag Louis Nebert, Halle.
31. Gavanski I., Roskos-Ewoldsen D.R. Representativeness and conjoint probability. Journal of Personality and Social Psychology 1991, 61:181-194.
32. Gigerenzer G. How to make cognitive illusions disappear: beyond 'heuristics and biases'. European review of social psychology 1991, Vol. 2:83-115. Wiley, Chichester.
33. Gigerenzer G. Why the distinction between single-event covariations and frequencies is relevant for psychology and vice versa. Subjective probability 1994, 129-161. Wiley, Chichester. G. Wright, P. Ayton (Eds.).
34. Gigerenzer G. On narrow norms and vague heuristics: a reply to Kahneman and Tversky. Psychological Review 1996, 103:592-596.
35. Gigerenzer G. Ecological intelligence: an adaptation for frequencies. The evolution of mind 1998, Oxford University Press, New York. D.D. Cummins, C. Allen (Eds.).
36. Gigerenzer G. Adaptive thinking: rationality in the real world 2000, Oxford University Press, London.
37. Gigerenzer G., Hoffrage U. How to improve Bayesian reasoning without instruction: frequency formats. Psychological Review 1995, 102:684-704.
38. Gigerenzer G., Hoffrage U. The role of representation in Bayesian reasoning: correcting common misconceptions. Behavioral and Brain Sciences 2007, 30:264-267.
39. Heurstics and biases. The psychology of intuitive judgement 2002, Cambridge University Press. T. Gilovich, D. Griffin, D. Kahneman (Eds.).
40. Girotto V., Gonzales M. Solving probabilistic and statistical problems: a matter of information structure and question form. Cognition 2001, 78:247-276.
41. Goodman N.D., Tenenbaum J.B., Feldman J., Griffiths T.L. A rational analysis of rule-based concept learning. Cognitive Science 2008, 32:108-154.
42. Grice H.P. Logic and conversation. Syntax and semantics 1975, Vol. 3:41-58. Academic Press, New York.
43. Griffiths T.L., Tenenbaum J.B. Structure and strength in causal induction. Cognitive Psychology 2005, 51:334-384.
44. Hagmayer Y., Sloman S.A., Lagnado D.A., Waldmann M.R. Causal reasoning through intervention. Causal learning: psychology, philosophy, and computation 2007, 86-100. Oxford University Press, Oxford. A. Gopnik, L. Schulz (Eds.).
45. Hahn U., Oaksford M. The rationality of informal argumentation: a Bayesian approach to reasoning fallacies. Psychological Review 2007, 114:704-732.
46. Hájek A. Probability, logic, and probability logic. The blackwell companion to logic 2001, 362-384. Blackwell, Oxford. L. Goble (Ed.).
47. Hájek, P. (2002). Fuzzy logic. In: Zelta, E.N. (Ed.), The stanford encyclopedia of philosophy. URL: (3rd September). http://plato.stanford.edu/entries/logic-fuzzy/.
48. Hattori M. A quantitative model of optimal data selection in Wason's selection task. Quarterly Journal of Experimental Psychology, Section A 2002, 55:1241-1272.
49. Hattori M., Oaksford M. Adaptive non-interventional heuristics for covariation detection in causal induction: model comparison and rational analysis. Cognitive Science 2007, 31:765-814.
50. Hempel C.G. Studies in the logic of confirmation. Mind 1945, 54:1-25. 7-121.
51. Hertwig R., Benz B., Krauss B.S. The conjunction fallacy and the many meanings of and. Cognition 2008, 108:740-753.
52. Hertwig R., Chase V.M. Many reasons or just one: how response mode affects reasoning in the conjunction problem. Thinking & Reasoning 1998, 4:319-352.
53. Hertwig R., Gigerenzer G. The 'conjunction fallacy' revisited. Journal of Behavioral Decision Making 1999, 12:275-305.
54. Hilton D.J. The social context of reasoning: conversational inference and rational judgment. Psychological Bulletin 1995, 118:248-271.
55. Hintikka J. A fallacious fallacy?. Synthese 2004, 140:25-35.
56. Hoffrage U., Gigerenzer G., Krauss S., Martignon L. Representation facilitates reasoning: what natural frequencies are and what they are not. Cognition 2002, 84:343-352.
57. Johnson-Laird P.N., Byrne R.M.J. A theory of meaning, pragmatics, and inference. Psychological Review 2002, 109:646-678.
58. Johnson-Laird P.N., Legrenzi P., Girotto V., Legrenzi S.M., Caverni J.-P. Naive probability: a mental model theory of extensional reasoning. Psychological Review 1999, 106:62-88.
59. Kahneman D., Frederick S. Representativeness revised: attribute substitution in intutitive judgment. Heurstics and biases. The psychology of intuitive judgement 2002, 49-81. Cambridge University Press. T. Gilovich, D. Griffin, D. Kahneman (Eds.).
60. Kahneman D., Frederick S. A model of heuristic judgment. The cambridge handbook of thinking & reasoning 2005, 267-293. Cambridge University Press. K.J. Holyoak, R.G. Morris (Eds.).
61. Kahneman D., Tversky A. On the reality of cognitive illusions. Psychological Review 1996, 103:582-591.
62. Kahneman D., Tversky A. On the psychology of prediction. Psychological Review 1973, 80:237-251.
63. Kahneman D., Tversky A. Subjective probability: a judgment of representativeness. Cognitive Psychology 1972, 3:430-454.
64. Kao S.-F., Wassermann E.A. Assessment of an information integration account of contingency judgment with examination of subjective cell importance and method of information presentation. Journal of Experimental Psychology: Learning, Memory, and Cognition 1993, 19:1363-1386.
65. Kennedy J.J. Analyzing qualitative data: log-linear analysis for behavioral research 1992, Praeger, New York. 2nd ed.
66. Kolmogorov A. Grundbegriffe der Wahrscheinlichkeitsrechnung 1933, Springer, Berlin.
67. Kruschke J.K. Bayesian approaches to associative learning: from passive to active learning. Learning & Behavior 2008, 36:210-226.
68. Lagnado D.A., Shanks D.R. Probability judgment in hierarchical learning: a conflict between predictiveness and coherence. Cognition 2002, 93:81-112.
69. Marr D. Vision: a computational approach 1982, Freeman & Co., San Francisco.
70. McKenzie C.R.M., Mikkelsen L.A. A Bayesian view of covariation assessment. Cognitive Psychology 2007, 54:33-61.
71. Mellers B.A., Hertwig R., Kahneman D. Do frequency representations eliminate conjunction effects? An exercise in adversarial collaboration. Psychological Science 2001, 12:269-275.
72. Messer W.S., Griggs R.A. Another look at Linda. Bulletin of the Psychonomic Society 1993, 31:193-196.
73. Milch B., Marthi B., Russell S., Sontag D., Ong D.L., Kolobov A. BLOG: probabilistic models with unknown objects. Dragstuhl Seminar Proceedings 2006, 2005:1-6.
74. Morier D.M., Borgida E. The conjunction fallacy: a task specific phenomenon?. Personality and Social Psychology Bulletin 1984, 10:243-253.
75. Moutier S., Houdé O. Judgement under uncertainty and conjunction fallacy inhibition training. Thinking and Reasoning 2003, 9:185-201.
76. Neace W.P., Michaud St., Bolling L., Deer K., Zecevic L. Frequency formats, probability formats, or problem structure? A test of the nested-sets hypothesis in an extensional reasoning task. Judgment and Decision Making 2008, 3:140-152.
77. Nelson J. Finding useful questions: on Bayesian diagnosticity, probability, impact, and information gain. Psychological Review 2005, 112:979-999.
78. Nickerson R.S. Cognition and chance. The psychology of probabilistic reasoning 2004, Lawrence Erlbaum Associates, Mahwah.
79. Nickerson R.S. Hempel's paradox and Wason's selection task: logical and psychological puzzles of confirmation. Thinking and Reasoning 1996, 4:231-248.
80. Nilsson H. Exploring the conjunction fallacy within a category learning framework. Journal of Behavioral Decision Making 2008, 21:471-490.
81. Nilsson H., Juslin P., Olsson H. Exemplars in the mist: the cognitive substrate of the representativeness heuristic. Scandinavian Journal of Psychology 2008, 49:201-212.
82. Oaksford M., Chater N. Bayesian rationality. The probabilistic approach to human reasoning 2007, Oxford University Press, Oxford.
83. Oaksford M., Chater N. A rational analysis of the selection task as optimal data selection. Psychological Review 1994, 101:608-631.
84. Oaksford M., Chater N. Optimal data selection: revision, review, and reevaluation. Psychological Bulletin & Review 2003, 10:289-318.
85. Oberauer K., Weidenfeld A., Fischer K. What makes us believe a conditional? The roles of covariation and causaltity. Thinking and Reasoning 2007, 13:340-369.
86. Osman M. An evaluation of dual-process theories of reasoning. Psychonomic Bulletin & Review 2004, 11:988-1010.
87. Over D.E. Naïve probability and its model theory. The shape of reason: essays in honour of Paolo Legrenzi 2004, 139-160. Psychology Press, Hove. V. Girotto, P.N. Johnson-Laird (Eds.).
88. Over D.E., Hadjichristidis C., Evans J.St.B.T., Handley S.J., Sloman St.A. The probability of causal conditionals. Cognitive Psychology 2007, 54:62-97.
89. Pearl J. Causality: models, reasoning, and inference 2000, Cambridge University Press.
90. Piaget J., Garcia R. Toward a logic of meanings 1991, Erlbaum, Hillsdale. P. Davidson, J. Easley (Eds.).
91. Pineno O., Miller R.R. Comparing associative, statistical, and inferential reasoning accounts of human contingency learning. The Quarterly Journal of Experimental Psychology 2007, 60:310-329.
92. Popper K.R. Logik der Forschung 2005, Mohr-Siebeck, Tübingen, (Original work published 1934). 11th ed.
93. Reeves T., Lockhart R.S. Distributional versus singular approaches to probability and errors in probabilistic reasoning. Journal of Experimental Psychology: General 1993, 122:207-226.
94. Reichenbach H. Wahrscheinlichkeitslogik [probability logic]. Erkenntnis 1935, 5:37-43.
95. Romeyn, J. W. (2005). Bayesian inductive logic. In Inductive prediction from statistical hypotheses. Doctoraat aan de Wijsbegeerte, Rijksuniversiteit Groningen.
96. Schurz G. Normische Gesetzeshypothesen und die wissenschaftsphilosophische Bedeutung des nichtmonotonen Schliessens. Journal for General Philosophy of Science 2001, 32:65-107.
97. Schurz G. Non-monotonic reasoning from an evolutionary viewpoint: ontic, logical and cognitive foundations. Synthese 2005, 146:37-51.
98. Sedlmeier P., Gigerenzer G. Teaching Bayesian reasoning in less than two hours. Journal of Experimental Psychology: General 2001, 130:380-400.
99. Shafir E., Smith E., Osherson D. Typicality and reasoning fallacies. Memory & Cognition 1990, 18:229-239.
100. Sides A., Osherson D., Bonini N., Viale R. On the reality of the conjunction fallacy. Memory & Cognition 2002, 30:191-198.
101. Skyrms B. Choice and chance. An introduction to inductive logic 1986, Wadsworth Publishing Company, Belmont, CA. 3rd ed.
102. Sloman S.A., Lagnado D. Do we "do"?. Cognitive Science 2005, 29:5-39.
103. Sloman S.A., Over D. Probability judgement from the inside and out. Evolution and the psychology of thinking: the debate 2003, 145-169. Psychology Press, Hove, New York. D. Over (Ed.).
104. Sloman S.A., Over D., Slovak L., Stibel J.M. Frequency illusions and other fallacies. Organizational Behavior and Human Decision Processes 2003, 91:296-309.
105. Stalnaker R. A theory of conditionals. American Philosophical Quarterly Monograph Series 1968, 2:98-112.
106. Stewart N., Brown G.D.A., Chater N. Absolute identification by relative judgement. Psychological Review 2005, 112:881-911.
107. Stolarz-Fantino S., Fantino E., Kulik J. The conjunction fallacy: differential incidence as a function of descriptive frames and educational context. Contemporary Educational Psychology 1996, 21:208-218.
108. Teigen K.H. Variants of subjective probabilities: concepts, norms, and biases. Subjective probability 1994, 211-238. John Wiley, Chichester. G. Wright, P. Ayton (Eds.).
109. Tenenbaum J., Griffiths T.L. Generalization, similarity, and Bayesian inference. Behavioral and Brain Sciences 2001, 24:629-640.
110. Tenenbaum J.B., Griffiths T.L., Kemp C. Theory-based Bayesian models of inductive learning and reasoning. Trends in Cognitive Science 2006, 10:309-318.
111. Tentori K., Bonini N., Osherson D. The conjunction fallacy: a misunderstanding about conjunction?. Cognitive Science 2004, 28:467-477.
112. Thüring M., Jungermann H. The conjunction fallacy: causality vs. event probability. Journal of Behavioral Decision Making 1990, 3:61-74.
113. Tversky A. Features of similarity. Psychological Review 1977, 84:327-352.
114. Tversky A., Kahneman D. Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review 1983, 90:293-315.
115. Tversky A., Kahneman D. Judgments of and by representativeness. Judgment under uncertainty: heuristics and biases 1982, 84-98. Cambridge University Press. D. Kahneman, P. Slovic, A. Tversy (Eds.).
116. Tversky A., Koehler D.J. Support theory: a nonextensional representation of subjective probability. Psychological Review 1994, 101:547-567.
117. von Sydow M. On a general Bayesian pattern logic of frequency-based logical inclusion fallacies. Proceedings of the thirty-first annual conference of the cognitive science society 2009, 248-253. Cognitive Science Society, Austin, TX.
118. von Sydow M. The Bayesian logic of the conjunction fallacy: effects of probabilities and frequencies in contingency tables. Proceedings of the twenty-nineth annual conference of the cognitive science society 2007, 1611-1616. Cognitive Science Society, Austin, TX.
119. von Sydow M. The Bayesian logic of conjunction fallacies: probability rating tasks and pattern-sensitivity. Proceedings of the twenty-nineth annual conference of the cognitive science society 2008, 1795-1800. Cognitive Science Society, Austin, TX.
120. von Sydow M. Testing descriptive or prescriptive conditionals and differential effects of frequency information. Proceedings of the twenty-ninth annual conference of the cognitive science society 2007, 1617-1622. Erlbaum, Mahwah, NJ.
121. von Sydow, M. (2006). Towards a flexible Bayesian and deontic logic of testing descriptive and prescriptive rules. Doctoral dissertation in psychology, Georg-August-Universität Göttingen.
122. von Sydow M. Structural Bayesian models of conditionals. Proceedings of the twenty-sixth annual conference of the cognitive science society 2004, 1411-1416. Erlbaum, Mahwah, NJ. K. Forbus, D. Gentner, T. Regier (Eds.).
123. Vranas P.B.M. Hempel's raven paradox. Lacuna in the standard Bayesian solution. British Journal for the Philosophy of Science 2004, 55:545-560.
124. Waldmann M.R. Combining versus analyzing multiple causes: how domain assumptions and task context affect integration rules. Cognitive Science 2007, 31:233-256.
125. Wedell D., H., Moro R. Testing boundary conditions for the conjunction fallacy: effects of response mode, conceptual focus, and problem type. Cognition 2008, 107:105-136.
126. White P.A. Causal attribution from covariation information: the evidential evaluation model. European Journal of Social Psychology 2002, 32:667-684.
127. Wolford G. The conjunction fallacy? A reply to Bar-Hillel. Memory & Cognition 1991, 19:415-417.
128. Wolford G., Taylor H.A., Beck J.R. The conjunction fallacy?. Memory & Cognition 1990, 18:47-53.
129. Yates J.F., Carlson B.W. Conjunction errors: evidence for multiple judgment procedures, including 'signed summation'. Organizational Behavior and Human Decision Processes 1986, 37:230-253.
130. Zhu L., Gigerenzer G. Children can solve Bayesian problems: the role of representation in mental computation. Cognition 2006, 98:287-293.