ernment funds are allocated to resolve specific problems (for example, to protect a particular species), these funds are normalized and extrapolated to obtain a cost figure; in this case, the value of maintaining biodiversity is established by normalizing the government's annual budget for species protection. If no funds have been allocated, then the method of contingent valuation is employed. This method (or set of methods) is based on direct inquiries of representative populations to determine their willingness to pay to avoid specific effects. As might be expected, this last approach to establishing the appropriate costs of avoidance is controversial because it is hard, both conceptually and practically, to design questions that demonstrably extract the correct measure of value.

The second of these valuation questions reflects the fact that the mathematical structure of the value function is a consequence of critical assumptions about the nature of the subject's preferences. The valuation used in the EPS system is an example of a linear, additive preference structure. Each unit effect is reduced to a monetary value, normalized for risk and exposure and for material quantity. Thereafter, the net impact of each increment in unit effect is the same, regardless of both how large the effect is and the size of any other unit effect. Although such value functions are simple to represent and employ (i.e., as linear combinations of linear functions), they are not the most accurate, general-purpose formulation of value functions for environmental impact. Although the appropriate form of the value function may be linear, EPS does not explicitly make this assumption. Rather, the linearity of the EPS valuation is based on the assumption that, because monetization reduces all effects to a common metric, the resulting metrics should be additive. In fact, most individuals do not even exhibit linear preferences for money, much less for more subjective attributes. (For example, most individuals would consider paying $0.50 to play a game offering a 50:50 chance of winning $1.00, while rejecting out of hand paying $5,000 for a 50:50 chance of winning $10,000.) In practice, preferences usually reflect nonlinearities both in individual effects and in substitution between effects.

A Third Limitation: Individuals Versus Groups

Viewing money as a measure of value and calculating linear additive preferences are not necessarily unworkable approaches when considering the development of value functions for the environment. Although difficult, it may be possible for someone to establish the dollar value that exactly offsets a particular unit effect. Similarly, linear additive preferences may be able to model the behavior of an individual over a restricted range. However, it is impossible to state that every individual in the affected population will agree to the same dollar value or the same summing of preferences for environmental considerations. If individuals cannot agree on the value or the structure of their preferences, then no single value function can be constructed to represent their wants.

Conceptually, value functions are based on the notion of individual prefer-

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