Contingent Free Choice: on Extending Quantum Theory to a Contextual, Deterministic Theory with Improved Predictive Power
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Decision Theory with a Human Face
Decision Theory with a Human Face Richard Bradley April 2016 ii For Shura Contents Preface xi Introduction xiii I Rationality, Uncertainty and Choice 1 1 Decision Problems 3 1.1 Maximisation of Expected Bene…t . 3 1.2 Framing Decisions . 6 1.3 Savage’sTheory . 9 2 Rationality 13 2.1 Moderate Humeanism . 13 2.2 The Choice Principle . 16 2.3 Subjectivism . 19 3 Uncertainty 23 3.1 Evaluative Uncertainty . 24 3.2 Option uncertainty . 27 3.3 Modal Uncertainty . 30 4 Justifying Bayesianism 33 4.1 Pragmatism . 34 4.2 Interpretations of Preference . 36 4.3 Representation Theorems . 38 4.4 Savage’sRepresentation Theorem . 40 4.5 Evaluation of Savage’saxioms . 44 4.5.1 The Sure-thing Principle . 45 4.5.2 State Independence / Rectangular Field . 46 4.5.3 Probability Principle . 47 4.6 Evaluation of Savage’sargument . 49 II Prospective Rationality 53 5 Rational Belief and Desire 55 5.1 Agents . 55 5.2 Prospects . 56 iii iv CONTENTS 5.2.1 Vocabulary . 58 5.2.2 Boolean Algebras* . 58 5.2.3 Conditional Algebras* . 59 5.3 Attitudes . 60 5.3.1 Comparative Relations . 63 5.3.2 Numerical Representation of Comparative Relations* . 65 5.4 Rational Belief and Desire . 66 5.4.1 Numerical Degrees of Belief and Desire . 66 5.4.2 Probabilism . 68 5.4.3 Desirabilism . 69 5.5 Aspirations of Objectivity . 73 6 Conditional Attitudes 77 6.1 Suppositions . 78 6.2 Suppositional Probability and Desirability . 80 6.3 Evidential Supposition . 82 6.3.1 Evidential Conditional Belief . 82 6.3.2 Evidential Conditional Desire . -
Extracting Money from Causal Decision Theorists
Extracting Money from Causal Decision Theorists Caspar Oesterheld∗ , Vincent Conitzer Duke University, Department of Computer Science focaspar, [email protected] Abstract that Newcomb’s problem closely resembles playing a Pris- oner’s Dilemma against a similar opponent [Brams, 1975; Newcomb’s problem has spawned a debate about Lewis, 1979]. Whereas CDT recommends defecting even which variant of expected utility maximization (if in a Prisoner’s Dilemma against an exact copy, EDT rec- any) should guide rational choice. In this paper, ommends cooperating when facing sufficiently similar op- we provide a new argument against what is proba- ponents. What degree of similarity is required and whether bly the most popular variant: causal decision the- EDT and CDT ever come apart in this way in practice has ory (CDT). In particular, we provide two scenarios been the subject of much discussion [Ahmed, 2014, Sec- in which CDT voluntarily loses money. In the first, tion 4.6]. A common view is that CDT and EDT come an agent faces a single choice and following CDT’s apart only under fairly specific circumstances that do not recommendation yields a loss of money in expec- include most human interactions. Still, Hofstadter [1983], tation. The second scenario extends the first to a for example, argues that “superrational” humans should co- diachronic Dutch book against CDT. operate with each other in a real-world one-shot Prisoner’s Dilemma, reasoning in a way that resembles the reasoning done under EDT. Economists have usually been somewhat 1 Introduction dismissive of such ideas, sometimes referring to them as In Newcomb’s problem [Nozick, 1969; Ahmed, 2014], a “be- “(quasi-)magical thinking” when trying to explain observed ing” offers two boxes, A and B. -
Arxiv:1712.05723V4 [Cs.GT] 18 Mar 2020 Department of Computer Science E-Mail: [email protected] 2 Ghislain Fourny
Noname manuscript No. (will be inserted by the editor) Perfect Prediction in Normal Form: Superrational Thinking Extended to Non-Symmetric Games Ghislain Fourny Originally December 15, 2017. Updated February 19, 2020. Abstract This paper introduces a new solution concept for non-cooperative games in normal form with no ties and pure strategies: the Perfectly Transpar- ent Equilibrium. The players are rational in all possible worlds and know each other's strategies in all possible worlds { which, together, we refer to as Perfect Prediction. The anticipation of a player's decision by their opponents is coun- terfactually dependent on the decision, unlike in Nash Equilibria where the decisions are made independently. The equilibrium, when it exists, is unique and is Pareto optimal. This equilibrium is the normal-form counterpart of the Perfect Prediction Equilibrium; the prediction happens \in another room" rather than in the past. The equilibrium can also be seen as a natural extension of Hofstadter's superrationality to non-symmetric games. Algorithmically, an iterated elimi- nation of non-individually-rational strategy profiles is performed until at most one remains. An equilibrium is a strategy profile that is immune against knowl- edge of strategies in all possible worlds and rationality in all possible worlds, a stronger concept than common knowledge of rationality but also stronger than common counterfactual belief of rationality. We formalize and contrast the Non-Nashian Decision Theory paradigm, common to this and several other papers, with Causal Decision Theory and Evidential Decision Theory. We define the Perfectly Transparent Equilibrium algorithmically and prove (when it exists) that it is unique, that it is Pareto- optimal, and that it coincides with Hofstadter's Superrationality on symmetric games. -
Multiverse-Wide Cooperation Via Correlated Decision Making
Multiverse-wide Cooperation via Correlated Decision Making Caspar Oesterheld Abstract Some decision theorists argue that when playing a prisoner’s dilemma-type game against a sufficiently similar opponent, we should cooperate to make it more likely that our opponent also cooperates. This idea, which Hofstadter calls superrationality, has strong implications when combined with the insight from modern physics that we probably live in a large universe or multiverse of some sort. If we care about what happens in civilizations located elsewhere in the multiverse, we can superrationally cooperate with some of their inhabitants. That is, if we take their values into account, this makes it more likely that they do the same for us. In this paper, I attempt to assess the practical implications of this idea. I argue that to reap the full gains from trade, everyone should maximize the same impartially weighted sum of the utility functions of all collaborators. I also argue that we can obtain at least weak evidence about the content of these utility functions. In practice, the application of superrationality implies that we should promote causal cooperation, moral pluralism, moral reflection, and ensure that our descendants, who will be smarter and thus better at finding out how to benefit other superrationalists in the universe, engage in superrational cooperation. Contents 1 Introduction – the basic idea 3 1.1 An overview of the paper . 5 2 Superrationality 7 2.1 Lack of knowledge is evidential power, part I: the other agents . 9 2.2 A short survey of decision theories and their relation to superrationality . 11 2.3 CDT would self-modify to behave like a non-causal decision theory in some Newcomb-like problems . -
Newcomb's Problem, Prisoners' Dilemma, and Collective Action*
S. L, HURLEY NEWCOMB'S PROBLEM, PRISONERS' DILEMMA, AND COLLECTIVE ACTION* ABSTRACT. Among various cases that equally admit of evidentialist reasoning, the supposedly evidentialist solution has varying degrees of intuitive attractiveness. I suggest that cooperative reasoning may account for the appeal of apparently evidentialist behavior in the cases in which it is intuitively attractive, while the inapplicability of cooperative reasoning may account for the unattractiveness of evidentialist behaviour in other cases. A collective causal power with respect to agreed outcomes, not evidentialist reasoning, makes cooperation attractive in the Prisoners' Dilemma. And a natural though unwar- ranted assumption of such a power may account for the intuitive appeal of the one-box response in Newcomb's Problem. 1. NEWCOMB~S PROBLEM AND COMMON CAUSES In Newcomb's Problem, I am offered the choice of taking either just the opaque box in front of me, or both it and another transparent box, in which I can see $1,000. I am told, and believe, that a predictor of human behaviour has already put either nothing or $1,000,000 into the opaque box. He has done so on the basis of whether he predicts that I will take both boxes, or only one. That is, he has put $1,000,000 in the opaque box if and only if he has predicted that I will take just it, and not the other as well. Concerning 99% (or some very high per- centage) of the many other cases of choices made by persons in the same circumstances as myself, the predictor has predicted correctly.