Relative Expectation Theory

Journal of Philosophy 105 (1):37-44 (2008)
Authors
Mark Colyvan
University of Sydney
Abstract
Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. Petersburg game. The problem is that standard decision theory counsels us to be indifferent between any two actions that have infinite expected utility. So, for example, consider the decision problem of whether to play the St. Petersburg game or a game where every payoff is $1 higher. Let’s call this second game the Petrograd game (it’s the same as St. Petersburg but with a bit of twentieth century inflation). Standard decision theory is indifferent between these two options. Indeed, it might be argued that any intuition that the Petrograd game is better than the St. Petersburg game is a result of misguided and na¨ıve intuitions about infinity.2 But this argument against the intuition in question is misguided. The Petrograd game is clearly better than the St. Petersburg game. And what is more, there is no confusion about infinity involved in thinking this. When the series of coin tosses comes to an end (and it comes to an end with probability 1), no matter how many tails precede the first head, the payoff for the Petrograd game is one dollar higher than the St. Petersburg game. Whatever the outcome, you are better off playing the Petrograd game. Infinity has nothing to do with it. Indeed, a straightforward application of dominance reasoning backs up this line of reasoning.3 Standard decision theory
Keywords Analytic Philosophy  Contemporary Philosophy
Categories (categorize this paper)
ISBN(s) 0022-362X  
DOI 10.5840/jphil200810519
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,086
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

No references found.

Add more references

Citations of this work BETA

Surreal Decisions.Eddy Keming Chen & Daniel Rubio - forthcoming - Philosophy and Phenomenological Research.

Add more citations

Similar books and articles

A Micro-Phenomenology of Consonance and Dissonance.Richard Lind - 1997 - Journal of Philosophical Research 22:321-355.
Linearity of Expectation Functionals.Stanley P. Gudder - 1985 - Foundations of Physics 15 (1):101-111.
Probability and Relative Frequency.Michael Drieschner - 2016 - Foundations of Physics 46 (1):28-43.
From Relative Confirmation to Real Confirmation.Aron Edidin - 1988 - Philosophy of Science 55 (2):265-271.
Trust, Staking, and Expectations.Philip J. Nickel - 2009 - Journal of the Theory of Social Behaviour 39 (3):345–362.
Can an Act-Consequentialist Theory Be Agent Relative?Douglas W. Portmore - 2001 - American Philosophical Quarterly 38 (4):363-77.
Complex Expectations.Alan Hájek & Harris Nover - 2008 - Mind 117 (467):643 - 664.
Strange Expectations.Ian Hacking - 1980 - Philosophy of Science 47 (4):562-567.

Analytics

Added to PP index
2009-01-28

Total views
567 ( #5,155 of 2,313,330 )

Recent downloads (6 months)
3 ( #260,283 of 2,313,330 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature