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Fair bets and inductive probabilities1

Published online by Cambridge University Press:  12 March 2014

John G. Kemeny
John G. Kemeny*
Affiliation:
Dartmouth College
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Extract

The question of what constitutes fairness in betting quotients has been studied by Ramsey, deFinetti, and Shimony. Thanks to their combined efforts we now have a satisfactory definition of fairness.

On the other hand, the explication of the concept of degree of confirmation (inductive probability) has progressed rapidly in recent years, thanks primarily to Carnap. This explication has usually proceeded by laying down the axioms for frequency-probabilities, and elaborating on these. While in the case where a frequency interpretation is intended these axioms are clearly justified, in our case they have been laid down without any justification. Carnap's presentation has been criticized for just this reason.

The purpose of this paper is to show that the probability axioms are necessary and sufficient conditions to assure that the degrees of confirmation form a set of fair betting quotients. In addition it will be shown that one additional, highly controversial, axiom is precisely the condition needed to assure that not only deFinetti's weaker criterion but Shimony's criterion of fairness is also satisfied.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 20 , Issue 3 , September 1955 , pp. 263 - 273
Copyright
Copyright © Association for Symbolic Logic 1955

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Footnotes

1

A summary of sections 1–5 was presented to the conference on induction. May 1953, at New York University, sponsored by the Institute for the Unity of Science. Section 6 has been added more recently. It has come to my attention since then that Sherman Lehman found a similar result independently of me. He will publish this in a forthcoming paper.

References

BIBLIOGRAPHY

[1]Carnap, Rudolf, Logical foundations of probability, University of Chicago Press, 1950.Google Scholar
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