Re: Objection to the Doomsday Argument?

Nick Bostrom (
Thu, 13 Aug 1998 22:02:22 +0000

Doug Baily wrote:

> My objection deals with the problem I see in being able to
> discern between an urn with 10 balls that does not experience an
> increase in its contents in the future and an urn with 10 balls
> that will experience such an increase. The sample that is taken
> which leads us to believe the DA foretells impending doom is
> based on sampling a snapshot population of the "human" urn.

According to the doomsdayer, you are a sample not from a current snapshot of the human race, but rather from the set of all humans (or observers) that will ever have existed (setting to one side John Leslie's view on the relevance of indeterminism). It seems wrong to assume that the the sampling picture works only spatially but not temporally. Ignorance about you spatial position is on a par with ignorance about your temporal position. (Recall Leslie's analogy about the emeralds.)

> We
> currently judge the urn to represent the urn with 10 balls. But,
> how can we be so sure it is not an urn with 10 balls that will
> receive an additional of 9,999,990 balls in the future?

That would be the wrong analogy. Since you are supposed to be a random sample from all observers that will ever have existed, we have to pick the ball from an urn containing all balls that it will ever contain in order to mirror the real situation truthfully

>I don't
> think this is the same objection as the one discussed by Leslie
> on pg. 233 of "The End of the World" (dealing with indeterminism).

No, it rather seems to be similar to the objections he replies to on pp. 214 ff.

> Estimates of human population growth show an exponential growth
> rate back to the origin of population graphs. If you perform the
> DA sample at any point during the history of home sapiens you would
> reach the same conclusion, that extinction is imminent. Yet we've
> done quite well for the past few millions of years. Furthermore, it
> would be obvious that there was a mistake in judgement when applying
> the DA, i.e., strict sampling would have led us to believe we had
> the "urn of 10" situation when, in fact, we had an urn with 10 that
> would experience a vast increase in its contents in the future.

It is true that cavemen would have been misled if they had applied the doomsday argument. As with every probabilistic argument, it doesn't guarantee that you get the right answer; if you are unlucky and happen to be placed in an unusual situation, then you your guess will be wrong.

But try this: Imagine that everybody that will ever have lived applies the doomsday argument and make guesses accordingly. Compare what fraction will turn out to have been right in this case with what happens if they reject the doomsday argument. You'll find that reasoning in accordance with the doomsday argument maximizes the fraction that will be right.

Nick Bostrom
Department of Philosophy, Logic and Scientific Method London School of Economics