# Thesis

# Phd thesis: Preference Bayesianism: Foundation and Updating

**Abstract. **Uncertainty is prevailing in our lives. Reasoning about uncertainty is thus important. Concerning uncertainty, formal epistemologists extensively study the following two issues: (i) how rational beliefs should be constrained, and (ii) how rational beliefs should be revised upon the receipt of new information. A popular school of thought in formal epistemology that addresses both issues is called Bayesianism, which I will call Classical Bayesianism, to distinguish it from other versions of Bayesianism that I will present in this thesis. Classical Bayesianism assumes that, when faced with uncertainty, rational agents have degrees of belief. And it presents the following two norms to address the two issues, respectively. For (i), Classical Bayesianism imposes Probabilism, which says that rational agents’ degrees of belief are representable by a single probability function. For (ii), Classical Bayesianism imposes Conditionalization, which says that rational agents’ degrees of belief should be revised via Bayes rule. However, both norms are controversial. For Probabilism, it is frequently contended that the precision requirement is unreasonable, and rational agents are allowed to have imprecise degrees of belief. For Conditionalization, the rationale offered for Bayes rule is not uncontroversial. Further, many suggest that Bayes rule can only deal with event occurrence, yet in real-life scenarios, it is unclear how to model various kinds of information as event occurrence. Hence Bayes rule seems to be inapplicable in many real-life scenarios.

In this thesis, I develop a new version of Bayesianism, called Preference Bayesianism, to address these challenges. For the challenges faced by Probabilism, I relax the precision requirement underlying Probabilism. And Preference Bayesianism’s answer to (i) coincides with an existing thesis called Imprecise Probabilism (IP), which says that rational agents’ degrees of belief are representable by a set of probability functions. For the challenges faced by Conditionalization, I use preference relations to model various kinds of information and present a preference revision theory for dealing with general information. The preference revision theory requires agents to make minimal changes to incorporate the newly received information. I offer a novel characterization of Bayes rule as a special case of the preference revision process that makes minimal change, and I also present a theorem characterizing posterior for general information. After that, I show how Preference Bayesianism can address dilation, which is an important problem IP is faced with.

**Thesis Committee:** Uwe Steinhoff (Chair); Max E. Deutsch; Jennifer E. Nado; Richard Pettigrew (External); David P. McCarthy (Supervisor)

# MPhil thesis: Proper scoring rules in epistemic decision theory

**Abstract.** Epistemic decision theory (EpDT) aims to defend a variety of epistemic norms in terms of their facilitation of epistemic ends. One of the most important components of EpDT is known as a scoring rule (used to measure inaccuracies of credences). This thesis addresses some problems about scoring rules in EpDT. I consider scoring rules both for precise credences and for imprecise credences. For scoring rules in the context of precise credences, I examine the rationale for requiring a scoring rule to be strictly proper, and argue that no satisfactory justification has been given. I then investigate one possible response to my argument and show the problems with this response. The conclusion is that there is a further need for justifying the requirement that a scoring rule should be strictly proper for precise credences. For scoring rules in the context of imprecise credences, an impossibility result has been established in the literature purporting to show that no strictly proper, continuous and real-valued scoring rule exists. However, a precise statement of the impossibility result requires precise definitions both of strict propriety and of continuity in the context of imprecise credences. Moreover, the result implies that we need to drop one of the three properties - strict propriety, continuity or being real-valued - to have a scoring rule for applying EpDT to imprecise credences. So, firstly, I offer definitions of strict propriety and of continuity and clarify the impossibility result. Then, I investigate what will happen if we drop one of the three properties. I argue that we should drop the property of being real-valued and I offer the general forms of two kinds of strictly proper, continuous and lexicographic scoring rules for imprecise credences.

**Thesis Committee:** Rafael de Clercq (Chair); Wei Xiong (External); Daniel Waxman; Jiji Zhang (Supervisor).