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When Fair Betting Odds are not Degrees of Belief

Published online by Cambridge University Press:  31 January 2023

T. Seidenfeld ,
M.J. Schervish  and
J.B. Kadane
T. Seidenfeld
Affiliation:
Carnegie Mellon University
M.J. Schervish
Affiliation:
Carnegie Mellon University
J.B. Kadane
Affiliation:
Carnegie Mellon University
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Extract

The “Dutch Book” argument, tracing back to Ramsey (1926) and deFinetti (1974), offers prudential grounds for action in conformity with personal probability. Under several structural assumptions about combinations of stakes (that is, assumptions about the combination of wagers), your betting policy is consistent (coherent) only if your fair-odds are probabilities. The central question posed here is the following one: Besides providing an operational test of coherent betting, does the “Book” argument also provide for adequate measurement (elicitation) of the agent’s degrees of beliefs? That is, are an agent’s fair odds also his/her personal probabilities for those events?

We argue the answer is “No!” The problem is created by state-dependent utilities. The methods of elicitation proposed by Ramsey, by deFinetti and by Savage (1954), are inadequate to the challenge of state-dependent values.1

Type
Part IX. Belief, Cause and Induction
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1990 , Issue 1: Volume One: Contributed Papers 1990 , 1990 , pp. 517 - 524
Copyright
Copyright © Philosophy of Science Association 1990

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