Implications of the Dutch Book: Following Ramsey’s axioms

Frontiers of Philosophy in China 6 (2):334-344 (2011)
Abstract
The Dutch Book Argument shows that an agent will lose surely in a gamble 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 and beliefs are both incoherent or disordered if a Dutch Book is made.
Keywords Dutch Book  coherence  degree of belief  decision making
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DOI 10.1007/s11466-011-0142-6
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The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.

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