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The Effect of Exchange Rates on Statistical Decisions

Published online by Cambridge University Press:  01 January 2022

Mark J. Schervish ,
Teddy Seidenfeld  and
Joseph B. Kadane
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Abstract

Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unit-less numerical measures of value for consequences. Here, we address the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential decisions. When multiple currencies are available for paying the loss, one must take explicit account of which currency is used as well as the exchange rates between the various available currencies.

Type
Research Article
Information
Philosophy of Science , Volume 80 , Issue 4 , October 2013 , pp. 504 - 532
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

The authors thank two anonymous referees for their helpful suggestions in preparing this article. The first author was supported, in part, by a grant from the Institute of New Economic Thinking.

References

Anscombe, F., and Aumann, R.. 1963. “A Definition of Subjective Probability.” Annals of Mathematical Statistics 34:99–205.CrossRefGoogle Scholar
Braithwaite, R. B. 1955. Theory of Games as a Tool for the Moral Philosopher. Cambridge: Cambridge University Press.Google Scholar
De Finetti, B. 1974. Theory of Probability. 2 vols. New York: Wiley.Google Scholar
Degroot, M. 1970. Optimal Statistical Decisions. New York: Wiley.Google Scholar
Fisburn, P. 1970. Utility Theory for Decision Making. New York: Wiley.CrossRefGoogle Scholar
Gneiting, T. 2011a. “Making and Evaluating Point Forecasts.” Journal of the American Statistical Association 106:746–62.CrossRefGoogle Scholar
Gneiting, T. 2011b. “Quantiles as Optimal Point Forecasts.” International Journal of Forecasting 27:197–207.CrossRefGoogle Scholar
Harsanyi, J. C. 1977. Rational Behavior and Bargaining Equilibrium in Games and Social Situations. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Karni, E., Schmeidler, D., and Vind, K.. 1983. “On State Dependent Preferences and Subjective Probabilities.” Econometrica 51:1021–31.CrossRefGoogle Scholar
Rubin, H. 1987. “A Weak System of Axioms for ‘Rational’ Behavior and the Non-separability of Utility from Prior.” Statistics and Decisions 5:47–58.Google Scholar
Savage, L. 1954. Foundations of Statistics. New York: Wiley.Google Scholar
Savage, L. 1971. “Elicitation of Personal Probabilities and Expectations.” Journal of the American Statistical Association 66:783–801.CrossRefGoogle Scholar
Schervish, M. J. 1989. “A General Method for Comparing Probability Assessors.” Annals of Statistics 17:1856–79.CrossRefGoogle Scholar
Schervish, M. J., Kadane, J. B., and Seidenfeld, T.. 1991. “Shared Preferences and State-Dependent Utilities.” Management Science 37:1575–89.CrossRefGoogle Scholar
Schervish, M. J., Seidenfeld, T., and Kadane, J. B.. 1990. “State-Dependent Utilities.” Journal of the American Statistical Association 85:840–47.CrossRefGoogle 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 45:329–40.CrossRefGoogle Scholar
Shimony, A. 1955. “Coherence and the Axioms of Confirmation.” Journal of Symbolic Logic 20:1–28.CrossRefGoogle Scholar
Smith, C. A. B. 1961. “Consistency in Statistical Inference and Decision.” Journal of the Royal Statistical Society B 23 (1): 1–37..Google Scholar
Von Neumann, J., and Morgenstern, O.. 1947. Theory of Games and Economic Behavior. 2nd ed. Princeton, NJ: Princeton University Press.Google Scholar
Wald, A. 1950. Statistical Decision Functions. New York: Wiley.Google Scholar