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Harris Nover & Alan Hájek (2004). Vexing Expectations.

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  1. Surreal Decisions.Eddy Keming Chen & Daniel Rubio - forthcoming - Philosophy and Phenomenological Research.
    Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...)
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    Decision Theory Without Finite Standard Expected Value.Luc Lauwers & Peter Vallentyne - forthcoming - Economics and Philosophy:1-25.
  3.  11
    Interval Values and Rational Choice.Martin Peterson - forthcoming - Economics and Philosophy:1-8.
  4.  26
    Stakes Sensitivity and Transformative Experience.Rachel Elizabeth Fraser - 2018 - Analysis 78 (1):34-39.
    I trace the relationship between the view that knowledge is stakes sensitive and Laurie Paul’s account of the epistemology of transformative experience. The view that knowledge is stakes sensitive comes in different flavours: one can go for subjective or objective conceptions of stakes, where subjective views of stakes take stakes to be a function of an agent’s non-factive mental states, and objective views of stakes do not. I argue that there is a tension between subjective accounts of stakes sensitivity and (...)
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  5.  26
    Axiological Absolutism and Risk1.Seth Lazar & Chad Lee‐Stronach - 2017 - Noûs 53 (1):97-113.
    Consider the following claim: given the choice between saving a life and preventing any number of people from temporarily experiencing a mild headache, you should always save the life. Many moral theorists accept this claim. In doing so, they commit themselves to some form of ‘moral absolutism’: the view that there are some moral considerations that cannot be outweighed by any number of lesser moral considerations. In contexts of certainty, it is clear what moral absolutism requires of you. However, what (...)
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  6.  25
    We Turing Machines Can't Even Be Locally Ideal Bayesians.Beau Madison Mount - 2016 - Thought: A Journal of Philosophy 5 (4):285-290.
    Vann McGee has argued that, given certain background assumptions and an ought-implies-can thesis about norms of rationality, Bayesianism conflicts globally with computationalism due to the fact that Robinson arithmetic is essentially undecidable. I show how to sharpen McGee's result using an additional fact from recursion theory—the existence of a computable sequence of computable reals with an uncomputable limit. In conjunction with the countable additivity requirement on probabilities, such a sequence can be used to construct a specific proposition to which Bayesianism (...)
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  7.  71
    Satan, Saint Peter and Saint Petersburg.Paul Bartha, John Barker & Alan Hájek - 2014 - Synthese 191 (4):629-660.
    We examine a distinctive kind of problem for decision theory, involving what we call discontinuity at infinity. Roughly, it arises when an infinite sequence of choices, each apparently sanctioned by plausible principles, converges to a ‘limit choice’ whose utility is much lower than the limit approached by the utilities of the choices in the sequence. We give examples of this phenomenon, focusing on Arntzenius et al.’s Satan’s apple, and give a general characterization of it. In these examples, repeated dominance reasoning (...)
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  8.  31
    Orderly Expectations.Jeremy Gwiazda - 2014 - Mind 123 (490):503-516.
    In some games, the products of the probabilities times the payouts result in a series that is conditionally convergent, which means that the sum can vary based on the order in which the products are summed. The purpose of this paper is to address the question: How should such games be valued? We first show that, contrary to widespread belief, summing in the order determined by the mechanism of the game does not lead to the correct value. We then consider (...)
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  9.  44
    Unexpected Expectations.Alan Hájek - 2014 - Mind 123 (490):533-567.
    A decade ago, Harris Nover and I introduced the Pasadena game, which we argued gives rise to a new paradox in decision theory even more troubling than the St Petersburg paradox. Gwiazda's and Smith's articles in this volume both offer revisionist solutions. I critically engage with both articles. They invite reflections on a number of deep issues in the foundations of decision theory, which I hope to bring out. These issues include: some ways in which orthodox decision theory might be (...)
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    Is Evaluative Compositionality a Requirement of Rationality?Nicholas J. J. Smith - 2014 - Mind 123 (490):457-502.
    This paper presents a new solution to the problems for orthodox decision theory posed by the Pasadena game and its relatives. I argue that a key question raised by consideration of these gambles is whether evaluative compositionality (as I term it) is a requirement of rationality: is the value that an ideally rational agent places on a gamble determined by the values that she places on its possible outcomes, together with their mode of composition into the gamble (i.e. the probabilities (...)
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  11.  89
    Idealisations in Normative Models.Mark Colyvan - 2013 - Synthese 190 (8):1337-1350.
    In this paper I discuss the kinds of idealisations invoked in normative theories—logic, epistemology, and decision theory. I argue that very often the so-called norms of rationality are in fact mere idealisations invoked to make life easier. As such, these idealisations are not too different from various idealisations employed in scientific modelling. Examples of the latter include: fluids are incompressible (in fluid mechanics), growth rates are constant (in population ecology), and the gravitational influence of distant bodies can be ignored (in (...)
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  12.  10
    A Generalization of the Pasadena Puzzle.Martin Peterson - 2013 - Dialectica 67 (4):597-603.
    By generalizing the Pasadena puzzle introduced by Nover and Hájek (2004) we show that the sum total of value produced by an act can be made to converge to any real number by applying the Riemann rearrangement theorem, even if the scenario faced by the decision maker is non-probabilistic and fully predictable. A wide range of solutions put forward in the literature for solving the original puzzle cannot solve this generalized version of the Pasadena puzzle.
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  13. Null Probability, Dominance and Rotation.A. R. Pruss - 2013 - Analysis 73 (4):682-685.
    New arguments against Bayesian regularity and an otherwise plausible domination principle are offered on the basis of rotational symmetry. The arguments against Bayesian regularity work in very general settings.
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  14. Why the Angels Cannot Choose.J. McKenzie Alexander - 2012 - Australasian Journal of Philosophy 90 (4):619 - 640.
    Decision theory faces a number of problematic gambles which challenge it to say what value an ideal rational agent should assign to the gamble, and why. Yet little attention has been devoted to the question of what an ideal rational agent is, and in what sense decision theory may be said to apply to one. I show that, given one arguably natural set of constraints on the preferences of an idealized rational agent, such an agent is forced to be indifferent (...)
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    Is Strict Coherence Coherent?Alan Hájek - 2012 - Dialectica 66 (3):411-424.
    Bayesians have a seemingly attractive account of rational credal states in terms of coherence. An agent's set of credences are synchronically coherent just in case they conform to the probability calculus. Some Bayesians impose a further putative coherence constraint called regularity: roughly, if X is possible, then it is assigned positive probability. I look at two versions of regularity – logical and metaphysical – and I canvass various defences of it as a rationality norm. Combining regularity with synchronic coherence, we (...)
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  16. Rationality and Indeterminate Probabilities.Alan Hájek & Michael Smithson - 2012 - Synthese 187 (1):33-48.
    We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our (...)
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  17. Expectations and Choiceworthiness.J. McKenzie Alexander - 2011 - Mind 120 (479):803-817.
    The Pasadena game is an example of a decision problem which lacks an expected value, as traditionally conceived. Easwaran (2008) has shown that, if we distinguish between two different kinds of expectations, which he calls ‘strong’ and ‘weak’, the Pasadena game lacks a strong expectation but has a weak expectation. Furthermore, he argues that we should use the weak expectation as providing a measure of the value of an individual play of the Pasadena game. By considering a modified version of (...)
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  18. Bayesianism I: Introduction and Arguments in Favor.Kenny Easwaran - 2011 - Philosophy Compass 6 (5):312-320.
    Bayesianism is a collection of positions in several related fields, centered on the interpretation of probability as something like degree of belief, as contrasted with relative frequency, or objective chance. However, Bayesianism is far from a unified movement. Bayesians are divided about the nature of the probability functions they discuss; about the normative force of this probability function for ordinary and scientific reasoning and decision making; and about what relation (if any) holds between Bayesian and non-Bayesian concepts.
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  19.  46
    The Bounded Strength of Weak Expectations.J. Sprenger & R. Heesen - 2011 - Mind 120 (479):819-832.
    The rational price of the Pasadena and Altadena games, introduced by Nover and Hájek (2004 ), has been the subject of considerable discussion. Easwaran (2008 ) has suggested that weak expectations — the value to which the average payoffs converge in probability — can give the rational price of such games. We argue against the normative force of weak expectations in the standard framework. Furthermore, we propose to replace this framework by a bounded utility perspective: this shift renders the problem (...)
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  20.  58
    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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