appearance of a newspaper story of this sort to raise the probability of Henry having been
the winner to well above 0.5. And I think that most people would have a similar response.
If we decide that this response is not rational, not epistemically proper in some way, then
we will have to give up almost all uses of testimony. For in most cases, the events to
which eyewitnesses testify have an extremely low antecedent probability.
If my response is rational, however, then it seems to be the case that a single testimony, a
testimony given in many cases by someone whom we do not know at all, is sufficient to
produce an enormous change in probability. Something whose initial probability is so
small as to be almost unimaginable is converted by a single testimony into something that
is substantially more probable than not. I call this the Lottery Surprise. How could a
single testimony have such an enor mous effect on probability? And how does this fact
bear on our assessment of the probability of miracles when there is some testimony at
hand?
I think that there is an answer to these questions, and that answer has a bearing on the
general question of the relation of testimony to probability. The very low initial
probability of Henry's being the winner is generated by thinking of Henry simply as
being one of the 100 million entrants and as having the same chance of winning as any
other entrant. Of course, if there were to be 70 or 80 million grand prize winners drawn,
then Henry would have quite a good chance. His winning would be fairly probable. As it
is, however, grand prize winners are very rare in this lottery—only one in 100 million. So
Henry's winning is very improbable. But it could happen. After all, someone will win,
and it could be Henry.
What about the antecedent probability of this testimony? Not the probability that the
testimony is true, but the probability that this testimony would actually be given
regardless of whether it is true or false. For it is the fact that this testimony is actually
given that constitutes the evidence in this case. And remember that this testimony does
not merely say that someone (unspecified) has won the lottery. It names a particular
person.
The antecedent probability of just that testimony being given is very low. And that
judgment is borne out by experience. For example, in my whole life (so far as I know) I
have never been named in a news story as being a big lottery winner. I cannot recall any
of my friends or acquaintances being identified in this way. Nor can I recall any of my
friends or acquaintances recalling any of their friends or acquaintances being identified in
that way. And so on.
It is crucial to understanding the Lottery Surprise that we be clear about the items to
which we are assigning probabilities. The general proposition that there are mistakes in
newspapers has a probability so close to 1.0 as to be morally certain. And the probability
that the New York Times will have some mistake tomorrow is very high. (After all, that
newspaper regularly publishes about five or ten corrections of stories in the previous
edition.) But the probability that the Times will name me tomorrow as a big lottery
winner is vanishingly low. That particular mistake is so rare that it has not happened even
one single time in the past seventy-five years, and probably it will never happen.
The news story about a lottery winner, therefore, involves two items, and each of them
has a very low antecedent probability. It was antecedently improbable that Henry would
win, for he was only one entrant among 100 million. It was also antecedently improbable
that he would be named in the story as the winner, for his was only one name among 100
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