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Infinite Prospects *
Author(s) -
Russell Jeffrey Sanford,
Isaacs Yoaav
Publication year - 2021
Publication title -
philosophy and phenomenological research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.7
H-Index - 39
eISSN - 1933-1592
pISSN - 0031-8205
DOI - 10.1111/phpr.12704
Subject(s) - countable set , mathematical economics , axiom independence , axiom , generalization , independence (probability theory) , von neumann architecture , outcome (game theory) , constraint (computer aided design) , mathematics , preference , representation theorem , independence of irrelevant alternatives , epistemology , discrete mathematics , philosophy , pure mathematics , social choice theory , statistics , geometry
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.