Abstract
Indices and orderings are developed for evaluating alternative strategies in the management of risk. They reflect the goals of reducing individual and collective risks, of increasing equity, and of assigning priority to the reduction and to the equity of high risks. Individual risk is defined as the (random or non-random) level of exposure to a danger. In particular the role of a lower negligibility level is investigated. A class of indices is proposed which involves two parameters, a negligibility level and a parameter of inequality aversion, and several interpretations of the indices are discussed. We provide a set of eight axioms which are necessary and sufficient for this class of indices, and we present an approach to deal with partial information on the parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Atkinson, A.B.: 1970, ‘On the measurement of inequality’, J. of Economic Theory 2, 244-263.
Debreu, G.: 1960, ‘Topological methods in cardinal utility theory’, in Mathematical Models in the Social Sciences, K.J. Arrow, S. Karlin, and P. Suppes (eds.), 16-26. Stanford: Stanford University Press.
Døderlein, J.M.: 1987, ‘Introduction’, in Risk and Decisions, W.T. Singleton and J. Hovden (eds.), 1-8. Chichester: J. Wiley.
Fishburn, P.C.: 1976, ‘Continua of stochastic dominance relations for bounded probability distributions’, Journal of Mathematical Economics 3, 295-311.
Fishburn, P.C.: 1980, ‘Continua of stochastic dominance relations for unbounded probability distributions’, Journal of Mathematical Economics 7, 271-285.
Foster, J.E., and Shorrocks A.F.: 1987, ‘Transfer sensitive inequality measures’, Review of Economic Studies 54, 485-497.
Gollier, C.: 1993, Comment on Working Paper No. 2. Proceedings of the CEC Workshop, June 1993. CEPN, Report No. 217, pp. 51-54.
Harsanyi, J.C.: 1953, ‘Cardinal utility in welfare economics and in the theory of risk-taking’, Journal of Political Economy 61, 434-435.
International Commission on Radiological Protection [ICRP]: 1991, 1990 Recommendations of the ICRP. ICRP Publication 60. Oxford and New York: Pergamon Press.
Kolm, S.C.: 1969, ‘The optimal production of social justice’, in Public Economics, J. Marjolis and H. Guitton, (eds.), 145-200. New York: Macmillan.
Mosler, K.: 1994, ‘Majorization in economic disparity measures’, Linear Algebra and Its Applications 199, 91-114.
Raiffa, H.: 1982, ‘Science and policy: their separation and integration in risk decisions’, in Risk Analysis Controversy, H.C. Kunreuther and E.V. Ley (eds.), 27-37. Berlin: Springer-Verlag.
Rolski, T.: 1976, ‘Order Relations in the Set of Probability Distribution Functions and Their Applications in Queueing Theory’, Warszawa, Dissertationes Mathematicae No. 132.
Schneider, T., Schieber, C., and Eeckhoudt, L.: 1993, ‘Equity and Radiological Risk Management,’ Proceedings of the CEC Workshop, June 1993. CEPN, Report No. 217, pp 36-50.
Vlek, C., and Stallen P.J.: 1981, ‘Judging risks and benefits in the small and in the large’, Organizational Behaviour and Human Performance 38, 235-271.
von Winterfeldt, D., and Edwards, W.: 1986, Decision Analysis and Behavioral Research. Cambridge: University Press.
Wakker, P.: 1989, Additive Representations of Preferences, Dordrecht: Kluwer.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mosler, K. De minimis and equity in risk. Theory and Decision 42, 215–233 (1997). https://doi.org/10.1023/A:1004963010158
Issue Date:
DOI: https://doi.org/10.1023/A:1004963010158