The Language of Argument

2 4 1

S o m e F a l l a c i e s o f P r o b a b i l i t y

we can go back to flipping coins. Toss a coin until it comes up heads three

times in a row. (This will take less time than you might imagine.) What is the

probability that it will come up heads a fourth time? Put crudely, some people

think that the probability of it coming up heads again must be very small,

because it is unlikely that a fair coin will come up heads four times in a row,

so a tails is needed to even things out. That is wrong. The chances of getting

heads on any given toss are the same, regardless of what happened on previ-

ous tosses. Previous results cannot affect the probabilities on this new toss.

Heuristics

In daily life, we often have to make decisions quickly without full informa-

tion. To deal with this overload of decisions, we commonly employ what

cognitive psychologists call heuristics. Technically, a heuristic is a general

strategy for solving a problem or coming to a decision. For example, a good

heuristic for solving geometry problems is to start with the conclusion you

are trying to reach and then work backward.

Recent research in cognitive psychology has shown, first, that human

beings rely very heavily on heuristics and, second, that we often have too

much confidence in them. The result is that our probability judgments often

go very wrong, and sometimes our thinking gets utterly mixed up. In this

regard, two heuristics are particularly instructive: the representativeness

heuristic and the availability heuristic.

Th e Re pRe s e nT a T i v e n e s s he uR i sT i c. A simple example illustrates how

errors can arise from the representativeness heuristic. Imagine that you are

randomly dealt five-card hands from a standard deck. Which of the follow-

ing two hands is more likely to come up?

Hand #1 Hand #2

Three of clubs Ace of spades

Seven of diamonds Ace of hearts

Nine of diamonds Ace of clubs

Queen of hearts Ace of diamonds

King of spades King of spades

A surprisingly large number of people will automatically say that the second

hand is much less likely than the first. Actually, if you think about it a little,

it should be obvious that any two specific hands have exactly the same like-

lihood of being dealt in a fair game. Here people get confused because the

first hand is unimpressive; and, because unimpressive hands come up all the

time, it strikes us as a representative hand. In many card games, however,

the second hand is very impressive—something worth talking about—and

thus looks unrepresentative. Our reliance on representativeness blinds us

to a simple and obvious point about probabilities: Any specific hand is as

likely to occur as any other.

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