Minkyung Wang

This paper employs epistemic decision theory to explore rational bridge principles between probabilistic beliefs and deductively cogent beliefs. I re-examine Hempel and Levi’s epistemic decision theories and generalize them by introducing a novel rationality norm for belief binarization. This norm posits that an agent ought to have binary beliefs that maximize expected utility in light of their credences. Our findings reveal that the proposed norm implies certain geometrical principles, namely convexity norms. Building upon this framework, I critically evaluate the Humean thesis in Leitgeb’s stability theory of belief and Lin-Kelly’s tracking theory. We establish the impossibility results, demonstrating that those theories violate the proposed norms and consequently fail to do the job of expected utility maximization. In contrast, we discover alternative approaches that align with all of the proposed norms, such as generating beliefs that minimize a Bregman divergence from credences. Our epistemic decision theory for belief binarization can be compared to Dorst’s accuracy argument for the Lockean thesis. We conclude that deductively cogent expected accuracy maximizers are neither Lockean nor Humean.

Hybrid belief aggregation addresses aggregation of individual probabilistic beliefs into collective binary beliefs. In line with the development of judgment aggregation theory, our research delves into the identification of precise agenda conditions associated with some key impossibility theorems in the context of hybrid belief aggregation. We determine the necessary and sufficient level of logical interconnection between the propositions in an agenda for some key impossibilities to arise. Specifically, we prove three characterization theorems about hybrid belief aggregation: (i) Precisely the path-connected and pair-negatable agendas lead to the ‘oligarchy result’—only oligarchic rules satisfy universal domain, proposition-wise independence, respect for unanimity, and deductive closure of collective beliefs. (ii) Precisely the negation-connected agendas lead to the ‘triviality result’—only unanimity rules satisfy those conditions as well as anonymity. (iii) Precisely the blocked agendas lead to the ‘non-existence result’—no rules satisfy those conditions as well as completeness and consistency of collective beliefs. Furthermore, we compare these novel findings with existing agenda-theoretic characterization theorems in the domains of judgment aggregation and belief binarization.

This paper investigates the question of how subjective probability should relate to binary belief. We propose new distance minimization methods, and develop epistemic decision-theoretic accounts. Both approaches can be shown to get “close” to the truth: the first one by getting “close” to a given probability, and the second by getting expectedly “close” to the truth. More specifically, we study distance minimization with a refined notion of Bregman divergence and expected utility maximization with strict proper scores. Our main results reveal that the two ways to get “close” to the truth can coincide.

This paper addresses how multiple individual credences on logically related issues should be aggregated into collective binary beliefs. We call this binarizing belief aggregation. It is vulnerable to dilemmas such as the discursive dilemma or the lottery paradox: proposition-wise independent aggregation can generate inconsistent or not deductively closed collective judgments. Addressing this challenge using the familiar axiomatic approach, we introduce general conditions on a binarizing belief aggregation rule, including rationality conditions on individual inputs and collective outputs, and determine which rules (if any) satisfy different combinations of these conditions. Furthermore, we analyze similarities and differences between our proofs and other related proofs in the literature and conclude that the problem of binarizing belief aggregation is a free-standing aggregation problem not reducible to judgment aggregation or probabilistic opinion pooling.