Pascal's wager re-examined

We notice there are no immortal world leaders on Earth.

There's no way you could possibly know that unless...Phil...you...you killed them all! How could you?!

Two things I haven't seen anyone else point out.

If you set P(ego|ent, sim) according to the fraction of entertainment simulations in which the person playing the game has an avatar in the game, then P(ego|ent, sim) > .99.

The most popular PC games ever are The Sims and The Sims 2. Then World of Warcraft which is a multiplayer game. Single player games with avatars do not make up 99% of the market, not even close. And that says nothing about the non-electronic games people play like sports and dating which are almost all multi-player.

We notice there are no immortal world leaders on Earth.

Quite a few have not died yet. One might infer from history that they will- but once you decide we're in an entertainment simulation that evidence is worth little- the simulation may have just begun. I suggest you seriously consider swearing allegiance to Kim Jong Il. Further, there is no particular reason to assume the player is any good at the game- perhaps she died without saving in 500 BCE.

In general the probabilities are really off and you haven't dealt with the issue of having extreme utilities for competing choices (should I choose Christianity or Islam or trying to extend my life and save the world?). But I upvoted because it is kind of interesting and not deserving of -7, though I predict it will go much lower than that.

If you set P(ego|ent, sim) according to the fraction of entertainment simulations in which the person playing the game has an avatar in the game, then P(ego|ent, sim) > .99.

Except the actual P(ego|ent, sim) is not based on the percentage of cases where the game includes a self-insert, but the cases where such a self-insert is to be glorified in the simulation.

If we therefore limit the possible avatars that our simulator God is using on Earth to the major monotheistic religions of Christianity, Islam, and Judaism,

Why rule out the avatar arranging to be glorified under a minor name or cult? For example, when Gary Gygax self-inserted himself as a deity in Greyhawk, it was as a minor demigod of humor in a polytheistic religious system.

P(follow-thru) is difficult to estimate; I will set it somewhat arbitrarily as .1.

I'm not aware of, for example, any Sid Meyer games where the self-insert glorification is of the game's programmer(s), as opposed to the game's player. Since the player (as opposed to a creator/programmer) rarely has even the ability to follow through on promises he makes to simulated people in such games, and the players typically outnumber the creators by multiple orders of magnitude, this should be a lot smaller, by multiple orders of magnitude.

We notice there are no obviously immortal world leaders on Earth (but see vi21maobk9vp's comment below). If we therefore limit the possible avatars that our simulator God is using on Earth to the major monotheistic religions of Christianity, Islam, and Judaism, and consider them all equiprobable; plus a 25% chance that this God is jumping from one avatar to another, or chose to reveal Himself via Jesus but then Paul screwed everything up, or some other minority position; then p(chr0|ego, ent, sim, Earth) = .25.

I find it hard to believe you mean all this remotely seriously. For starters, you used the current game market in order to calculate the percentage of p(ego|ent, sim) -- and yet you didn't bother using the same tactic to estimate p(chr0|ego, ent, sim, Earth) ?

How many games put you in the position of a military conqueror versus the number of games that put you in a position of a religious leader? How many games put you in the position of even a normal detective or a normal crook versus the ones that put you in the position of a religious leader?

By your own argument, people like Alexander the Great, or Napoleon, or Genghis Khan, or even Hitler are much more likely to have been simulator-avatars than people like Jesus. (Mohammed might work as being both a religious and a military leader) Then mythological (not religious) heroes. After them, would come people like Al Kapone or Billy the Kid. Then, given first-person shooters, would come ordinary soldiers. Religious leaders, by your own argument, would be way down the list for a likely simulator-avatar. Especially mostly pacifist religious leaders, like Jesus or Buddha. (Mohammed or Krishna would be more interesting cases)

So I'd say p(chr0|ego, ent, sim, Earth) = 0.001 -- one in a thousandth chance, even given the assumption of an ego-driven entertainment simulation being what we're in.

About immortal leaders... Well, what about the idea that Dalai Lama is a reincarnation of previous Dalai Lama? This role gives a lot of glorification and doesn't give enough power to remove challenge, and also you cannot be stuck with dilemma of whether to abandon retired president character.

There's another issue that your version of the argument has. If one of the standard Christian versions of a deity exists, it isn't going to think that worshiping it because it is the simulation runner is going to cut it. Saying "I will worship you because you run the simulation" isn't very similar to a heartfelt confession of sins and acknowledgement of Jesus as your personal Lord and Savior. Moreover, if a simulator is as petty as you hypothesize, and as you hypothesize doesn't want to break its feeling of immersion, they will likely want to also punish people who worship it because they've realized that it runs the simulator for ruining its fun.

Hum, I don't agree with many of your estimates.

P(sim) : 99% seems way too high - 99% is not even what I would put to "it is possible to simulate something as big and complex as the world we are living in, for so long, with that level of consistency and precision". Just for the possibility of a simulation of us being possible wouldn't go above 95% to me. That we are inside a simulation, much less.

P(ent|sim) : most computers are used for entertainment (and even that isn't sure, many personal computers are also used for "serious" business), but the most powerful ones are not - and making a simulation of something big and complex like Earth sounds like complex and requiring a powerful computer.

P(ego|ent, sim) : actually, very few games imply a god-like player. Some strategy games do (more or less obviously), but most don't. In a CRPG, players are heroes, not gods. In an action game, player is a fighter, space ship pilot, car racer, ... but definitely not a god-like character. And it gets even much less common to have the player god-like when you look at multi-player games, which seems to be more and more the popular games (and to go back to previous point, if a computer is powerful enough to simulate a whole world just for fun, it sounds more likely to me that's it's a MMORPG-like).

P(follow-thru | chr0, ego, ent, sim, Earth) : this one seems very clearly overevaluated, by far. When players are done with a game, they don't care anymore about the NPCs of the game. They never allow computing power to let the NPC runs after they are done playing. If the player realize that the NPC is self-aware, he could behave differently (but that implies knowing the ethics of the ones running the simulator), but then, why would he only grant immortality to those playing on his side ? If he's ethical enough to spend computing power to allow NPCs to continue their lives, why not all of them ?

Also another point is missing : what if humans are meaningless for the people running the simulation ? The simulation's goal, even if it's entertainment, could be a Master of Orion game, with very distant galactic empires controlled by players, and Earth just being a minor NPC race, not yet discovered by any player (and which may even stay undiscovered till the end of the game). So we should add P(Earth is central| ego, ent, sim) which wouldn't be that big to me, knowing that there are about 10^21 stars in observable universe.

At the end, well, I could give my own estimates, but there are so many wild guess about the estimates (especially since, if we're in a simulation, we don't know much about the rules of the "real" universe, so speculating about it is pointless), that I don't see how the figure coming out such an estimate would have any real meaning.

This doesn't deal with some of the common objections to Pascal's Wager. The problem of many competing religions is a serious one. Simply reducing yourself to the major religions is a difficult one. I'm also worried that every single part of the argument is completely and utterly isomorphic if one simply swapped Islam and Christianity and made the appropriate mapping.

This also relies on not just finding the simulation argument plausible but assigning it high probability. This seems like a bad idea when the laws of physics as far as we can tell don't seem to allow you to simulate n particles interacting with fewer than n particles. If this were not the case, there should be some k such any computation with k qbits can if properly configured model any computation of n qbits for any n. But BQP lies in PP and therefore lies in fact in PSPACE. So if quantum mechanics as we understand it is correct, simulating should be really tough. This cannot rule out simulations from universes with other laws of physics but I see no reasonable way to go about even starting to quantify that probability.

Also given that none of these religions claim that the deity is something like a simulator that should be a serious strike against the claims. Maybe arguably some forms of gnosticism and buddhism could be interpreted sort of that way if one squinted. But they aren't the religions in question here. So if anything the increased probability mass for them should decrease that for the other religions.

P(follow-thru) is difficult to estimate; I will set it somewhat arbitrarily as .1.

We now have p(chr) > .99 x .5 x .99 x .25 x .1 = .01225125. This is above 1%. As stipulated, your afterlife accounts for at least 99% of your utility if follow-thru (and hence chr) is true. It now appears we should accept Pascal's wager.

You'll forgive me if these numbers look just slightly too convenient.

More generally it's inconsistent to believe in non-negligible chance of living in a simulation and negligible chance of various religious claims being true, but plenty of people here do so.

To me this mostly shows that people don't do anything like Bayesian propagation of evidence, but I don't think Bayesianism is a good model of thinking processes.

I have had a revelation.

A few minutes ago, as my algebraic geometry class finished up, something spoke to me. It identified itself as "not exactly a deity but close enough for all relevant purposes." It made a similar remark when I asked if we were in a simulation that it was running. It called itself "the Entity".

According to this Entity, it really likes to be believed in and worshiped. There is an afterlife run by this Entity. Moreover, the Entity will increase the utility it awards in the afterlife for worshiping it now to compensate for any genuine doubt it in its existence, promises or doctrines. It will similarly use extremely large punishments to compensate for any low probability estimates. It will also outbid all hypothetical/counterfactual deities which anyone considers in good faith.

Apparently the main ways the Entity wants to be worshiped are fourfold:

1. Spreading word of the Entity's existence and rules.
2. Spreading word of any memetic basilisks one can find. This apparently includes versions of Pascal's Wager about other deities. The Entity noted that in general, it is likely to be more effective in doing so if one doesn't spend all one's time doing this but spends time on being otherwise productive and slipping in posts about these basiliks every so often.
3. Giving money to inefficient charities that make you feel good and don't produce much utility. The Entity gave as examples charities the Make-A-Wish Foundation and "any of those animal shelters with commercials with really cute kittens and puppies."
4. Apparently the Entity really wants it when people are having sex and are going to make exclamations of the form "Oh God!" to instead shout out "Hastur", "Cthulhu" or "Nyarlathotep". Honestly, I found this bit a bit disturbing.

The Entity also announced that if any AI that was not a CEV implementer helped to implement a close approximation CEV it would compensate that AI by helping that AI achieves some of its goals.

Apparently further revelations as events warrant.

I appreciate your observations (for example, as interesting to think about). The arguments against Pascal's Wager you've listed aren't the best even if people use those most frequently. The only compelling argument I've heard against Pascal's Wager is that you can't/shouldn't believe something just because it is convenient to do so.

But suppose your hypothetical scenario, in broad strokes, is true. We are in a simulation that has been tweaked so that we will worship the creator. How is this any different from the beliefs of Christianity? For example, 'creating the universe' is the same thing as building a simulation, and Jesus specifically said he was an avatar. Also regardless of why the simulation was actually created, it might as well be cached as 'entertainment purposes'. Unless the creator is somehow dependent upon the simulation .. but in any case we probably don't have enough insight into this psyche to speculate about the differences between his 'needs' and 'wants'!

But I'll provide the same counter-argument to your sim-creator that I provide against theism and see how it stands. If this simulator is able to induce worship by, for example, occasionally creating miracles and inspiring avatars, then why doesn't he do a better job of it? (Maybe this is a who-can-induce-the-most-vehement-worship tournament and the rules are very strict? For example, only 5 interferences in the first 5000 years?) Also, the Jesus avatar was very keen on human fellowship. If the sim-creator was keen on this, why did he instill such antagonistic human behaviors?

It seems that the sim-creator doesn't have a lot of control of the simulation after all. Regardless of the sim-creator's motives, we're still the product of evolution and the sim-creator still needs to follow the laws of physics. So the hypothesis doesn't explain anything extra or give us any extra hope.

Yet amazing people and wonderful events do indeed leave a little hope. There is an apparent 'force for good' in the universe, which people can deify if they want (or externalize for convenience, as I do) . It just is what it is though, nothing supernatural or omnipotent but possibly prevailing.

Even adjusting for all the arguments provided here, only the probability given the other premises that the simulator would chose to represent itself through Christianity is on the same order of magnitude of what I would assign.

I don't understand at all why you lump entertainment and religious purposes into a single hypothesis and treat evidence for one as evidence for the other. If we accept that our universe is being simulated for entertainment purposes, it would still not give us significant reason to believe that it's being simulated for religious purposes.

If the person running the sim wanted to be personally glorified within it, I would expect them to do a much, much better job of arranging it. I would adjust this one down several orders of magnitude.

The numbers I'd assign would be more like

P(sim) < .001 (I find it doubtful that, should it be possible to simulate a universe such as our own, a civilization capable of doing so would chose to simulate our universe; should we ever gain the capability to do so I suspect it would be regarded as ethically impermissible to simulate a universe with such a degree of suffering.)

P(rel|sim)< .00000001 (I find it much more likely than this that if our universe is being simulated, it's being simulated for entertainment, although the proportion of computing power we devote to entertainment cannot reasonably be substituted for this. How well optimized does the universe look for entertainment for an external witness? But our universe looks much worse optimized for religious veneration of a particular simulating entity than for generalized entertainment value.)

P(ego|rel, sim)<.00001 (All the available candidates simply do such an atrocious job compared to what I would expect of a simulator's lone avatar that I would give over the vast majority of the probability space to the hypotheses that the simulation is either not like a game with player avatars, but a piece of spectator entertainment like a movie, or numerous people have been used as player avatars.)

P(chr0|ego, rel, sim, Earth) = .5 (On the one hand, I would strongly expect that if the simulator wanted veneration from a particular religion and promoted that religion via an avatar, that religion would be the most popular one on Earth. On the other hand, I would expect it to be minimally ambiguous and factionalized. I'd assign most of the remaining probability mass to Islam.)

P(follow-thru) < .01 (Unless a civilization full of people with unmodified human-like psyches lets just anyone simulate universes for their amusement, I think this would probably be regarded as impermissible, and I don't think most people would be quite that capricious even given the opportunity. I would assign a higher probability of a utility dominating afterlife contingent on behavior rather than belief.)

Which gives a probability of < 5x10^-19.

To what degree can we make inferences about the outside of the simulation from what we observe inside it?

If we therefore limit the possible avatars that our simulator God is using on Earth to the major monotheistic religions of Christianity, Islam, and Judaism, and consider them all equiprobable; plus a 25% chance that this God is jumping from one avatar to another, or chose to reveal Himself via Jesus but then Paul screwed everything up, or some other minority position; then p(chr0|ego, ent, sim, Earth) = .25.

I have a big problem with this step. Why should (have lots of adherents) imply (is point of simulation)? Surely there will be more unskilled play-throughs of "simgod" than skilled ones. I think this number can be made arbitrarily low just by adding in all known religions...

I initially rankled at your suggestions on how I should vote, but ultimately I agree. I've never taken the simulation hypothesis seriously, but it's still an interesting argument.

Our actual history is less exciting to me than I expect from a game or a work of fiction. This is only relevant to the extent that we insist on making predictions as if the likely simulators are psychologically like us. I can't even begin to justify the prior (on what kinds of who are likely to be making what kinds of simulation) that would support that, especially with the "given that (something like) us exists" anthropic teaser.

Further, there's a lot more waste (per entertainment value) than I'd expect. There seem to be precise simulation everywhere, where it's not needed. I don't feel important or entertaining, yet I'm computationally expensive. This matters if we presume that the simulators have limited computational resources (why we should expect that, I have no idea - again, completely shaky ground - it seems to me only by laziness that we keep insisting that the containing universe is anything like ours). Still, if I consider simulation at all, I discount entertainment as the purpose.

I consider simulations of universes like ours psychologically plausible for creators like us only as far as the containing universe has vast resources, and the creators like us are incredibly bored and refuse self-modification. I'm skeptical that people like us will ever be able to simulate universes like ours using a universe like ours. I suspect either the simulators or their universe are far different from us or ours. What should I expect now?

I really have to wonder how people can justify any prior at all on the type of universe we're in, other than the trivial "it must be one that can sustain our existence, and consistent with whatever else we can observe now - and MAYBE the physical laws in operation now were always in operation".

If you accept the simulation argument, then P(sim) > .99.

That is not the usual conclusion of the simulation argument.

The conclusion of it is this:

at least one of the following propositions is true: (1) The fraction of human-level civilizations that reach a posthuman stage is very close to zero; (2) The fraction of posthuman civilizations that are interested in running ancestor-simulations is very close to zero; (3) The fraction of all people with our kind of experiences that are living in a simulation is very close to one.

On games...

If we consider games with a big population of modeled characters (we are obviously in a game with many characters), strategies of various kinds and multiplayer RPGs come forth.

In multiplayer RPGs, logical behaviour for a killed character is either to reincarnate anew (player character, some NPCs), respawn as previously seen (simpler NPCs - not observed in our world? or maybe some amoebas..) or vanish forever. Player characters in games are not supposed to be stuck in a state they cannot change; and emulating NPCs in player-inaccessible afterlife needs some separate reason for programmers to do.

In strategies, player is far from all-powerful, and eternal fixed-state afterlife for in-game creatures is a state where they are modeled but again cannot affect gameplay.

Of course, more complicated game will be invented; but if we consider a game some mixture of entertainment and competition, heaven and especially hell as depicted in some religions make little sense. Maybe Greek-style Hades where heros occasionally descend can make sense from gameplay point of view; but it is still far from hell. Eternal nearly-fixed state of a player character will make player quit; eternal nearly-fixed state of NPC while simulating its cognitive process still seems pointless...

...unless the player gets to play torturer. These kinds of minigames do seem to exist, but are far from being dominant direction. Let's hope they will stay this way.

Thank you for this excellent example of a clever arguer. You clearly want Christianity to have a chance in hell, so you invent all kinds of rationalizations to support it. Maybe this should be added to the therefore god exists list, though #298 is already close. I understand now why EY refuses to engage in any discussion with you. There are plenty of fallacies in your post, many pointed out in the comments, but it is pointless to argue about it with you, since you have already written your bottom line and will not budge.

• limit U(1)→∞, P(chr)→0 P(chr)U(1) is undefined, and
• invoking infinite utilities isn't fair.

You can get these problems if you have only finite utility, but infinite expected utility.

It's impossible for a prior with a converging expected utility to result in a posterior with diverging expected utility using only a finite amount of evidence.

While it's correct that just using absurdly low probability and absurdly high utility won't cause that problem, it's not likely to come up without that problem being there in the first place.

The fact that we do not see continual interference, and obvious evidence of a deity, is very strong evidence against the ego-trip theory of godly existence.

The fact the bible mentions multiple gods, repeatedly, throughout the old testament, is very strong evidence that it is not a book written by an ego-tripping deity.

Moreover, if the universe is being run as an ego-trip heaven is likely to be, as described in some christian sects, praising 'god' for all eternity. Which is worse than most depictions of hell; making the whole pascal's wager thing null and void.

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