David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Mind 113 (450):237-249 (2004)
We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as we want, simply by reordering the pay-off table, yet the game remains unchanged throughout. Formally speaking, the expectation does not exist; but we contend that this presents a serious problem for decision theory, since it goes silent when we want it to speak. We argue that the Pasadena game is more paradoxical than the St. Petersburg game in several respects. We give a brief review of the relevant mathematics of infinite series. We then consider and rebut a number of replies to our paradox: that there is a privileged ordering to the expectation series; that decision theory should be restricted to finite state spaces; and that it should be restricted to bounded utility functions. We conclude that the paradox remains live.
|Keywords||Pasadena game infinite utility|
|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
Kenny Easwaran (2011). Bayesianism I: Introduction and Arguments in Favor. Philosophy Compass 6 (5):312-320.
Jeremy Gwiazda (2014). Orderly Expectations. Mind 123 (490):503-516.
Nicholas J. J. Smith (2014). Is Evaluative Compositionality a Requirement of Rationality? Mind 123 (490):457-502.
A. R. Pruss (2013). Null Probability, Dominance and Rotation. Analysis 73 (4):682-685.
J. McKenzie Alexander (2012). Why the Angels Cannot Choose. Australasian Journal of Philosophy 90 (4):619 - 640.
Similar books and articles
Terrence L. Fine (2008). Evaluating the Pasadena, Altadena, and St Petersburg Gambles. Mind 117 (467):613-632.
Mark Colyvan (2008). Relative Expectation Theory. Journal of Philosophy 105 (1):37-44.
Alan Hájek & Harris Nover (2006). Perplexing Expectations. Mind 115 (459):703 - 720.
Alan Hájek & Harris Nover (2008). Complex Expectations. Mind 117 (467):643 - 664.
J. McKenzie Alexander (2011). Expectations and Choiceworthiness. Mind 120 (479):803-817.
Alan Baker (2007). Putting Expectations in Order. Philosophy of Science 74 (5):692-700.
Kenny Easwaran (2008). Strong and Weak Expectations. Mind 117 (467):633-641.
Martin Peterson (2011). A New Twist to the St. Petersburg Paradox. Journal of Philosophy 108 (12):697-699.
Added to index2009-01-28
Total downloads89 ( #39,728 of 1,781,282 )
Recent downloads (6 months)13 ( #58,736 of 1,781,282 )
How can I increase my downloads?