David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophy 105 (1):37-44 (2008)
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||No keywords specified (fix it)|
|Categories||categorize this paper)|
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.
Citations of this work BETA
No citations found.
Similar books and articles
Andrew M. Colman (2007). Love is Not Enough: Other-Regarding Preferences Cannot Explain Payoff Dominance in Game Theory. Behavioral and Brain Sciences 30 (1):22-23.
Jeremy Gwiazda (2012). Repeated St Petersburg Two-Envelope Trials and Expected Value. The Reasoner 6 (3).
Alan Baker (2007). Putting Expectations in Order. Philosophy of Science 74 (5):692-700.
Terrence L. Fine (2008). Evaluating the Pasadena, Altadena, and St Petersburg Gambles. Mind 117 (467):613-632.
Alan Hajek (2004). Vexing Expectations. Mind 113 (450):237 - 249.
Alan Hájek & Harris Nover (2008). Complex Expectations. Mind 117 (467):643 - 664.
Harris Nover & Alan Hájek (2008). Complex Expectations. Mind 117 (467):643 - 664.
Alan Hájek & Harris Nover (2006). Perplexing Expectations. Mind 115 (459):703 - 720.
Harris Nover & Alan Hájek (2004). Vexing Expectations. Mind 113 (450):237-249.
Martin Peterson (2011). A New Twist to the St. Petersburg Paradox. Journal of Philosophy 108 (12):697-699.
Added to index2009-01-28
Total downloads17 ( #96,123 of 1,098,955 )
Recent downloads (6 months)3 ( #114,551 of 1,098,955 )
How can I increase my downloads?