WHEN NO PRICE IS RIGHT

The Review of Symbolic Logic · 2024

• Economics

Abstract In this paper, we show how to represent a non-Archimedean preference over a set of random quantities by a nonstandard utility function. Non-Archimedean preferences arise when some random quantities have no fair price. Two common situations give rise to non-Archimedean preferences: random quantities whose values must be greater than every real number, and strict preferences between random quantities that are deemed closer in value than every positive real number. We also show how to extend a non-Archimedean preference to a larger set of random quantities. The random quantities that we consider include real-valued random variables, horse lotteries, and acts in the theory of Savage. In addition, we weaken the state-independent utility assumptions made by the existing theories and give conditions under which the utility that represents preference is the expected value of a state-dependent utility with respect to a probability over states.

Learning and total evidence with imprecise probabilities

International Journal of Approximate Reasoning · 2022 · 2 citations

• Computer Science
• Artificial Intelligence
• Machine Learning

Deceptive Credences

Ergo an Open Access Journal of Philosophy · 2021 · 1 citations

• Computer Science
• Artificial Intelligence
• Mathematical economics

A familiar defense of Personalist or Subjective Bayesian theory is that, under a variety of sufficient conditions, asymptotically—with increasing shared evidence—almost surely, each non-extreme, countably additive Bayesian opinion, when updated by conditionalization, converges to certainty that is veridical about the truth/falsity of hypotheses of interest. Then, with probability 1 over possible evidential histories, personal probabilities track the truth. In this note we examine varieties of failures of these asymptotics. In an extreme case, conditional probabilities are deceptive when they converge to certainty for a false hypothesis. We establish that proposals for so-called “modest” credences, offered by Elga (2016) and by Nielsen and Stewart (2019) in response to a concern about Bayesian orgulity raised by Belot (2013), instead support deceptive credences. We argue that deceptive credences are not modest, but for a reason different than Belot adduces.