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Bayesianism, Infinite Decisions, and Binding

Frank Arntzenius, Adam Elga and John Hawthorne
Mind
New Series, Vol. 113, No. 450 (Apr., 2004), pp. 251-283
Published by: Oxford University Press on behalf of the Mind Association
Stable URL: http://www.jstor.org/stable/3489134
Page Count: 33
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Bayesianism, Infinite Decisions, and Binding
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Abstract

We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as 'Trumped' (Arntzenius and McCarthy 1997), 'Rouble trouble' (Arntzenius and Barrett 1999), 'The airtight Dutch book' (McGee 1999), and 'The two envelopes puzzle' (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses.

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