Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T11:15:20.421Z Has data issue: false hasContentIssue false

UNACCEPTABLE RISKS AND THE CONTINUITY AXIOM

Published online by Cambridge University Press:  22 March 2012

Karsten Klint Jensen*
Affiliation:
University of Copenhagen, [email protected]

Abstract

Consider a sequence of outcomes of descending value, A > B > C > . . . > Z. According to Larry Temkin, there are reasons to deny the continuity axiom in certain ‘extreme’ cases, i.e. cases of triplets of outcomes A, B and Z, where A and B differ little in value, but B and Z differ greatly. But, Temkin argues, if we assume continuity for ‘easy’ cases, i.e. cases where the loss is small, we can derive continuity for the ‘extreme’ case by applying the axiom of substitution and the axiom of transitivity. The rejection of continuity for ‘extreme’ cases therefore renders the triad of continuity in ‘easy’ cases, the axiom of substitution and the axiom of transitivity inconsistent.

As shown by Arrhenius and Rabinowitz, Temkin's argument is flawed. I present a result which is stronger than their alternative proof of an inconsistency. However, this result is not quite what Temkin intends, because it only refers to an ordinal ranking of the outcomes in the sequence, whereas Temkin appeals to intuitions about the size of gains and losses. Against this background, it is argued that Temkin's trilemma never gets off the ground. This is because Temkin appeals to two mutually inconsistent conceptions of aggregation of value. Once these are clearly separated, it will transpire, in connection with each of them, that one of the principles to be rejected does not appear plausible. Hence, there is nothing surprising or challenging about the result; it is merely a corollary to Expected Utility Theory.

Type
Articles
Copyright
Copyright © Cambridge University Press 2012

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

Arrhenius, G. and Rabinowicz, W. 2005. Value and unacceptable risk. Economics and Philosophy 21: 177197.Google Scholar
Danielsson, S. 2004. Temkin, Archimedes and the transitivity of ‘Better’. In Patterns of Value: Essays on Formal Axiology and Value Analysis, Volume 2, ed. W. Rabinowicz and T. Rønnow-Rasmussen, 175–179. Lund Philosophy Reports.Google Scholar
Hausner, M. 1954. Multidimensional utilities. In Decision Processes, ed. Thrall, R.M., Coombs, C.H. and Davis, R.L., 167180. New York: John Wiley.Google Scholar
Jensen, K.K. 2008. Millian superiorities and the repugnant conclusion. Utilitas 20: 279300.Google Scholar
Krantz, D.H., Luce, D.R., Suppes, P. and Tversky, A. 1971. Foundations of Measurement. Vol. 1: Additive and Polynomial Representations. San Diego: Academic Press.Google Scholar
Narens, L. 1974. Minimal conditions for additive conjoint measurement and qualitative probability. Journal of Mathematical Psychology 11: 404430.Google Scholar
Robinson, A. 1974. Non-Standard Analysis, Revised edition. Amsterdam: North-Holland.Google Scholar
Temkin, L. 2001. Worries about continuity, expected utility theory, and practical reasoning. In Exploring Practical Philosophy: From Action to Values, eds. Egonsson, D., Josefsson, J., Petersson, B. and Rønnow-Rasmusen, T., 95108. Aldershot: Ashgate Publishers.Google Scholar