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  1. A Paradox for Tiny Probabilities and Enormous Values.Nick Beckstead & Teruji Thomas - forthcoming - Noûs.
    We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...)
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  2. How to Save Pascal (and Ourselves) From the Mugger.Avram Hiller & Ali Hasan - forthcoming - Dialogue:1-17.
    In this article, we re-examine Pascal’s Mugging, and argue that it is a deeper problem than the St. Petersburg paradox. We offer a way out that is consistent with classical decision theory. Specifically, we propose a “many muggers” response analogous to the “many gods” objection to Pascal’s Wager. When a very tiny probability of a great reward becomes a salient outcome of a choice, such as in the offer of the mugger, it can be discounted on the condition that there (...)
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  3. Know Your Way Out of St. Petersburg: An Exploration of "Knowledge-First" Decision Theory.Frank Hong - forthcoming - Erkenntnis:1-20.
    This paper explores the consequences of applying two natural ideas from epistemology to decision theory: (1) that knowledge should guide our actions, and (2) that we know a lot of non-trivial things. In particular, we explore the consequences of these ideas as they are applied to standard decision theoretic puzzles such as the St. Petersburg Paradox. In doing so, we develop a “knowledge-first” decision theory and we will see how it can help us avoid fanaticism with regard to the St. (...)
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  4. Unbounded Utility.Zachary Goodsell - 2023 - Dissertation, University of Southern California
  5. On Two Arguments for Fanaticism.Jeffrey Sanford Russell - 2023 - Noûs.
    Should we make significant sacrifices to ever-so-slightly lower the chance of extremely bad outcomes, or to ever-so-slightly raise the chance of extremely good outcomes? *Fanaticism* says yes: for every bad outcome, there is a tiny chance of extreme disaster that is even worse, and for every good outcome, there is a tiny chance of an enormous good that is even better. I consider two related recent arguments for Fanaticism: Beckstead and Thomas's argument from *strange dependence on space and time*, and (...)
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  6. A St Petersburg Paradox for risky welfare aggregation.Zachary Goodsell - 2021 - Analysis 81 (3):420-426.
    The principle of Anteriority says that prospects that are identical from the perspective of every possible person’s welfare are equally good overall. The principle enjoys prima facie plausibility, and has been employed for various theoretical purposes. Here it is shown using an analogue of the St Petersburg Paradox that Anteriority is inconsistent with central principles of axiology.
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  7. How to co-exist with nonexistent expectations.Randall G. McCutcheon - 2021 - Synthese 198 (3):2783-2799.
    Dozens of articles have addressed the challenge that gambles having undefined expectation pose for decision theory. This paper makes two contributions. The first is incremental: we evolve Colyvan's ``Relative Expected Utility Theory'' into a more viable ``conservative extension of expected utility theory" by formulating and defending emendations to a version of this theory proposed by Colyvan and H\'ajek. The second is comparatively more surprising. We show that, so long as one assigns positive probability to the theory that there is a (...)
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  8. The past of predicting the future: A review of the multidisciplinary history of affective forecasting.Maya A. Pilin - 2021 - History of the Human Sciences 34 (3-4):290-306.
    Affective forecasting refers to the ability to predict future emotions, a skill that is essential to making decisions on a daily basis. Studies of the concept have determined that individuals are often inaccurate in making such affective forecasts. However, the mechanisms of these errors are not yet clear. In order to better understand why affective forecasting errors occur, this article seeks to trace the theoretical roots of this theory with a focus on its multidisciplinary history. The roots of affective forecasting (...)
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  9. Infinite Prospects.Jeffrey Sanford Russell & Yoaav Isaacs - 2021 - Philosophy and Phenomenological Research 103 (1):178-198.
    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 (...)
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  10. From the St. Petersburg paradox to the dismal theorem.Susumu Cato - 2020 - Environment and Development Economics 25 (5):423–432.
    This paper aims to consider the meaning of the dismal theorem, as presented by Martin Weitzman [(2009) On modeling and interpreting the economics of catastrophic climate change. Review of Economics and Statistics 91, 1–19]. The theorem states that a standard cost–benefit analysis breaks down if there is a possibility of catastrophes occurring. This result has a significant influence on debates regarding the economics of climate change. In this study, we present an intuitive similarity between the dismal theorem and the St. (...)
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  11. Non-Archimedean Preferences Over Countable Lotteries.Jeffrey Sanford Russell - 2020 - Journal of Mathematical Economics 88 (May 2020):180-186.
    We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.
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  12. Difference Minimizing Theory.Christopher J. G. Meacham - 2019 - Ergo: An Open Access Journal of Philosophy 6.
    Standard decision theory has trouble handling cases involving acts without finite expected values. This paper has two aims. First, building on earlier work by Colyvan (2008), Easwaran (2014), and Lauwers and Vallentyne (2016), it develops a proposal for dealing with such cases, Difference Minimizing Theory. Difference Minimizing Theory provides satisfactory verdicts in a broader range of cases than its predecessors. And it vindicates two highly plausible principles of standard decision theory, Stochastic Equivalence and Stochastic Dominance. The second aim is to (...)
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  13. A Tree Can Make a Difference.Luc Lauwers & Peter Vallentyne - 2017 - Journal of Philosophy 114 (1):33-42.
    We show that it is not possible to extend the ranking of one-stage lotteries based on their weak-expectation to a reflexive and transitive relation on the collection of one- and two-stage lotteries that satisfies two basic axioms, the minimal value axiom and the reduction axiom. We propose an extension that satisfies only the first axiom. This ranking takes payoffs, their probabilities, and the tree structure into account.
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  14. Decision theory without finite standard expected value.Luc Lauwers & Peter Vallentyne - 2016 - Economics and Philosophy 32 (3):383-407.
    :We address the question, in decision theory, of how the value of risky options should be assessed when they have no finite standard expected value, that is, where the sum of the probability-weighted payoffs is infinite or not well defined. We endorse, combine and extend the proposal of Easwaran to evaluate options on the basis of their weak expected value, and the proposal of Colyvan to rank options on the basis of their relative expected value.
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  15. Principal Values and Weak Expectations.K. Easwaran - 2014 - Mind 123 (490):517-531.
    This paper evaluates a recent method proposed by Jeremy Gwiazda for calculating the value of gambles that fail to have expected values in the standard sense. I show that Gwiazda’s method fails to give answers for many gambles that do have standardly defined expected values. However, a slight modification of his method (based on the mathematical notion of the ‘Cauchy principal value’ of an integral), is in fact a proper extension of both his method and the method of ‘weak expectations’. (...)
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  16. The Enigma Of Probability.Nick Ergodos - 2014 - Journal of Cognition and Neuroethics 2 (1):37-71.
    Using “brute reason” I will show why there can be only one valid interpretation of probability. The valid interpretation turns out to be a further refinement of Popper’s Propensity interpretation of probability. Via some famous probability puzzles and new thought experiments I will show how all other interpretations of probability fail, in particular the Bayesian interpretations, while these puzzles do not present any difficulties for the interpretation proposed here. In addition, the new interpretation casts doubt on some concepts often taken (...)
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  17. Capitalization in the St. Petersburg game: Why statistical distributions matter.Mariam Thalos & Oliver Richardson - 2014 - Politics, Philosophy and Economics 13 (3):292-313.
    In spite of its infinite expectation value, the St. Petersburg game is not only a gamble without supply in the real world, but also one without demand at apparently very reasonable asking prices. We offer a rationalizing explanation of why the St. Petersburg bargain is unattractive on both sides (to both house and player) in the mid-range of prices (finite but upwards of about $4). Our analysis – featuring (1) the already-established fact that the average of finite ensembles of the (...)
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  18. A New Twist to the St. Petersburg Paradox.Martin Peterson - 2011 - Journal of Philosophy 108 (12):697-699.
    In this paper I add a new twist to Colyvan's version of the Petrograd paradox.
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  19. Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting.Marie Pfiffelmann - 2011 - Theory and Decision 71 (3):325-341.
    Cumulative Prospect Theory (CPT) does not explain the St. Petersburg Paradox. We show that the solutions related to probability weighting proposed to solve this paradox, (Blavatskyy, Management Science 51:677–678, 2005; Rieger and Wang, Economic Theory 28:665–679, 2006) have to cope with limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggest replacing the weighting functions generally proposed in the literature by another specification which respects the following properties: (1) to solve the paradox, the slope at (...)
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  20. Preference for equivalent random variables: A price for unbounded utilities.Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane - 2009 - Journal of Mathematical Economics 45:329-340.
    When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference and the status quo, (...)
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  21. Relative Expectation Theory.Mark Colyvan - 2008 - Journal of Philosophy 105 (1):37-44.
    Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. (...)
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  22. Strong and weak expectations.Kenny Easwaran - 2008 - Mind 117 (467):633-641.
    Fine has shown that assigning any value to the Pasadena game is consistent with a certain standard set of axioms for decision theory. However, I suggest that it might be reasonable to believe that the value of an individual game is constrained by the long-run payout of repeated plays of the game. Although there is no value that repeated plays of the Pasadena game converges to in the standard strong sense, I show that there is a weaker sort of convergence (...)
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  23. Evaluating the pasadena, altadena, and st petersburg gambles.Terrence L. Fine - 2008 - Mind 117 (467):613-632.
    By recourse to the fundamentals of preference orderings and their numerical representations through linear utility, we address certain questions raised in Nover and Hájek 2004, Hájek and Nover 2006, and Colyvan 2006. In brief, the Pasadena and Altadena games are well-defined and can be assigned any finite utility values while remaining consistent with preferences between those games having well-defined finite expected value. This is also true for the St Petersburg game. Furthermore, the dominance claimed for the Altadena game over the (...)
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  24. Complex Expectations.Alan Hájek & Harris Nover - 2008 - Mind 117 (467):643 - 664.
    In our 2004, we introduced two games in the spirit of the St Petersburg game, the Pasadena and Altadena games. As these latter games lack an expectation, we argued that they pose a paradox for decision theory. Terrence Fine has shown that any finite valuations for the Pasadena, Altadena, and St Petersburg games are consistent with the standard decision-theoretic axioms. In particular, one can value the Pasadena game above the other two, a result that conflicts with both our intuitions and (...)
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  25. Putting expectations in order.Alan Baker - 2007 - Philosophy of Science 74 (5):692-700.
    In their paper, “Vexing Expectations,” Nover and Hájek (2004) present an allegedly paradoxical betting scenario which they call the Pasadena Game (PG). They argue that the silence of standard decision theory concerning the value of playing PG poses a serious problem. This paper provides a threefold response. First, I argue that the real problem is not that decision theory is “silent” concerning PG, but that it delivers multiple conflicting verdicts. Second, I offer a diagnosis of the problem based on the (...)
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  26. In Memory of Richard Jeffrey: Some Reminiscences and Some Reflections on The Logic of Decision.Alan Hájek - 2006 - Philosophy of Science 73 (5):947-958.
    This paper is partly a tribute to Richard Jeffrey, partly a reflection on some of his writings, The Logic of Decision in particular. I begin with a brief biography and some fond reminiscences of Dick. I turn to some of the key tenets of his version of Bayesianism. All of these tenets are deployed in my discussion of his response to the St. Petersburg paradox, a notorious problem for decision theory that involves a game of infinite expectation. Prompted by that (...)
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  27. On the normative dimension of the St. Petersburg paradox.David Teira - 2006 - Studies in History and Philosophy of Science Part A 37 (2):210-223.
    In this paper I offer an account of the normative dimension implicit in D. Bernoulli’s expected utility functions by means of an analysis of the juridical metaphors upon which the concept of mathematical expectation was moulded. Following a suggestion by the late E. Coumet, I show how this concept incorporated a certain standard of justice which was put in question by the St. Petersburg paradox. I contend that Bernoulli would have solved it by introducing an alternative normative criterion rather than (...)
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  28. E. I. Kolchinskii;, K. V. Manoilenko;, M. B. Konashev . U istokov akademicheskoi genetiki v Sankt‐Peterburge. [At the roots of academic genetics in St. Petersburg]. St. Petersburg: Nauka, 2002. [REVIEW]Nikolai Krementsov - 2004 - Isis 95 (4):726-728.
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  29. The St. Petersburg two-envelope paradox.David J. Chalmers - 2002 - Analysis 62 (2):155–157.
    I reason: (1) For any x, if I knew that A contained x, then the odds are even that B contains either 2x or x/2, so the expected amount in B would be 5x/4. So (2) for all x, if I knew that A contained x, I would have an expected gain in switching to B. So (3) I should switch to B. But this seems clearly wrong, as my information about A and B is symmetrical.
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  30. The st. petersburg paradox and Pascal's Wager.Jeff Jordan - 1994 - Philosophia 23 (1-4):207-222.
  31. Time, bounded utility, and the St. Petersburg paradox.Tyler Cowen & Jack High - 1988 - Theory and Decision 25 (3):219-223.
  32. False expectations.Amos Nathan - 1984 - Philosophy of Science 51 (1):128-136.
    Common probabilistic fallacies and putative paradoxes are surveyed, including those arising from distribution repartitioning, from the reordering of expectation series, and from misconceptions regarding expected and almost certain gains in games of chance. Conditions are given for such games to be well-posed. By way of example, Bernoulli's "Petersburg Paradox" and Hacking's "Strange Expectations" are discussed and the latter are resolved. Feller's generalized "fair price, in the classical sense" is critically reviewed.
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  33. Probability and certainty.Emile Borel - 1963 - New York,: Walker.
  34. The Establishment of the Criminological Institute in St. Petersburg.Simeon Grusenberg - 1910 - The Monist 20 (3):472-476.
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