I'll keep this quick:

In general, the problem presented by the Mugging is this: As we examine the utility of a given act for each possible world we could be in, in order from most probable to least probable, the utilities can grow much faster than the probabilities shrink. Thus it seems that the standard maxim "Maximize expected utility" is impossible to carry out, since there is no such maximum. When we go down the list of hypotheses multiplying the utility of the act on that hypothesis, by the probability of that hypothesis, the result does not converge to anything. 

Here's an idea that may fix this:

For every possible world W of complexity N, there's another possible world of complexity N+c that's just like W, except that it has two parallel, identical universes instead of just one. (If it matters, suppose that they are connected by an extra dimension.) (If this isn't obvious, say so and I can explain.)

Moreover, there's another possible world of complexity N+c+1 that's just like W except that it has four such parallel identical universes.

And a world of complexity N+c+X that has R parallel identical universes, where R is the largest number that can be specified in X bits of information. 

So, take any given extreme mugger hypothesis like "I'm a matrix lord who will kill 3^^^^3 people if you don't give me $5." Uncontroversially, the probability of this hypothesis will be something much smaller than the probability of the default hypothesis. Let's be conservative and say the ratio is 1 in a billion. 

(Here's the part I'm not so confident in)

Translating that into hypotheses with complexity values, that means that the mugger hypothesis has about 30 more bits of information in it than the default hypothesis. 

So, assuming c is small (and actually I think this assumption can be done away with) there's another hypothesis, equally likely to the Mugger hypothesis, which is that you are in a duplicate universe that is exactly like the universe in the default hypothesis, except with R duplicates, where R is the largest number we can specify in 30 bits.

That number is very large indeed. (See the Busy Beaver function.) My guess is that it's going to be way way way larger than 3^^^^3. (It takes less than 30 bits to specify 3^^^^3, no?)

So this isn't exactly a formal solution yet, but it seems like it might be on to something. Perhaps our expected utility converges after all.

Thoughts?

(I'm very confused about all this which is why I'm posting it in the first place.)

 

I started this as a comment on "Being half wrong about pascal's wager is even worse" but its really long, so I'm posting it in discussion instead.

 

Also I illustrate here using negative examples (hell and equivalents) for the sake of followability and am a little worried about inciting some paranoia so am reminding you here that every negative example has an equal and opposite positive partner. For example pascal's wager has the opposite where accepting sends you to hell, it also has the opposite where refusing sends you to heaven. I haven't mentioned any positive equivalents or opposites below. Also all of these possibilities are literally effectively 0 so don't be worrying.

 

"For so long as I can remember, I have rejected Pascal's Wager in all its forms on sheerly practical grounds: anyone who tries to plan out their life by chasing a 1 in 10,000 chance of a huge pay-off is almost certainly doomed in practice.  This kind of clever reasoning never pays off in real life..."

 

Pascal's wager shouldn't be in in the reference class of real life. It is a unique situation that would never crop up in real life as you're using it. In the world in which pascal's wager is correct you would still see people who plan out their lives on a 1 in 10000 chance of a huge pay-off fail 9999 times out of 10000. Also, this doesn't work for actually excluding pascal's wager. If pascal's wager starts off excluded from the category real life you've already made up your mind so this cannot quite be the actual order of events.

 

In this case 9999 times you waste your Christianity and 1/10000 you don't go to hell for eternity, which is, at a vast understatement, much worse than 10000 times as bad as worshipping god even at the expense of the sanity it costs to force a change in belief, the damage it does to your psyche to live as a victim of self inflicted Stockholm syndrome, and any other non obvious cost: With these premises choosing to believe in God produces infinitely better consequences on average.

 

Luckily the premises are wrong. 1/10000 is about 1/10000 too high for the relevant probability. Which is:

the probability that the wager or equivalent, (anything whose acceptance would prevent you going to hell is equivalent) is true

MINUS

the probability that its opposite or equivalent, (anything which would send you to hell for accepting is equivalent), is true 

 

1/10000 is also way too high even if you're not accounting for opposite possibilities.

 

 

Equivalence here refers to what behaviours it punishes or rewards. I used hell because it is in the most popular wager but it applies to all wagers. To illustrate: If its true that there is one god: ANTIPASCAL GOD, and he sends you to hell for accepting any pascal's wager, then that's equivalent to any pascal's wager you hear having an opposite (no more "or equivalent"s will be typed but they still apply) which is true because if you accept any pascal's wager you go to hell. Conversely, If PASCAL GOD is the only god and he sends you to hell unless you accept any pascal's wager, that's equivalent to any pascal's wager you hear being true.

 

The real trick of pascals wager is the idea that they're generally no more likely than their opposite. For example, there are lots of good, fun, reasons to assign the Christian pascal's wager a lower probability than its opposite even engaging on a Christian level:

 

Hell is a medieval invention/translation error: the eternal torture thing isn't even in the modern bibles.

The belief or hell rule is hella evil and gains credibility from the same source (Christians, not the bible) who also claim that god is good as a more fundamental belief, which directly contradicts the hell or belief rule.

The bible claims that God hates people eating shellfish, taking his name in vain, and jealousy. Apparently taking his name in vain is the only unforgivable sin. So if they're right about the evil stuff, you're probably going to hell anyway.

It makes no sense that god would care enough about your belief and worship to consign people to eternal torture but not enough to show up once in a while.

it makes no sense to reward people for dishonesty.

The evilness really can't be overstated. eternal torture as a response to a mistake which is at its worst due to stupidity (but actually not even that: just a stacked deck scenario), outdoes pretty much everyone in terms of evilness. worse than pretty much every fucked up thing every other god is reputed to have done put together. The psychopath in the bible doesn't come close to coming close.

 

The problem with the general case of religious pascal's wagers is that people make stuff up (usually unintentionally) and what made up stuff gains traction has nothing to do with what is true. When both Christianity and Hinduism are taken seriously by millions (as were the Roman/Greek gods, and Viking gods, and Aztec gods, and Greek gods, and all sorts of other gods at different times, by large percentages of people) mass religious belief is 0 evidence. At most one religion set (e.g. Greek/Roman, Christian/Muslim/Jewish, etc) is even close to right so at least the rest are popular independently of truth.

 

The existence of a religion does not elevate the possibility that the god they describe exists above the possibility that the opposite exists because there is no evidence that religion has any accuracy in determining the features of a god, should one exist.

 

You might intuitively lean towards religions having better than 0 accuracy if a god exists but remember there's a lot of fictional evidence out there to generalise from. It is a matter of judgement here. there's no logical proof for 0 or worse accuracy (other than it being default and the lack of evidence) but negative accuracy is a possibility and you've probably played priest classes in video games or just seen how respected religions are and been primed to overestimate religion's accuracy in that hypothetical. Also if there is a god it has not shown itself publicly in a very long time, or ever. So it seems to have a preference for not being revealed.  Also humans tend to be somewhat evil and read into others what they see in themselves. and I assume any high tier god (one that had the power to create and maintain a hell, detect disbelief, preserve immortal souls and put people in hell) would not be evil. Being evil or totally unscrupled has benefits among humans which a god would not get. I think without bad peers or parents there's no reason to be evil. I think people are mostly evil in relation to other people.  So I religions a slight positive accuracy in the scenario where there is a god but it does not exceed priors against pascal's wager (another one is that they're pettily human) or perhaps even the god's desire to stay hidden. 

 

Even if God itself whispered pascal's wager in your ear there is no incentive for it to actually carry out the threat: 

These threats aren't being made in person by the deity. They are either second hand or independently discovered so:

The deity has no use for making the threat true, to claim it more believably, as it might if it was an imperfect liar (at a level detectable by humans) that made the threats in person.

The deity has total plausible deniability.

Which adds up to all of the benefits of the threat having already being extracted by the time the punishment is due and no possibility of a rep hit (which wouldn't matter anyway.)

 

So, All else being equal. i.e. unless the god is the god of threats or pascal's wagers (whose opposites are equally likely):

 

If God is good (+ev on human happiness -ev on human sadness that sort of thing), actually carrying out the threats has negative value.

If god is scarily-doesn't-give-a-shit-neutral to humans, it still has no incentive to actually carry out the threat and a non zero energy cost.

if god gives the tiniest most infinitesimal shit about humans its incentive to actually carry out the threat is negative.

 

If God is evil you're fucked anyway:

The threat gains no power by being true, so the only incentive a God can have for following through is that it values human suffering. If it does, why would it not send you to hell if you believed in it? (remember that the god of commitments is as likely as the god of breaking commitments)

 

Despite the increased complexity of a human mind I think the most (not saying its at all likely just that all others are obviously wrong) likely motivational system for a god which would make it honour the wager is that that God thinks like a human and therefore would keep its commitment out of spite or gratitude or some other human reason. So here's why I think that one is wrong. It's generalizing from fictional evidence: humans aren't that homogeneous (and one without peers would be less so), and if a god gains likelihood to keep a commitment from humanness it also gains not -designed-to-be-evil-ness that would make it less likely to make evil wagers.  It also has no source for spite or gratitude, having no peers. Finally could you ever feel spite towards a bug? Or gratitude? We are not just ants compared to a god, we're ant-ant-ant-etc-ants.

 

Also there's the reasons that refusing can actually get you in trouble:  bullies don't get nicer when their demands are met. It's often not the suffering they're after but the dominance, at which point the suffering becomes an enjoyable illustration of that dominance.  As we are ant-ant-etc-ants this probability is lower but The fact that we aren't all already in hell suggests that if god is evil it is not raw suffering that it values. Hostages are often executed even when the ransom is paid. Even if it is evil, it could be any kind of evil: its preferences cannot have been homogenised by memes and consensus.

 

There's also the rather cool possibility that if human-god is sending people to hell, maybe its for lack of understanding. If it wants belief it can take it more effectively than this. If it wants to hurt you it will hurt you anyway. Perhaps peerless, it was never prompted to think through the consequences of making others suffer. Maybe god, in the absence of peers just needs someone to explain that its not nice to let people burn in hell for eternity. I for one remember suddenly realising that those other fleshbags hosted people. I figured it out for myself but if I grew up alone as the master of the universe maybe I would have needed someone to explain it to me.

 

Just for the fun of it....

The Devil Went Down to Paris

This is a spoiler for a game being run by Scott in Cork, Ireland, so you might not want to read it if you might be in that game.

 

Eliezer Yudkowsky wrote that Robin Hanson solved the Pascal's mugging thought experiment:

Robin Hanson has suggested penalizing the prior probability of hypotheses which argue that we are in a surprisingly unique position to affect large numbers of other people who cannot symmetrically affect us. Since only one in 3^^^^3 people can be in a unique position to ordain the existence of at least 3^^^^3 other people who are not symmetrically in such a situation themselves, the prior probability would be penalized by a factor on the same order as the utility.

I don't quite get it, is there a post that discusses this solution in more detail?

To be more specific, if a stranger approached me, offering a deal saying, "I am the creator of the Matrix. If you fall on your knees, praise me and kiss my feet, I'll use my magic powers from outside the Matrix to run a Turing machine that simulates 3^^^^3 copies of you having their coherent extrapolated volition satisfied maximally for 3^^^^3 years." Why exactly would I penalize this offer by the amount of copies being offered to be simulated? I thought the whole point was that the utility, of having 3^^^^3 copies of myself experiencing maximal happiness, does outweigh the low probability of it actually happening and the disuility of doing what the stranger asks for?

I would love to see this problem being discussed again and read about the current state of knowledge.

I am especially interested in the following questions:

• Is the Pascal's mugging thought experiment a "reduction to the absurd" of Bayes’ Theorem in combination with the expected utility formula and Solomonoff induction?¹
• Could the "mugger" be our own imagination?²
• At what point does an expected utility calculation resemble a Pascal's mugging scenario and should consequently be ignored?³

¹ If you calculate the expected utility of various outcomes you imagine impossible alternative actions. The alternatives are impossible because you already precommited to choosing the outcome with the largest expected utility. Problems: 1.) You swap your complex values for a certain terminal goal with the highest expected utility, indeed your instrumental and terminal goals converge to become the expected utility formula. 2.) Your decision-making is eventually dominated by extremely small probabilities of obtaining vast utility.

² Insignificant inferences might exhibit hyperbolic growth in utility: 1.) There is no minimum amount of empirical evidence necessary to extrapolate the expected utility of an outcome. 2.) The extrapolation of counterfactual alternatives is unbounded, logical implications can reach out indefinitely without ever requiring new empirical evidence.

³ Extrapolations work and often are the best we can do. But since there are problems like 'Pascal's Mugging', that we perceive to be undesirable and that lead to an infinite hunt for ever larger expected utility, I think it is reasonable to ask for some upper and lower bounds regarding the use and scope of certain heuristics. We agree that we are not going to stop pursuing whatever terminal goal we have chosen just because someone promises us even more utility if we do what that agent wants. We might also agree that we are not going to stop loving our girlfriend just because there are many people who do not approve our relationship and who together would experience more happiness if we divorced than the combined happiness of us and our girlfriend being married. Therefore we already informally established some upper and lower bounds. But when do we start to take our heuristics seriously and do whatever they prove to be the optimal decision?

 If Omega offered to give you 2^n utils with probability 1/n, what n would you choose?

This problem was invented by Armok from #lesswrong. Discuss.