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Bayesianism, Infinite Decisions, and Binding

Arntzenius, Frank and Elga, Adam and Hawthorne, John (2004) Bayesianism, Infinite Decisions, and Binding. [Preprint]

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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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    Item Type: Preprint
    Keywords: dutch book, infinite decision theory, unbounded utilities, paradoxes, nonconglomerability, two-envelopes, countable additivity, causal decision theory
    Subjects: General Issues > Decision Theory
    Depositing User: Adam Elga
    Date Deposited: 29 Jan 2004
    Last Modified: 07 Oct 2010 11:12
    Item ID: 1595
    URI: http://philsci-archive.pitt.edu/id/eprint/1595

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