Expected Overall Value or Expected Utility of a Choice

When we examine the effects that success or failure will have on a particular person relative to his or her own needs, resources, preferences, and so on, we are then examining what we shall call the expected overall value or expected utility of a choice. Considerations of this kind often force us to make adjust- ments in weighing the significance of costs and payoffs. In the examples we just examined, the immediate catastrophic consequences of a loss outweigh the long-term gains one can expect from participating in the lottery.

Another factor that typically affects the expected overall value of a bet is the phenomenon known as the diminishing marginal value or diminishing mar- ginal utility of a payoff as it gets larger. Suppose someone offers to pay a debt by buying you a hamburger. Provided that the debt matches the cost of a hamburger and you feel like having one, you might go along with this. But suppose this person offers to pay off a debt ten times larger by buying you ten hamburgers? The chances are that you will reject the offer, for even though ten hamburgers cost ten times as much as one hamburger, they are not worth ten times as much to you. At some point you will get stuffed and not want any more. After one or two hamburgers, the marginal value of one more hamburger becomes pretty low. The notion of marginal value applies to money as well. If you are starving, $10 will mean a lot to you. You might be willing to work hard to get it. If you are wealthy, $10 more or less makes little difference; losing $10 might only be an annoyance.

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