Newcomb’s Problem dissolved?

First read­ing about New­comb’s Prob­lem my re­ac­tion was petty much “wow, in­ter­est­ing thought” and “of course I would one box, I want to win $ 1 mil­lion af­ter all”. But I had a lin­ger­ing nag­ging feel­ing, that there is some­thing wrong with the whole premise. Now, af­ter think­ing about it for a few weeks I think I have found the prob­lem.

First of all I want to point out, that I would still one box af­ter see­ing Omega pre­dict­ing 50 or 100 other peo­ple cor­rectly, since 50 to 100 bits of ev­i­dence are enough to ove­come (nearly) any prior I have about how the uni­verse works. Only I do not think this sce­nario is phys­i­cally pos­si­ble in our uni­verse.

The mis­take is nicely stated here:

After all, Joe is a de­ter­minis­tic phys­i­cal sys­tem; his cur­rent state (to­gether with the state of his fu­ture self’s past light-cone) fully de­ter­mines what Joe’s fu­ture ac­tion will be. There is no Phys­i­cally Irre­ducible Mo­ment of Choice, where this same Joe, with his own ex­act ac­tual past, “can” go one way or the other.

This is only true in this sense if nei­ther MWI is true nor there are any quan­tum prob­a­bil­is­tic pro­cesses, i.e., our uni­verse al­lows for a true Laplace’s de­mon (a.k.a. Omega) to ex­ist.

If MWI is true Joe can set it up so, that “af­ter” Omega filled the boxes and left there “will” be Everett Branches, in which Joe “will” twobox and differ­ent Everett Branches in which Joe “will” onebox.

In­tu­itively I think Joe could even do this with his own brain by leav­ing it in “un­de­cided” mode un­til Omega leaves and then us­ing an al­gorithm which feels “ran­dom” to de­cide if he oneboxes or twoboxes. But of course I would not thrust my in­tu­ition here and I do not know enough about Joe’s brain to de­cide if this re­ally works. So Joe would use e.g. a sin­gle pho­ton re­flected/​trans­mit­ted off/​through a semi­trans­par­ent mir­ror, en­sur­ing, that he oneboxes re­spec­tively twoboxes in say 50% of the Everett Branches.

If MWI is not true but there are quan­tum prob­a­bil­is­tic pro­cess, Omega sim­ply can­not pre­dict the fu­ture state of the uni­verse. So the same pro­ce­dure used above would en­sure that Omega can­not pre­dict Joes de­ci­sion due to true ran­dom­ness.

So I would be very very VERY sur­prised if I saw Omega pull this trick 100 times in a row and I could some­how rule out Stage Magic (which I could not).

I am not even sure if there is any se­ri­ous in­ter­pre­ta­tion of quan­tum me­chan­ics that al­lows for the strict de­ter­minism Omega would need. Would love to hear about one in the com­ments!

Of course from an in­stru­men­tal stand­point it is always ra­tio­nal to firmly pre­com­mit to onebox, since the ex­tra $1000 are not worth tak­ing the risk. Even the model un­cer­tainity ac­counts for much more than 0.001.