Solving the Doomsday argument

The Dooms­day ar­gu­ment gives an an­thropic ar­gu­ment for why we might ex­pect doom to come rea­son­ably soon. It’s known that the Dooms­day ar­gu­ment works un­der SSA, but not un­der SIA.

Ok, but since differ­ent an­thropic prob­a­bil­ity the­o­ries are cor­rect an­swers to differ­ent ques­tions, what are the ques­tion ver­sions of the Dooms­day ar­gu­ment, and is the origi­nal claim cor­rect?

No Dooms­day on birth rank

Sim­plify the model into as­sum­ing there is a large uni­verse (no Dooms­day any time soon) with many, many fu­ture hu­mans, and a small one (a Dooms­day rea­son­ably soon—within the next 200 billion peo­ple, say), with equal prob­a­bil­ity. In or­der to think in terms of fre­quen­cies, which comes more nat­u­rally to hu­mans, we can imag­ine run­ning the uni­verse many, many times, each with the Dooms­day chance.

There are roughly a 108.5 billion hu­mans who have ever lived. So, ask­ing:

  • What pro­por­tion of peo­ple with birth rank 108.5 billion, live in a small uni­verse (with a Dooms­day rea­son­ably soon)?

The an­swer to that ques­tion con­verges to , the SIA prob­a­bil­ity. Half of the peo­ple with that birth rank live in small uni­verses, half in large uni­verses.

Dooms­day for time travellers

To get an SSA ver­sion of the prob­lem, we can ask:

  • What pro­por­tion of uni­verses, where a ran­domly se­lected hu­man has a birthrank of 108.5 billion, will be small (with a Dooms­day rea­son­ably soon)?

This will give an an­swer close to as it con­verges on the SSA prob­a­bil­ity.

But note that this is gen­er­ally not the ques­tion that the Dooms­day ar­gu­ment is pos­ing. If there is a time trav­el­ler who is choos­ing peo­ple at ran­dom from amongst all of space and time—then if they hap­pen to choose you, that is a bad sign for the fu­ture (and yet an­other rea­son you should go with them). Note that this is con­sis­tent with con­ser­va­tion of ex­pected ev­i­dence: if the time trav­el­ler is out there but doesn’t choose you, then this a (very mild) up­date to­wards no Dooms­day.

But for the clas­si­cal non-time-travel situ­a­tion, the Dooms­day ar­gu­ment fails.