Updating beliefs in light of uncertain evidence: Descriptive assessment of Jeffrey's rule

Jeffrey (1983) proposed a generalisation of conditioning as a means of updating probability distributions when new evidence drives no event to certainty. His rule requires the stability of certain conditional probabilities through time. We tested this assumption (“invariance”) from the psychological point of view. In Experiment 1 participants offered probability estimates for events in Jeffrey's candlelight example. Two further scenarios were investigated in Experiment 2, one in which invariance seems justified, the other in which it does not. Results were in rough conformity to Jeffrey's (1983) principle.

[1]  Jonathan Evans,et al.  Thinking about conditionals: A study of individual differences , 2007, Memory & cognition.

[2]  Gilbert Harman,et al.  Reasoning, Meaning, and Mind , 1999 .

[3]  S. Sloman,et al.  The probability of causal conditionals , 2007, Cognitive Psychology.

[4]  Adnan Darwiche,et al.  On the Revision of Probabilistic Beliefs using Uncertain Evidence , 2003, IJCAI.

[5]  O. Wilhelm,et al.  The meaning(s) of conditionals: conditional probabilities, mental models, and personal utilities. , 2003, Journal of experimental psychology. Learning, memory, and cognition.

[6]  P G rdenfors,et al.  Knowledge in flux: modeling the dynamics of epistemic states , 1988 .

[7]  David E. Over,et al.  Uncertain premises and Jeffrey's rule , 2009, Behavioral and Brain Sciences.

[8]  Peter Gärdenfors,et al.  Knowledge in Flux: Modeling the Dynamics of Epistemic States , 2008 .

[9]  Carl G. Wagner,et al.  Probability Kinematics And Commutativity* , 2002, Philosophy of Science.

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

[11]  S. Sloman,et al.  Causal invariance in reasoning and learning , 2003 .

[12]  N. Chater,et al.  Précis of Bayesian Rationality: The Probabilistic Approach to Human Reasoning , 2009, Behavioral and Brain Sciences.

[13]  I. Hacking.  An Introduction to Probability and Inductive Logic , 2001 .

[14]  D. Osherson.  Order Dependence and Jerey Conditionalization , 2002 .

[15]  F. Döring.  Why Bayesian Psychology Is Incomplete , 1999, Philosophy of Science.

[16]  Anuj K. Shah,et al.  On the provenance of judgments of conditional probability , 2009, Cognition.

[17]  R. Dawes,et al.  Equating Inverse Probabilities in Implicit Personality Judgments , 1993 .

[18]  P. M. Williams.  Bayesian Conditionalisation and the Principle of Minimum Information , 1980, The British Journal for the Philosophy of Science.

[19]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .