Implications of the Dutch Book: Following Ramsey’s Axioms

Implications of the Dutch Book: Following Ramsey’s Axioms The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for Subjective Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Frontiers of Philosophy in China Brill

Implications of the Dutch Book: Following Ramsey’s Axioms

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Publisher
BRILL
Copyright
Copyright © Koninklijke Brill NV, Leiden, The Netherlands
ISSN
1673-3436
eISSN
1673-355X
D.O.I.
10.1007/s11466-011-0142-6
Publisher site
See Article on Publisher Site

Abstract

The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for Subjective Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made.

Journal

Frontiers of Philosophy in ChinaBrill

Published: Jan 31, 2011

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