Quantum versus logical bombs

Child, I’m sorry to tell you that the world is about to end. Most likely. You see, this mad­woman has de­signed a dooms­day ma­chine that will end all life as we know it—painlessly and im­me­di­ately. It is at­tached to a su­per­com­puter that will calcu­late the 10100th digit of pi—if that digit is zero, we’re safe. If not, we’re doomed and dead.

How­ever, there is one thing you are al­lowed to do—switchout the log­i­cal trig­ger and re­placed it by a quan­tum trig­ger, that in­stead gen­er­ates a quan­tum event that will pre­vent the bomb from trig­ger­ing with 1/​10th mea­sure squared (in the other cases, the bomb goes off). You ok pay­ing €5 to re­place the trig­gers like this?

If you treat quan­tum mea­sure squared ex­actly as prob­a­bil­ity, then you shouldn’t see any rea­son to re­place the trig­ger. But if you be­lieved in many wor­lds quan­tum me­chan­ics (or think that MWI is pos­si­bly cor­rect with non-zero prob­a­bil­ity), you might be tempted to ac­cept the deal—af­ter all, ev­ery­one will sur­vive in one branch. But strict to­tal util­i­tar­i­ans may still re­ject the deal. Un­less they re­fuse to treat quan­tum mea­sure as akin to prob­a­bil­ity in the first place (mean­ing they would ac­cept all quan­tum suicide ar­gu­ments), they tend to see a uni­verse with a tenth of mea­sure-squared as ex­actly equally val­ued to a 10% chance of a uni­verse with full mea­sure. And they’d even do the re­verse, re­place a quan­tum trig­ger with a log­i­cal one, if you paid them €5 to do so.

Still, most peo­ple, in prac­tice, would choose to change the log­i­cal bomb for a quan­tum bomb, if only be­cause they were slightly un­cer­tain about their to­tal util­i­tar­ian val­ues. It would seem self ev­i­dent that risk­ing the to­tal de­struc­tion of hu­man­ity is much worse than re­duc­ing its mea­sure by a fac­tor of 10 - a pro­cess that would be un­de­tectable to ev­ery­one.

Of course, once you agree with that, we can start squeez­ing. What if the quan­tum trig­ger only has 120 mea­sured-squared “chance” of sav­ing us? 1/​000? 1/​10000? If you don’t want to fully ac­cept the quan­tum im­mor­tal­ity ar­gu­ments, you need to stop—but at what point?