A Plausible Entropic Decision Procedure for Many Worlds Living, Round 2

Hey LessWrong! I posted about a month ago about a de­ci­sion pro­ce­dure that I think could be op­ti­mal in a uni­verse where the Many Wor­lds In­ter­pre­ta­tion is true. The post was down­voted to zero and at least sev­eral peo­ple thought there were prob­lems with it. How­ever, none of the com­ments swayed me to be­lieve that my idea has been falsified yet, so I clar­ified my idea, rewrote a post about it, and am in­ter­ested again in your feed­back. It is cross-posted from my blog here.

Epistemic Status

While this idea seems log­i­cally co­her­ent to me given my con­cep­tion of MWI, my prior de­gree-of-be­lief in my idea is that it’s more than likely false be­cause I’m a layper­son and it’s one of the first ideas that came to me when think­ing about de­ci­sion the­ory un­der MWI.

I slowly lead into ex­plain­ing my pro­posal be­cause I think un­der­stand­ing the con­text of the prob­lem will make my idea more in­tu­itive. So let me be­gin:

The Problem

In any bi­nary de­ci­sion prob­lem that we face with op­tions A and B, we want to use the available ev­i­dence in some de­ci­sion pro­ce­dure to de­cide which op­tion we take. Tra­di­tion­ally, the idea is that when it comes time to make a de­ci­sion, an agent sim­ply ought to choose whichever op­tion looks more choice-wor­thy (has more ex­pected util­ity). If their com­pu­ta­tions and cost-benefit anal­y­sis show that A looks even slightly like a bet­ter op­tion then B, they want to go with A ev­ery sin­gle time.

How­ever, if Many Wor­lds is true, I think that mak­ing de­ci­sions in this fash­ion ‘damns’ the copies of this agent in nearly all the nearby child wor­lds to mak­ing the same de­ci­sion. By nearby child wor­lds, I mean the sister wor­lds that have re­cently branched out from a com­mon Everett branch. For ex­am­ple, sup­pose Bob is try­ing to de­cide to go left or right at an in­ter­sec­tion. In the mo­ments where he is de­cid­ing to go ei­ther left or right, many nearly iden­ti­cal copies in nearly iden­ti­cal sce­nar­ios are cre­ated. They are al­most en­tirely all the same, and if one Bob de­cides to go left, one can as­sume that 99%+ of Bobs made the same de­ci­sion. This is fine if go­ing left was the best de­ci­sion, but what if it’s not? If he hap­pens to sub­se­quently be kil­led by a moun­tain lion who was hid­ing in the bushes, nearly all the Bobs in all the wor­lds that were cre­ated since he ap­proached the in­ter­sec­tion are now dead. Those lives were all eth­i­cally-valuable and equally worth liv­ing, and all those fu­ture child wor­lds are go­ing to miss out on the pos­i­tive in­fluences of Bob.

Since go­ing left was a rel­a­tively ar­bi­trary de­ci­sion based on the sum of ev­i­dence Bob had available, wouldn’t it have been nice if only half of the Bobs cre­ated since he first ap­proached the in­ter­sec­tion went left, and the other half went right? Then, in case there are any moun­tain li­ons or other threats, in at least in half of fu­ture child wor­lds, Bob is still al­ive.

If go­ing left seemed a good bit more wor­thy than go­ing right (but not over­whelm­ingly), per­haps it would be op­ti­mal if 80% of Bobs went left, and only 20% went right.

Ineffec­tive Solutions

If this di­ver­sifi­ca­tion of fu­ture child wor­lds is op­ti­mal, how can Bob co­or­di­nate with the other re­cently cre­ated Bobs to di­ver­sify out­comes by mak­ing differ­ent de­ci­sions? He can’t just choose to feel very un­cer­tain or sub­jec­tively try to feel like do­ing ei­ther one. The hu­man brain is too ro­bust against in­di­vi­d­ual quan­tum phe­nom­ena to en­sure Bob re­li­ably makes differ­ent choices. Many trillions of quan­tum op­er­a­tions oc­cur in the brain all the time, yet the brain pro­duces com­par­a­tively few high-level de­ci­sions, so the brain is ro­bust against most in­di­vi­d­ual quan­tum phe­nom­ena. In most nearby child wor­lds, Bob prob­a­bly makes the same de­ci­sions, es­pe­cially when pre­sented with nearly iden­ti­cal sen­sory stim­uli.

Back to how Bob can co­or­di­nate with the other ‘copies’ of him­self, he can­not even di­ver­sify out­comes by flip­ping a coin, go­ing left if heads and right if tails; in most re­cently cre­ated child wor­lds, the flip of the coin is too ro­bust against in­di­vi­d­ual quan­tum op­er­a­tions and lands roughly the same way each time. If he em­ploys the coin method, nearly all the re­cently made copies of Bob in this sce­nario will make the same coin flip and then make the same de­ci­sion.

My Pro­posed Solution

The only method that I be­lieve works is to look at in­di­vi­d­ual quan­tum phe­nom­ena that has a par­tic­u­lar prob­a­bil­ity of oc­cur­ring, such as the ra­dioac­tive de­cay of an atom. If Bob has a Geiger counter, he can em­ploy an al­gorithm that yields a 0 or a 1 bit 50% of the time based off whether the time be­tween 2 con­sec­u­tive mea­sured ra­dioac­tive de­cays is greater than the time be­tween the next two con­sec­u­tive ra­dioac­tive de­cays. If Bob first had the in­tent to em­ploy this de­ci­sion pro­ce­dure as he ap­proached the in­ter­sec­tion, nearly all of the Bobs that split off from him also in­tend to em­ploy this de­ci­sion pro­ce­dure.

When it fi­nally comes time for all the copies of him to make a de­ci­sion, and he hap­pens to feel that go­ing left and right is equally choice-wor­thy, he can men­tally com­mit to a de­ci­sion pro­ce­dure, go­ing left if his true ran­dom num­ber is a 0 and right if it is a 1. Then, when he looks to see whether his true-ran­dom num­ber gen­er­a­tor yields a 0 or a 1, nearly half of the copies of him see a 0 and the other half see a 1. When nearly all the copies of him con­tinue to com­mit to the de­ci­sion pro­ce­dure, 50% of them go right, and 50% go left. Thus, we get a di­ver­sity of out­comes, which is in­tu­itively a good thing, al­though I hope to prove this later.

Q: What if an agent Char­lie is 80% sure that op­tion A is su­pe­rior to op­tion B?

In that case, Char­lie should seek out a ran­dom num­ber that is equally likely to be be­tween 1 and 5, in­clu­sive, and go with op­tion A if the gen­er­ated num­ber is any­thing but a 5. He can do this by seek­ing out 3 quan­tum-gen­er­ated bits, which cre­ate a bi­nary num­ber. As long as the num­ber is be­tween 1 and 5, Char­lie can use it. Other­wise, he must dis­card it. Then, Char­lie can base his de­ci­sion off the first num­ber that qual­ifies–ei­ther 001, 010, 011, 100, or 101. Of note, he only has to dis­card strictly less than 50% of the num­bers with this scheme.

For more pre­cise choice-wor­thy es­ti­mates, one can round one’s sub­jec­tive prob­a­bil­ity es­ti­mates to ar­bi­trary pre­ci­sion, or em­ploy other en­cod­ing schemes.

Q: But un­der Many Wor­lds, we have enough di­ver­sity of out­comes that we do not need to worry about de­liber­ately di­ver­sify­ing them, right?

No, I do not think we end up with a proper di­ver­sifi­ca­tion of out­comes when we ap­ply tra­di­tional de­ci­sion pro­ce­dures. Not ev­ery­thing that one can imag­ine hap­pen­ing does hap­pen. I can imag­ine jump­ing out the win­dow right now, but it’s en­tirely pos­si­ble that in no child wor­lds, I do this, es­pe­cially over a finite time pe­riod like the next 15 min­utes.

Many Wor­lds doesn’t im­ply that ev­ery­thing one can imag­ine hap­pen­ing hap­pens an equal num­ber of times. Rather, Many Wor­lds im­plies just that a lot of wor­lds are cre­ated each mo­ment, and that more sub­jec­tively prob­a­ble phe­nom­ena, in­so­far as one is cal­ibrated well, tend to oc­cur in more wor­lds.

Im­por­tantly, “A util is a util” and each in­stance of suffer­ing and well-be­ing is eth­i­cally-rele­vant, even in a Many-Wor­lds uni­verse.

Q: What are the haz­ards of this de­ci­sion pro­ce­dure if Many Wor­lds isn’t true, or if your con­cep­tion of Many Wor­lds is ut­terly wrong?

I don’t think the haz­ards are great for the well-cal­ibrated per­son. If you re­ally would tell only 9 out of 10 copies of your­self to make the same de­ci­sion, it should not be the end of the world to some­times be that 10th copy that makes a slightly sub­jec­tively sub­op­ti­mal de­ci­sion.

For the poorly-cal­ibrated per­son, you could ex­pect them to make sub­jec­tively less op­ti­mal de­ci­sions more of­ten than they oth­er­wise should. How­ever, I don’t think we need perfect cal­ibra­tion for the Many Wor­lds to reap the benefits of this de­ci­sion pro­ce­dure—slight over-di­ver­sifi­ca­tion is prob­a­bly bet­ter than none.

Q: To what sorts of de­ci­sions does this de­ci­sion pro­ce­dure ap­ply?

I think it should ap­ply to ev­ery sort of de­ci­sion. It would be great for us all to have ac­cess to re­cently-pro­duced, quan­tum-gen­er­ated ran­dom num­bers and em­ploy this pro­ce­dure to rel­a­tively ar­bi­trary and sig­nifi­cant phe­nom­ena al­ike. We don’t want you go­ing with the cheese­cake and get­ting food-pois­ing in all fu­ture child wor­lds, nor do we want to see all fu­ture child wor­lds damned to the same out­comes from the de­ci­sion to re­tal­i­ate nu­cle­arly.

Q: What is a prac­ti­cal source of quan­tum-gen­er­ated ran­dom num­bers?

I’m glad you asked! For this pro­ce­dure, ran­dom num­bers must be based off quan­tum phe­nom­ena, like ra­dioac­tive de­cay or the pho­to­elec­tric effect, they must be re­cently gen­er­ated, and highly prefer­ably, no one else can use them for this de­ci­sion pro­ce­dure. HotBits won’t work—I reached out to them—be­cause they send out bits from a pool of en­tropy which in­cludes ran­dom num­bers gen­er­ated from some time ago. The only web­site that I found that works is hosted by some­one at the Aus­tralia Na­tional Univer­sity: https://​​qrng.anu.edu.au/​​RainBin.php.

If this de­ci­sion pro­ce­dure is ever pop­u­larized, though, we want a way to make sure differ­ent peo­ple can­not use the same ran­dom num­bers for their de­ci­sion pro­ce­dures, which would pre­vent the max­i­mum di­ver­sifi­ca­tion of child wor­lds. We would want to use a sys­tem like HotBits, which never sends out the same bits twice. We would also want to build and dis­tribute phys­i­cal quan­tum ran­dom num­ber gen­er­a­tors that peo­ple could use when they didn’t have in­ter­net ac­cess.

Thanks for read­ing! I’m cu­ri­ous what you think of this.