The Language of Argument

2 6 8

C H A P T E R 1 2 ■ C h o i c e s

1. Though the situation is somewhat far-fetched, suppose you are going to
   the drugstore to buy medicine for a friend who will die without it. You
   have only $10—exactly what the medicine costs. Outside the drugstore
   a young man is playing three-card monte, a simple game in which the
   dealer shows you three cards, turns them over, shifts them briefly from
   hand to hand, and then lays them out, face down, on the top of a box.
   You are supposed to identify a particular card (usually the ace of spades);
   and, if you do, you are paid even money. You yourself are a magician and
   know the sleight-of-hand trick that fools most people, and you are sure
   that you can guess the card correctly nine times out of ten. First, what is
   the expected monetary value of a bet of $10? In this context, would it be
   reasonable to make this bet? Why or why not?


2. Provide an example of your own where a bet can be reasonable even
   though the expected monetary value is unfavorable. Then provide
   another example where the bet is unreasonable even though the expected
   monetary value is favorable. Explain what makes these bets reasonable or
   unreasonable.

Exercise III

Consider the following game: You flip a coin continuously until you get tails

once. If you get no heads (tails on the first flip), then you are paid nothing.

If you get one heads (tails on the second flip), then you are paid $2. If you get

two heads (tails on the third flip), then you are paid $4. If you get three heads,

then you are paid $8. And so on. The general rule is that for any number n, if

you get n heads, then you are paid $2n. What is the expected monetary value

of this game? What would you pay to play this game? Why that amount rather

than more or less?

Discussion Question

Decisions Under Ignorance

So far we have discussed choices where the outcomes of the various options

are not certain, but we know their probabilities. Decisions of this kind are

called decisions under risk. In other cases, however, we do not know the prob-

abilities of various outcomes. Decisions of this kind are called decisions under

ignorance (or, sometimes, decisions under uncertainty). If we do not have any

idea where the probabilities of various outcomes lie, the ignorance is com-

plete. If we know that these probabilities lie within some general range, the

ignorance is partial.

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