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KOLMOGOROV CONDITIONALIZERS CAN BE DUTCH BOOKED (IF AND ONLY IF THEY ARE EVIDENTIALLY UNCERTAIN)

Published online by Cambridge University Press:  21 October 2020

ALEXANDER MEEHAN
Affiliation:
DEPARTMENT OF PHILOSOPHY PRINCETON UNIVERSITY 1879 HALL PRINCETON, NJ08544, USAE-mail: alexandermeehan@princeton.eduE-mail: xueyinz@princeton.edu
SNOW ZHANG
Affiliation:
DEPARTMENT OF PHILOSOPHY PRINCETON UNIVERSITY 1879 HALL PRINCETON, NJ08544, USAE-mail: alexandermeehan@princeton.eduE-mail: xueyinz@princeton.edu

Abstract

A vexing question in Bayesian epistemology is how an agent should update on evidence which she assigned zero prior credence. Some theorists have suggested that, in such cases, the agent should update by Kolmogorov conditionalization, a norm based on Kolmogorov’s theory of regular conditional distributions. However, it turns out that in some situations, a Kolmogorov conditionalizer will plan to always assign a posterior credence of zero to the evidence she learns. Intuitively, such a plan is irrational and easily Dutch bookable. In this paper, we propose a revised norm, Kolmogorov–Blackwell conditionalization, which avoids this problem. We prove a Dutch book theorem and converse Dutch book theorem for this revised norm, and relate our results to those of Rescorla (2018).

Type
Research Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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