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

Abstract

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.

Keywords:

• Belief updating
• Jeffrey's rule
• Reasoning

Acknowledgments

We thank Nick Chater, David Over, Mike Oaksford, Steven Sloman, and an anonymous reviewer for very helpful comments. The research reported here was facilitated by a grant from the Henry Luce Foundation.

Notes

¹Many authors, including Oaksford and Chater (2007) and Over and Hadjichristidis (2009) use the term “rigidity” instead of “invariance”.

²It is straightforward to extend (4) to finer partitions, in place of the binary partition B, [Bbar]. We stick to the binary case in this paper.

³We thank Steve Sloman for suggesting this analysis.

⁴We thank an anonymous reviewer for this observation.

⁵Without giving details, we note that Experiment 2 was repeated with 330 participants recruited over the internet via Amazon Turk. The results were in close agreement with those reported here.