Alternatives to expected utility

Suppose we don't want to (or can't) come up with reasonable probabilities for our decision tree. Then we can't use all that nice mathematical machinery I just described. Are we dead in the water?¹² No. There are a couple of alternatives we can try.

Let's return to our example of whether to regulate air pollution.¹³ Suppose that there could be either no damage, low damage, or high damage to forest trees and there could be either lax pollution control, moderate control, or stringent control. That makes nine possible combinations of levels of regulation and damage. With each of those combinations there's a cost: the cost of regulation and the costs associated with damage to the forest. Those costs are summarized in Table 1.

Table 1: Total costs associated with different combinations of regulation and forest damage (modified [3]).

	No damage	Low damage	High damage
Stringent control	9	10	11
Moderate control	1	5	14
Lax control	0	10	30

If we knew the probability of each outcome given a choice of control measures, we could calculate the expected cost associated with each choice (low, moderate, or stringent control) and choose the one with the lowest expected cost. But that's not the only choice we could make.