Synthese 195 (10):4205--4241 (2018)

Haim Gaifman
Columbia University
Yang Liu
Cambridge University
In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent.
Keywords subjective probability  expected utilities  Savage postulates  Bayesian decision theory  Boolean algebra
Categories (categorize this paper)
Reprint years 2018
DOI 10.1007/s11229-017-1594-6
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
The Logic of Decision.Richard C. Jeffrey - 1965 - University of Chicago Press.
Truth and Probability.F. Ramsey - 1926 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 52-94.

View all 23 references / Add more references

Citations of this work BETA

Countable Additivity, Idealization, and Conceptual Realism.Yang Liu - 2020 - Economics and Philosophy 36 (1):127-147.
Incomplete Preference and Indeterminate Comparative Probability.Yang Liu - forthcoming - British Journal for the Philosophy of Science:axaa009.

Add more citations

Similar books and articles

Causal Decision Theory.David Lewis - 1981 - Australasian Journal of Philosophy 59 (1):5 – 30.
Introduction.Paul Weirich - 2010 - Synthese 176 (1):1-3.
Subjective Distributions.Itzhak Gilboa & David Schmeidler - 2004 - Theory and Decision 56 (4):345-357.
Information Integration in Risky Decision Making.Norman H. Anderson & James C. Shanteau - 1970 - Journal of Experimental Psychology 84 (3):441.


Added to PP index

Total views
339 ( #26,505 of 2,449,084 )

Recent downloads (6 months)
26 ( #27,279 of 2,449,084 )

How can I increase my downloads?


My notes