Dominance in Decision Theory

Abstract

I explore dominance principles in decision theory.

In the first chapter, I argue that risk-sensitive preferences (e.g., the Allais Preferences) are compatible with a plausible event-wise dominance principle, Decomposability, which is closely tied to the Betweenness axiom. Though Betweenness is compatible with Allais Preferences, it is incompatible with popular approaches to accommodating those preferences, such as Lara Buchak's Risk-Weighted Expected Utility Theory. I propose a novel normative interpretation of Weighted Linear Utility Theory that does a better job of accommodating risk-sensitivity while respecting plausible dominance reasoning.

In Chapter 2, I turn to the ongoing debate between Causal and Evidential Decision Theorists. I argue that the debate between causalists and evidentialists is indeed at a stalemate, despite recent critiques of both positions. The common theme, whether it be sophisticated arguments from actual value (due to Ahmed and Spencer) or novel interpretations of decision instability (due to Egan), is that each critique presupposes an understanding of independence, which facts to hold fixed while deliberating, that the target view already rejects.

In Chapter 3, I consider a recent class of alleged counterexamples to Causal Decision Theory due to Ahmed. Ahmed's deterministic cases promise to break the stalemate by showing that CDT requires you to pay for bets you cannot possibly win (given that you take seriously the possibility that your acts might be predetermined). One of Ahmed's counterexamples, Betting on the Laws, can be defused by refining our semantics for counterfactuals with impossible worlds. Another counterexample, Betting on the Past, is indeed a counterexample to CDT. Nonetheless, I argue that a conservative modification of CDT, Selective Causal Decision Theory, overcomes Ahmed's challenge.

In Chapter 4, I suggest that 'standoff', rather than 'stalemate', is a better way of describing the state of the debate between causalists and evidentialists. In a standoff, no reasonable proponent of one view has a reason to change their mind. Nonetheless, from the perspective of someone not already committed to either view, I argue that EDT has significant pragmatic advantages over CDT. For one, CDT seemingly tells you to do things you do not believe you will do (if you consistently follow CDT). Moreover, CDT's advice is highly sensitive to how you frame your options. So, CDT fails to meet several intuitive desiderata for a decision theory - a good reason to adopt EDT.

In Chapter 5, I examine dominance for agents with cyclic preferences. I argue that standard dominance arguments against cyclic preferences, such as the Synchronic Money Pump and the Diachronic Money Pump, fail. Roughly, Money Pumps make vivid the structure of cyclic preferences, but they do not demonstrate that an agent with cyclic preferences would be better off with acyclic preferences. I then consider cyclic preferences in the context of risk. I present a paradoxical case, the EASY LOTTERY, and show that cyclic preferences require you to either i) pay to relabel the tickets of a fair lottery, or ii) violate state-wise dominance. I sketch a version of Skew-Symmetric Bilinear Utility Theory and argue that it is a reasonable rule for comparing acts, despite violating state-wise dominance.

In Chapter 6, I consider the general shape of decision theory without transitivity. Building on the previous chapter, I argue that it is reasonable to choose the option that minimises negative utility-difference when compared to available alternatives; that is, choose the Least Bad option. I sketch some advantages of this rule compared with others proposed in the literature. And though I will not argue that it is the only plausible decision rule, Least Bad serves as proof of concept that transitivity is not a precondition for having well-defined goals and engaging in means-end reasoning directed towards achieving those goals. Show more