10.2190/KC2F-MA8A-DTRE-NQKR KC2FMA8ADTRENQKR 6 Risk Assessment With Lower Probabilities: Application to Toxic Wastes 169 178 20020509 20020509 20020509 20020509 KC2FMA8ADTRENQKR.pdf http://baywood.metapress.com/link.asp?target=contribution&id=KC2FMA8ADTRENQKR 2 Bruce Tonn Carl Wagner Oak Ridge National Laboratory, Oak Ridge University of Tennessee, Knoxville Traditional approaches to the quantitative analysis of uncertainty employ probabilities, although evidence to support the principled assessment of such additive measures is often lacking. We show how both optimization and conditionalization can be carried out using the less structured, hence more realistic, class of lower probabilities, illustrating these techniques with a problem involving toxic wastes. A. Dempster, Upper and Lower Probabilities Induced by a Multivalued Mapping, <i>Annals of Mathematical Statistics, 38</i>, pp. 325-339, 1967. L. Shapley, Cores of Convex Games, <i>International journal of Game Theory, 1</i>, pp. 11-26, 1971. A. Chateauneuf and J. Jaffray, Some Characterizations of Lower Probabiliites and Other Monotone Capacities through the Use of Möbius Inversion, <i>Mathematical Social Sciences, 17</i>, pp. 263-283, 1989. C. Wagner, Generalized Probability Kinematics, <i>Research Report</i>, Mathematics Department, University of Tennessee, Knoxville, Tennessee, 1989. C. Wagner and B. Tonn, Diagnostic Conditionalization, <i>Mathematical Social Sciences, 19</i>, pp. 159-165, 1990. C. Sundberg and C. Wagner, <i>Convex Capacities and Generalized Conditionalization</i>, Technical Report, University of Tennessee, Knoxville, 1990. R. Jeffrey, <i>The Logic of Decision</i>, (2nd Edition), University of Chicago Press, Chicago, Illinois, 1983. R. Jeffrey, Conditioning, Kinematics, and Exchangeability, in <i>Causation, Chance, and Credence</i>, Vol. I, B. Skyrms and W. Harper (eds.), Kluwer, Dordrecht, Netherlands, 1988. G. Shafer, <i>A Mathematical Theory of Evidence</i>, Princeton University Press, Princeton, New Jersey, 1976. P. Diaconis and S. Zabell, Some Alternatives to Bayes' Rule, in <i>Information Pooling and Group Decision Making</i>, B. Grofman and G. Owen (eds.), JAI Press, Greenwich, Connecticut, 1986.