David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 187 (1):147 - 178 (2012)
The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method and argue that non-deceptiveness is a necessary condition for rational coherence. Infomin has been criticized on the grounds that there are no higher order probabilities that 'support' it, but the appeal to higher order probabilities is a substantial assumption that some might reject. Our elementary arguments from deceptiveness do not rely on this assumption. While deceptiveness implies lack of higher order support, the converse does not, in general, hold, which indicates that deceptiveness is a more objectionable property. We offer a new proof of the claim that infomin updating of any strictly-positive prior with respect to conditional-probability constraints is deceptive. In the case of expected-value constraints, infomin updating of the uniform prior is deceptive for some random variables but not for others. We establish both a necessary condition and a sufficient condition (which extends the scope of the phenomenon beyond cases previously considered) for deceptiveness in this setting. Along the way, we clarify the relation which obtains between the strong notion of higher order support, in which the higher order probability is defined over the full space of first order probabilities, and the apparently weaker notion, in which it is defined over some smaller parameter space. We show that under certain natural assumptions, the two are equivalent. Finally, we offer an interpretation of Jaynes, according to which his own appeal to infomin methods avoids the incoherencies discussed in this paper
|Keywords||Updating probabilities Minimal information Higher order probabilities Maximum entropy Cross entropy Jaynes|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Haim Gaifman (1983). Paradoxes of Infinity and Self-Applications, I. Erkenntnis 20 (2):131 - 155.
Haim Gaifman (2004). Reasoning with Limited Resources and Assigning Probabilities to Arithmetical Statements. Synthese 140 (1-2):97 - 119.
Haim Gaifman & Marc Snir (1982). Probabilities Over Rich Languages, Testing and Randomness. Journal of Symbolic Logic 47 (3):495-548.
Richard Jeffrey (1983). The Logic of Decision. University of Chicago Press.
Isaac Levi (1985). Imprecision and Indeterminacy in Probability Judgment. Philosophy of Science 52 (3):390-409.
Citations of this work BETA
No citations found.
Similar books and articles
R. I. G. Hughes & Bas C. Van Fraassen (1984). Symmetry Arguments in Probability Kinematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:851 - 869.
Soshichi Uchii (1973). Higher Order Probabilities and Coherence. Philosophy of Science 40 (3):373-381.
Cesaltina Pacheco Pires (2002). A Rule For Updating Ambiguous Beliefs. Theory and Decision 53 (2):137-152.
Matthew J. Ryan (2001). Capacity Updating Rules and Rational Belief Change. Theory and Decision 51 (1):73-87.
Henry E. Kyburg (1992). Getting Fancy with Probability. Synthese 90 (2):189-203.
Henry E. Kyburg Jr (1992). Getting Fancy with Probability. Synthese 90 (2):189 - 203.
James Hawthorne (2004). Three Models of Sequential Belief Updating on Uncertain Evidence. Journal of Philosophical Logic 33 (1):89-123.
Added to index2010-08-14
Total downloads23 ( #78,502 of 1,099,742 )
Recent downloads (6 months)3 ( #126,683 of 1,099,742 )
How can I increase my downloads?