In C', the probability of being behind a blue door remains at 99% (as you wished it to), both for whoever is killed, and for the survivor(s). But the reason for this is that everyone finds out all the facts, and the survivor(s) know that even if the coin flip had went the other way, they would have known the facts, only before being killed, while those who are killed know that they would have known the facts afterward, if the coin flip had went the other way.

Telling the people something just before death changes something for the survivors, because the sur... (Read more)(Click to expand thread. ⌘F to Expand All)Cmd/Ctrl F to expand all comments on this post

I don't see it. In D, you are informed that 100 people were created, separated in two groups, and each of them had then 50% chance of survival. You survived. So calculate the probability and

P(red|survival)=P(survival and red)/P(survival)=0.005/0.5=1%.

Not 50%.

0Stuart_Armstrong10y What is your feeling in the case where the victims are first told they will be killed, then the situation is explained to them and finally they are killed? Similarly, the survivors are first told they will survive, and then the situation is explained to them.

Avoiding doomsday: a "proof" of the self-indication assumption

by Stuart_Armstrong 10y23rd Sep 20092 min read238 comments


EDIT: This post has been superceeded by this one.

The doomsday argument, in its simplest form, claims that since 2/3 of all humans will be in the final 2/3 of all humans, we should conclude it is more likely we are in the final two thirds of all humans who’ve ever lived, than in the first third. In our current state of quasi-exponential population growth, this would mean that we are likely very close to the final end of humanity. The argument gets somewhat more sophisticated than that, but that's it in a nutshell.

There are many immediate rebuttals that spring to mind - there is something about the doomsday argument that brings out the certainty in most people that it must be wrong. But nearly all those supposed rebuttals are erroneous (see Nick Bostrom's book Anthropic Bias: Observation Selection Effects in Science and Philosophy). Essentially the only consistent low-level rebuttal to the doomsday argument is to use the self indication assumption (SIA).

The non-intuitive form of SIA simply says that since you exist, it is more likely that your universe contains many observers, rather than few; the more intuitive formulation is that you should consider yourself as a random observer drawn from the space of possible observers (weighted according to the probability of that observer existing).

Even in that form, it may seem counter-intuitive; but I came up with a series of small steps leading from a generally accepted result straight to the SIA. This clinched the argument for me. The starting point is:

A - A hundred people are created in a hundred rooms. Room 1 has a red door (on the outside), the outsides of all other doors are blue. You wake up in a room, fully aware of these facts; what probability should you put on being inside a room with a blue door?

Here, the probability is certainly 99%. But now consider the situation:

B - same as before, but an hour after you wake up, it is announced that a coin will be flipped, and if it comes up heads, the guy behind the red door will be killed, and if it comes up tails, everyone behind a blue door will be killed. A few minutes later, it is announced that whoever was to be killed has been killed. What are your odds of being blue-doored now?

There should be no difference from A; since your odds of dying are exactly fifty-fifty whether you are blue-doored or red-doored, your probability estimate should not change upon being updated. The further modifications are then:

C - same as B, except the coin is flipped before you are created (the killing still happens later).

D - same as C, except that you are only made aware of the rules of the set-up after the people to be killed have already been killed.

E - same as C, except the people to be killed are killed before awakening.

F - same as C, except the people to be killed are simply not created in the first place.

I see no justification for changing your odds as you move from A to F; but 99% odd of being blue-doored at F is precisely the SIA: you are saying that a universe with 99 people in it is 99 times more probable than a universe with a single person in it.

If you can't see any flaw in the chain either, then you can rest easy, knowing the human race is no more likely to vanish than objective factors indicate (ok, maybe you won't rest that easy, in fact...)

(Apologies if this post is preaching to the choir of flogged dead horses along well beaten tracks: I was unable to keep up with Less Wrong these past few months, so may be going over points already dealt with!)


EDIT: Corrected the language in the presentation of the SIA, after SilasBarta's comments.

EDIT2: There are some objections to the transfer from D to C. Thus I suggest sliding in C' and C'' between them; C' is the same as D, execpt those due to die have the situation explained to them before being killed; C'' is the same as C' except those due to die are told "you will be killed" before having the situation explained to them (and then being killed).