Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T10:19:35.444Z Has data issue: false hasContentIssue false
  • English
  • Français

DECISION THEORY WITHOUT FINITE STANDARD EXPECTED VALUE

Published online by Cambridge University Press:  13 August 2015

Luc Lauwers  and
Peter Vallentyne
Luc Lauwers
Affiliation:
KU Leuven, Faculty of Economics and Business, Naamsestraat 69 – bus 3565, 3000 Leuven, Belgium. Email: [email protected]. URL: http://feb.kuleuven.be/luc.lauwers.
Peter Vallentyne
Affiliation:
University of Missouri, 406 Strickland Hall, Columbia, MO 65211-4160, USA. Email: [email protected]. URL: http://Klinechair.missouri.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract:

We address the question, in decision theory, of how the value of risky options (gambles) should be assessed when they have no finite standard expected value, that is, where the sum of the probability-weighted payoffs is infinite or not well defined. We endorse, combine and extend (1) the proposal of Easwaran (2008) to evaluate options on the basis of their weak expected value, and (2) the proposal of Colyvan (2008) to rank options on the basis of their relative expected value.

Keywords

Pasadena paradoxexpected valueweak expectationsrelative expectations
Type
Articles
Information
Economics & Philosophy , Volume 32 , Issue 3 , November 2016 , pp. 383 - 407
Check for updates
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bartha, P. 2015. Making do without expectations. Mind forthcoming.Google Scholar
Baum, L. E. 1963. On convergence to + ∞ in the law of large numbers. Annals of Mathematical Statistics 34: 219–222.Google Scholar
Colyvan, M. 2008. Relative expectation theory. Journal of Philosophy 105: 37–44.CrossRefGoogle Scholar
Colyvan, M. and Hájek, A.. 2015. Making ado without expectations. Mind forthcoming.Google Scholar
Derman, C. and Robbins, H.. 1955. The strong law of large numbers when the first moment does not exist. Proceedings of the National Academy of Sciences USA 41: 586–587.Google Scholar
Durrett, R. 2005. Probability: Theory and Examples, 3rd edition. Belmont, CA: Thomson Brooks/Cole.Google Scholar
Easwaran, K. 2008. Strong and weak expectations. Mind 117: 633–641.Google Scholar
Easwaran, K. 2014a. Principal values and weak expectations. Mind 123: 517–531.Google Scholar
Easwaran, K. 2014b. Decision theory without representation theorems. Philosophers’ Imprint 14: 1–30.Google Scholar
Erickson, K. B. 1973. The strong law of large numbers when the mean is undefined. Transactions of the American Mathematical Society 185: 371–381.Google Scholar
Feller, W. 1971. An Introduction to Probability Theory and Its Applications, volume 2. New York: John Wiley & Sons.Google Scholar
Fine, T. L. 2008. Evaluating the Pasadena, Altadena, and St. Petersburg gambles. Mind 117: 613–632.Google Scholar
Fishburn, P. 1985. Interval Orders and Interval Graphs. New York, NY: John Wiley & Sons.Google Scholar
Gwiazda, J. 2014. Orderly expectations. Mind 123: 503–516.Google Scholar
Hájek, A. 2009. All values great and small. Manuscript.Google Scholar
Hájek, A. and Nover, H.. 2006. Perplexing expectations. Mind 115: 703–720.CrossRefGoogle Scholar
Hájek, A. and Nover, H.. 2008. Complex expectations. Mind 117: 643–664.CrossRefGoogle Scholar
Lauwers, L. and Vallentyne, P.. 2004. Infinite utilitarianism: more is always better. Economics and Philosophy 20: 307–330.Google Scholar
Lauwers, L. and Vallentyne, P.. 2015. A tree can make a difference. In progress.Google Scholar
Nover, H. and Hájek, A.. 2004. Vexing expectations. Mind 113: 237–249.Google Scholar
Peterson, M. 2011. A new twist to the St. Petersburg paradox. Journal of Philosophy 108: 697–699.Google Scholar
Seidenfeld, T., Schervish, M. J. and Kadane, J. B.. 2009. Preference for equivalent random variables: a price for unbounded utilities. Journal of Mathematical Economics 45: 329–340.Google Scholar
Smith, N. 2014. Is evaluative compositionality a requirement of rationality? Mind 123: 457–502.Google Scholar
Sprenger, J. and Heesen, R.. 2011. The bounded strength of weak expectations. Mind 120: 819–832.Google Scholar