Judging the Probability of Hypotheses Versus the Impact of Evidence: Which Form of Inductive Inference Is More Accurate and Time-Consistent?

Inductive reasoning requires exploiting links between evidence and hypotheses. This can be done focusing either on the posterior probability of the hypothesis when updated on the new evidence or on the impact of the new evidence on the credibility of the hypothesis. But are these two cognitive representations equally reliable? This study investigates this question by comparing probability and impact judgments on the same experimental materials. The results indicate that impact judgments are more consistent in time and more accurate than probability judgments. Impact judgments also predict the direction of errors in probability judgments. These findings suggest that human inductive reasoning relies more on estimating evidential impact than on posterior probability.

[1]  M. Bar-Hillel,et al.  How alike is it versus how likely is it: A disjunction fallacy in probability judgments. , 1993 .

[2]  Vincenzo Crupi,et al.  On Bayesian Measures of Evidential Support: Theoretical and Empirical Issues* , 2007, Philosophy of Science.

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

[4]  Vincenzo Crupi,et al.  Confirmation as partial entailment: A representation theorem in inductive logic , 2013, J. Appl. Log..

[5]  Alan Hájek,et al.  Dutch Book Arguments , 2009, The Handbook of Rational and Social Choice.

[6]  D. Osherson,et al.  Comparison of confirmation measures , 2007, Cognition.

[7]  S. Sloman Feature-Based Induction , 1993, Cognitive Psychology.

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

[9]  M. Bar-Hillel The base-rate fallacy in probability judgments. , 1980 .

[10]  Branden Fitelson,et al.  Probability, confirmation, and the conjunction fallacy , 2008 .

[11]  Vincenzo Crupi,et al.  On the determinants of the conjunction fallacy: probability versus inductive confirmation. , 2013, Journal of experimental psychology. General.

[12]  Christopher D. Manning,et al.  Probabilistic models of language processing and acquisition , 2006, Trends in Cognitive Sciences.

[13]  Vittorio Girotto,et al.  From is to ought, and back: how normative concerns foster progress in reasoning research , 2014, Front. Psychol..

[14]  Richard Pettigrew,et al.  An Objective Justification of Bayesianism I: Measuring Inaccuracy* , 2010, Philosophy of Science.

[15]  Vincenzo Crupi,et al.  Erratum to "Confirmation as partial entailment" [Journal of Applied Logic 11 (2013) 364-372] , 2014, J. Appl. Log..

[16]  Rajesh P. N. Rao,et al.  Bayesian brain : probabilistic approaches to neural coding , 2006 .

[17]  E. Heit Properties of inductive reasoning , 2000, Psychonomic bulletin & review.

[18]  D. Osherson,et al.  Determinants of confirmation , 2007, Psychonomic bulletin & review.

[19]  Thomas L. Griffiths,et al.  Learning the Form of Causal Relationships Using Hierarchical Bayesian Models , 2009, Cogn. Sci..

[20]  Vincenzo Crupi,et al.  State of the field: Measuring information and confirmation , 2014 .

[21]  Jonathan D. Nelson Finding useful questions: on Bayesian diagnosticity, probability, impact, and information gain. , 2005, Psychological review.

[22]  Irving John Good,et al.  C197. The best explicatum for weight of evidence , 1984 .

[23]  J. Stockman Pure Reasoning in 12-Month-Old Infants as Probabilistic Inference , 2013 .

[24]  Vincenzo Crupi,et al.  Broadening the study of inductive reasoning: Confirmation judgments with uncertain evidence , 2010, Memory & cognition.

[25]  Noah D. Goodman,et al.  Title : The imaginary fundamentalists : The unshocking truth about Bayesian cognitive science , 2011 .

[26]  Daniel N. Osherson,et al.  The conjunction fallacy: a misunderstanding about conjunction? , 2004, Cogn. Sci..

[27]  David H. Glass,et al.  Confirmation measures of association rule interestingness , 2013, Knowl. Based Syst..

[28]  Michael C. Frank,et al.  Predicting Pragmatic Reasoning in Language Games , 2012, Science.

[29]  Rodrigo Moro,et al.  On the nature of the conjunction fallacy , 2009, Synthese.

[30]  R. Hogarth,et al.  Order effects in belief updating: The belief-adjustment model , 1992, Cognitive Psychology.

[31]  D. Medin,et al.  A relevance theory of induction , 2003, Psychonomic bulletin & review.

[32]  P. Horwich Probability and Evidence , 1972 .

[33]  J. Tenenbaum,et al.  Probabilistic models of cognition: exploring representations and inductive biases , 2010, Trends in Cognitive Sciences.

[34]  Vincenzo Crupi,et al.  How the conjunction fallacy is tied to probabilistic confirmation: Some remarks on Schupbach (2009) , 2009, Synthese.

[35]  Jonathan Evans,et al.  Rationality and reasoning , 1996 .

[36]  H. Vincent Poor,et al.  Probabilistic Coherence and Proper Scoring Rules , 2007, IEEE Transactions on Information Theory.

[37]  J. Kemeny,et al.  Degree of Factual Support , 1952, Philosophy of Science.

[38]  Katya Tentori,et al.  On the determinants of the conjunction fallacy: Confirmation versus probability , 2013 .

[39]  J. Tenenbaum,et al.  Structured statistical models of inductive reasoning. , 2009, Psychological review.

[40]  Roberto Festa,et al.  “For unto every one that hath shall be given”. Matthew properties for incremental confirmation , 2009, Synthese.

[41]  R. Nickerson Confirmation Bias: A Ubiquitous Phenomenon in Many Guises , 1998 .

[42]  Peter W. Milne log[P(h/eb)/P(h/b)] Is the One True Measure of Confirmation , 1996, Philosophy of Science.

[43]  Tomoji Shogenji,et al.  Dwindling Confirmation , 2014, Philosophy of Science.

[44]  Daniel N. Osherson,et al.  Evidential diversity and premise probability in young children's inductive judgment , 2002, Cogn. Sci..

[45]  D. Osherson,et al.  Second-order probability affects hypothesis confirmation , 2010, Psychonomic bulletin & review.

[46]  E. Eells,et al.  Symmetries and Asymmetries in Evidential Support , 2002 .

[47]  Marcello D'Agostino,et al.  Epistemic Accuracy and Subjective Probability , 2009 .

[48]  N. Chater,et al.  New Axioms for Probability and Likelihood Ratio Measures , 2013, The British Journal for the Philosophy of Science.

[49]  Christopher R. Hitchcock,et al.  Probabilistic Measures of Causal Strength , 2011 .

[50]  B. Love,et al.  The myth of computational level theory and the vacuity of rational analysis , 2011, Behavioral and Brain Sciences.

[51]  J. Klayman,et al.  Confirmation, Disconfirmation, and Informa-tion in Hypothesis Testing , 1987 .

[52]  A. Tversky,et al.  Evidential impact of base rates , 1981 .

[53]  Nick Chater,et al.  Bayesian models of cognition. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[54]  M. Oaksford,et al.  The rationality of informal argumentation: a Bayesian approach to reasoning fallacies. , 2007, Psychological review.

[55]  H. Leitgeb,et al.  An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy* , 2010, Philosophy of Science.

[56]  Konrad Paul Kording,et al.  Review TRENDS in Cognitive Sciences Vol.10 No.7 July 2006 Special Issue: Probabilistic models of cognition Bayesian decision theory in sensorimotor control , 2022 .

[57]  T. Griffiths Probabilistic models of cognition 1 Running head : PROBABILISTIC MODELS OF COGNITION Probabilistic models of cognition : Exploring the laws of thought , 2009 .

[58]  Edward E. Smith,et al.  Category-Based Induction , 1990 .

[59]  W. Richards,et al.  Perception as Bayesian Inference , 2008 .

[60]  J. Tenenbaum,et al.  Predicting the future as Bayesian inference: people combine prior knowledge with observations when estimating duration and extent. , 2011, Journal of experimental psychology. General.

[61]  David Lindley,et al.  Logical foundations of probability , 1951 .

[62]  Peter Brössel The Problem of Measure Sensitivity Redux , 2013, Philosophy of Science.

[63]  Vincenzo Crupi,et al.  On the conjunction fallacy and the meaning of and, yet again: A reply to Hertwig, Benz, and Krauss (2008) , 2012, Cognition.

[64]  J. Keynes A Treatise on Probability. , 1923 .