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.