By Patrick Humphreys
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Additional resources for Analyzing and Aiding Decision Processes, 14
Unless one is willing t o conclude that this formulation and these definitions are all completely irrelevant to the problem of evaluating mortality risks, the inconsistency holds. If additional attributes are deemed appropriate EVALUAHON OF MORTALITY RISKS 37 for characterizing mortality risks or if additional concepts of equity and catastrophe avoidance seem reasonable, the degree (but not the fact) of the inconsistency may diminish. The implications of this paper provide some interesting insights, but in no way can be considered a solution to the general problem.
Observation 2. Given the basic model assumptions and a preference to minimize the expected number of lives lost, the utility function for mortality risks must be the additive form (4). This observation almost directly follows from the fact that the sum of the pi's is equal to the expected number of fatalities with any mortality risk vector. If we use expected fatalities as our criterion, the additive utility function must be appropriate. lf we define f to be the number of fatalities resulting from any particular risk situation, a utility function UF for fatalities consistent with the additive UR is UF(f) = -f.
Concerning the former problem, it may be reasonable to assume that an organization should evaluate an individual's risks as the individual would want t o evaluate them. Assuming that the individual wants t o minimize his or her risks, such a utility function should be linear in pi. This linearity condition also follows from a consistency argument which assumes that the relative utility of mortality risk vectors must equal the expected utility of the implied set of fatalities (see Keeney, 1 9 8 0 ~ ) Given .