2 6 7E x p e c t e d O v e r a l l V a l u ecertainly no, for, even though the expected monetary value is positive, the
odds of winning are still low, and the loss of your total resources would be
personally catastrophic.
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
adjustments in weighing the significance of costs and payoffs. In the exam-
ples 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
marginal 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.
Because of this phenomenon of diminishing marginal value, betting on lot-
teries is an even worse bet than most people suppose. A lottery with a payoff
of $20 million sounds attractive, but it does not seem to be twenty times more
attractive than a payoff of $1 million. So even if the expected monetary value
of your $1 bet in a lottery is the loss of $0.50, the actual value to you is really
something less than this, and so the bet is even worse than it seemed at first.
In general, then, when payoffs are large, the expected overall value of the
payoff to someone is reduced because of the effects of diminishing marginal
value. But not always. It is possible to think of exotic cases in which expected
overall value increases with the size of the payoff. Suppose a witch told you
that she would turn you into a toad if you did not give her $10 million by
tomorrow. You believe her, because you know for a fact that she has turned
others into toads when they did not pay up. You have only $1 to your name,
but you are given the opportunity to participate in the first lottery de-
scribed above, where a $1 ticket gives you 1 chance in 20 million of hitting a
$10 million payoff. We saw that the expected monetary value of that wager
was an unfavorable negative $0.50. But now consider the overall value of $1
to you if you are turned into a toad. Toads have no use for money, so to you,
as a toad, the value of the dollar would drop to nothing. Thus, unless some
other, more attractive alternatives are available, it would be reasonable to buy
a lottery ticket, despite the unfavorable expected monetary value of the wager.97364_ch12_ptg01_263-272.indd 267 15/11/13 11:00 AM
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