Economics and Philosophy 36 (1):127-147 (2020)

Authors
Yang Liu
Cambridge University
Abstract
This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory -- in particular, Savage's theory of subjective expected utility and personal probability. I show that Savage's reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealised assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value of sophisticated mathematical structures employed in applied sciences like decision theory. In the last part, I introduce countable additivity into Savage's theory and explore some technical properties in relation to other axioms of the system.
Keywords countable additivity  foundations of probability  Bayesian decision theory  idealisation  conceptual realism
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References found in this work BETA

The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
Countable Additivity and Subjective Probability.Jon Williamson - 1999 - British Journal for the Philosophy of Science 50 (3):401-416.

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