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Rationality and Expected Utility Rationality and Expected Utility by Maxwell Gee A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Philosophy in the Graduate Division of the University of California, Berkeley Committee in Charge: Associate Professor Lara Buchak, Co-Chair Professor Niko Kolodny, Co-Chair Associate Professor David Ahn Summer 2015 Abstract Rationality and Expected Utility by Maxwell Gee Doctor of Philosophy in Philosophy University of California, Berkeley Professor Niko Kolodny, Co-Chair Associate Professor Lara Buchak, Co-Chair We commonly make a distinction between what we simply tend to do and what we would have done had we undergone an ideal reasoning process|or, in other words, what we would have done if we were perfectly rational. Formal decision theories, like Expected Utility Theory or Risk-Weighted Expected Utility Theory, have been used to model the considerations that govern rational behavior. But questions arise when we try to articulate what this kind of modeling amounts to. Firstly, it is not clear how the components of the formal model correspond to real-world psychological or physical facts that ground judgments about what we ought to do. Secondly, there is a great deal of debate surrounding what an accurate model of rationality would look like. Theorists disagree about how much flexibility a rational agent has in weighing the risk of a loss against the value of potential gains, for example. The goal of this project is to provide an interpretation of Expected Utility Theory whereby it explicates or represents the pressure that fundamentally governs how human agents ought to behave. That means both articulating how the components of the formal model correspond to real-world facts, and defending Expected Utility Theory against alternative formal models of rationality. 1 Contents 1 Introduction 1 1.1 The Expected Utility Theorem and a Substantive Notion of Rationality1 1.1.1 Past Attempts at Answering These Questions . .4 1.1.2 Sen and the Problem of Action Explanation . .6 1.2 Project Thesis and Outline . .8 1.2.1 Chapter 1: Teleological Functionalism . 10 1.2.2 Chapter 2: The Steps in Practical Reasoning . 11 1.2.3 Chapter 3: Providing an EUM Interpretation . 11 1.2.4 Chapter 4: Coherentism . 12 1.2.5 Chapter 5: Defending the Independence Axiom . 12 2 Teleological Functionalism 15 2.1 Introduction . 15 2.1.1 Chapter Thesis and Plan . 16 2.2 The Deontic Normative Relation . 16 2.2.1 Challenges for a Theory of Deontic Normative Pressure . 18 2.2.2 4 Success Conditions on a Theory of Deontic Normative Pressure 21 2.3 Teleological Functionalism . 23 2.3.1 Teleological Functionalism Defined . 27 2.3.2 Teleological Functionalism and Causal Explanation . 31 2.3.3 Two Objections to Teleological Functionslism . 34 2.3.4 Teleological Functionalism and Deontic Normativity: our Four Success Conditions . 37 2.4 Foot and Biological Norms . 38 2.5 Conclusions . 39 3 The Steps in Practical Reasoning 41 3.1 Introduction . 41 i 3.1.1 Thesis and Plan . 42 3.2 Mental States and Deontic Normative Bridges . 43 3.3 Discovering the Steps in Practical Reasoning . 44 3.3.1 An Aside: Basic Versus Complex Normative Judgments . 45 3.3.2 Reasoning to a Particular Action . 46 3.3.3 From Judgments about Actions to Acting . 47 3.3.4 From What Is to What Ought to Be . 48 3.3.5 Objections to Externalism `Minus Desire' . 51 3.3.6 Two Objections to Internalism . 54 3.3.7 Externalism `Plus Desire' . 61 3.3.8 Conclusion: The Implications for EUM . 64 3.4 Teleological Functionalism and Normative Bridges . 65 3.4.1 Beliefs . 65 3.4.2 Desires . 66 3.4.3 Intentions and the Will . 73 3.4.4 Teleological Functionalism and Normative Bridges . 73 3.5 Formal Modeling and Resolute Choice . 75 3.5.1 McClennen and Gauthier . 77 3.5.2 Formal Separability and EUM . 78 3.5.3 Formal Separability and Feasibility . 81 3.6 Conclusions . 82 3.6.1 The Experience of Reasoning . 82 3.6.2 No Normative View from Nowhere . 82 3.6.3 Next Steps . 83 4 An Interpretation of Expected Utility Theory 85 4.1 Introduction . 85 4.1.1 Thesis and the Plan . 86 4.2 Interpreting the Formal Model . 87 4.2.1 Preference Orderings and Utility . 87 4.2.2 Outcomes . 88 4.2.3 The Axioms and/or the Idea of Maximizing Utility . 89 4.3 Basic `Ought' Judgments . 90 4.3.1 The v(φ) Function and No Interaction Effects . 94 4.4 A Rational Justification for Compliance with EUM Axioms . 98 4.4.1 Transitivity . 99 4.4.2 Completeness . 101 4.4.3 Continuity . 105 ii 4.4.4 Independence . 108 4.5 TF Solutions to the Tension between NR and CR . 109 4.5.1 TNC1 and Reply . 109 4.5.2 TNC2 and Reply . 112 4.5.3 Objection: Do we really need to respond to TNC? . 113 4.6 Conclusion . 114 5 Coherentism 115 5.1 Introduction . 115 5.1.1 The Thesis and the Plan . 117 5.2 Detecting the Presence of Norms of Coherence as Such . 118 5.3 Davidson and Lewis: Radical Interpretation . 121 5.3.1 Radical Interpretation and Norms of Coherence as Such . 124 5.3.2 My Objections . 125 5.4 Dreier: The Founding Spirit of Decision Theory . 128 5.5 Armendt: Being `Of Two Minds' . 136 5.6 Three Problems with Norms of Coherence as Such . 138 5.6.1 Radical Inconsistency . 143 5.7 Instrumentalism, Parity, and Exploitability . 143 5.8 Conclusions . 147 6 A Defense of the Independence Axiom 149 6.1 Introduction . 149 6.1.1 Thesis and the Plan . 153 6.2 EUM and Global Property Sensitivity . 155 6.3 Basic `Ought' Judgments in REU . 158 6.4 Independence and Group Decision . 161 6.5 Independence and Inferences about Efficacy . 164 6.6 Independence and Sequential Choice . 167 6.6.1 Long Term Decision Making . 167 6.6.2 Valuing Lotteries by their Parts . 173 6.7 Independence in the Real World . 178 6.8 On the Tendency to Violate Independence . 181 6.8.1 Objection: TF and the Problem of Reflective Irrationality . 183 6.8.2 Failed Reply 1: Coherence with Other Concepts . 183 6.8.3 Failed Reply 2: The Existence of Actual REU Agents . 184 6.8.4 Failed Reply 3: Practical Disjunctivism . 184 6.8.5 A Working Reply: Desires for Risk Profiles . 186 iii 6.8.6 A Working Reply: Evolved Heuristics, the Discovery of Risk, and Extrapolating Intuitions to Principles . 187 6.9 Conclusions . 189 6.9.1 On This Chapter . 189 6.9.2 Regarding the Overall Project . 190 7 Appendix 197 7.1 Introduction . 197 7.2 Chapter 3 . 198 7.2.1 Theorem 1: Linearity . 199 7.2.2 Theorem 2.1: That for any outcomes, !A and !B, that v(φ) is in compliance with the above axioms implies that a tradeoff rate ((1)-(3) for some r=s) exists between !A and !B...... 199 7.2.3 Theorem 2.2: That the tradeoff rate r=s between !A and !B is fixed. That is, if there exists a tradeoff rate x=y between !A and !B then x=y = r=s...................... 200 7.2.4 Theorem 3: That if l1 l2 then there exist two partitions Φl1 and Φl2, each with n members, such that for all i from 1 to n, v(φl1i) > v(φl2i)........................... 200 7.2.5 Continuity from the Definition of v(φ)............. 201 7.2.6 Independence from the Definition of v(φ)............ 201 7.3 Chapter 5 . 202 7.3.1 Mission to Mars . 202 7.3.2 Antibiotics . 203 7.3.3 Riflery Competition . 205 iv Chapter 1 Introduction 1.1 The Expected Utility Theorem and a Substan- tive Notion of Rationality This project is about the applicability of Expected Utility Theory to rational human decision making. By `rational' I do not mean representability by a complete and transitive preference ordering (although that may ultimately be a consequence of rationality). We make a common distinction between what we simply tend to do and what we would have done had we undergone an ideal reasoning process. For example, I might fail to accurately calculate the expected income from an investment, or I might be overcome by a desire for cake even though I would prefer to eat healthy. In cases like this there is a sense in which am not behaving ideally, that I am not as I ought to be|that I am getting in my own way. This sense of ideal decision making is what I mean by rationality. So another way of putting the goal of this project is to provide an interpretation of Expected Utility Theory whereby it explicates or represents the structure of deontic normative pressure|the pressure that fundamentally governs how human agents ought to behave. This description might not be perfectly clear baldly stated, so I want to make it a bit clearer by highlighting what exactly is involved in meeting this goal and why one would want to do it or expect it could be done. We will take Expected Utility Theory to refer, first and foremost, to a structure that is almost purely formal. This structure can be characterized by the Expected Utility Theorem, which is just the idea that if a ranking obeys certain axioms, then it will be possible to assign numbers called utilities to each object being ranked such that vector space mixtures of those objects have utility numbers according to the 1 following rule when N is the number of objects N (Utility of the mixture) = P (Utility of object n)∗(Weight of object n in the n=1 vector).
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