Jeffrey Sanford Russell
University of Southern California
Yoaav Isaacs
Baylor University
People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have.
Keywords infinite decision theory  St. Petersburg paradox  dominance principles  unbounded utilities  infinite utilities
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DOI 10.1111/phpr.12704
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Surreal Decisions.Eddy Keming Chen & Daniel Rubio - 2020 - Philosophy and Phenomenological Research 100 (1):54-74.
Evidence: A Guide for the Uncertain.Kevin Dorst - 2020 - Philosophy and Phenomenological Research 100 (3):586-632.
Time-Slice Rationality.Brian Hedden - 2015 - Mind 124 (494):449-491.

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