Avoiding doomsday: a “proof” of the self-indication assumption

EDIT: This post has been su­perceeded by this one.

The dooms­day ar­gu­ment, in its sim­plest form, claims that since 23 of all hu­mans will be in the fi­nal 23 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).