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I think the standard for accuracy would be very different. If Watson gets something right you think "Wow that was so clever", if it's wrong you're fairly forgiving. On that other hand, I feel like if an automated fact checker got even 1/10 things wrong it would be subject to insatiable rage for doing so. I think specifically correcting others is the situation in which people would have the highest standard for accuracy.

And that's before you get into the levels of subjectivity and technicality in the subject matter which something like Watson would never be subjected to.


You can do it first or you can do it best, usually both are different artists and each is well known. I think there's plenty of examples of both in all fields. Rachmaninov for instance is another classical (in the broad sense) composer in the "do it well" rather than "do it first" camp, he was widely criticised as behind the times in his own era, but listening now no-one cares that his writing music sounds like it's ~150 years old but written only ~100.


That's the result of compulsory voting not of preference voting.


As an Australian I can say I'm constantly baffled over the shoddy systems used in other countries. People seem to throw around Arrow's impossibility theorem to justify hanging on to whatever terrible system they have, but there's a big difference between obvious strategic voting problems that affect everyone, and a system where problems occur in only fairly extreme circumstances. The only real reason I can see why the USA system persists is that both major parties benefit from it and the system is so good at preventing third parties from having a say that even as a whole they can't generate the will to fix it.

In more direct answer to your question, personally I vote for the parties in exactly the order I prefer them. My vote is usually partitioned as: [Parties I actually like | Major party I prefer | Parties I'm neutral about | Parties I've literally never heard of | Major party I don't prefer | Parties I actively dislike]

A lot of people vote for their preferred party, as evidenced by more primary votes for minor parties. Just doing a quick comparison, in the last (2012) US presidential election only 1.74% of the vote went to minor candidates, while in the last Australian federal election (2013) an entire 21% of the votes went to minor parties.

Overall it works very well in the lower house.

In the upper house, the whole system is so complicated no-one understands it, and the ballot papers are so big that the effort required to vote in detail prevents most people from bothering. In the upper house I usually just vote for a single party and let their preference distribution be automatically applied for me. Of course I generally check what that is first, though you have to remember to do it beforehand since it's not available while you're voting. Despite all that though, it's a good system I wouldn't want it replaced with anything different.


(meta) Well, I'm quite relieved because I think we're actually converging rather than diverging finally.

No. Low complexity is not the same thing as symmetry.

Yes sorry symmetry was just how I pictured it in my head, but it's not the right word. My point was that the particles aren't acting independently, they're constrained.

Mostly correct. However, given a low-complexity program that uses a large random input, you can make a low-complexity program that simulates it by iterating through all possible inputs, and running the program on all of them.

By the same token you can write a low complexity program to iteratively generate every number. That doesn't mean all numbers have low complexity. It needs to be the unique output of the program. If you tried to generate every combination then pick one out as the unique output, the picking-one-out step would require high complexity.

I think as a result of this whole discussion I can simplify my entire "finite resources" section to this one statement, which I might even edit in to the original post (though at this stage I don't think many more people are ever likely to read it):

"It is not possible to simulate n humans without resources of complexity at least n."

Everything else can be seen as simply serving to illustrate the difference between a complexity of n, and a complexity of complexity(n).

It would be quite surprising if none of the "C-like" theories could influence action, given that there are so many of them

It's easy to give a theory a posterior probability of less than 1/3^^^^3, by giving it zero. Any theory that's actually inconsistent with the evidence is simply disproven. What's left are theories which either accept the observed event, i.e. those which have priors < 1/3^^^^3 (e.g. that the number chosen was 7 in my example), and theories which somehow reject either the observation itself or the logic tying the whole thing together.

It's my view that theories which reject either observation or logic don't motivate action because they give you nothing to go on. There are many of them, but that's part of the problem since they include "the world is like X and you've failed to observe it correctly" for every X, making it difficult to break the symmetry.

I'm not completely convinced there can't be alternative theories which don't fall into the two categories above (either disproven or unhelpful), but they're specific to the examples so it's hard to argue about them in general terms. In some ways it doesn't matter if you're right, even if there was always compelling arguments not to act on a belief which had a prior of less than 1/3^^^^3, Pascal's Muggle could give those arguments and not look foolish by refusing to shift his beliefs in the face of strong evidence. All I was originally trying to say was that it isn't wrong to assign priors that low to something in the first place. Unless you disagree with that then we're ultimately arguing over nothing here.

Here's my attempt at an analysis

This solution seems to work as stated, but I think the dilemma itself can dodge this solution by constructing itself in a way that forces the population of people-to-be-tortured to be separate from the population of people-to-be-mugged. In that case there isn't of the order of 3^^^^3 people paying the $5.

(meta again) I have to admit it's ironic that this whole original post stemmed from an argument with someone else (in a post about a median utility based decision theory), which was triggered by me claiming Pascal's Mugging wasn't a problem that needed solving (at least certainly not by said median utility based decision theory). By the end of that I became convinced that the problem wasn't considered solved and my ideas on it would be considered valuable. I've then spent most of my time here arguing with someone who doesn't consider it unsolved! Maybe I could have saved myself a lot of karma by just introducing the two of you instead.


there are large objects computed by short programs with short input or even no input, so your overall argument is still incorrect.

I have to say, this caused me a fair bit of thought.

Firstly, I just want to confirm that you agree a universe as we know it has complexity of the order of its size. I agree that an equivalently "large" universe with low complexity could be imagined, but its laws would have to be quite different to ours. Such a universe, while large, would be locked in symmetry to preserve its low complexity.

Just an aside on randomness, you might consider a relatively small program generating even this universe, by simply simulating the laws of physics, which include a lot of random events quite possibly including even the Big Bang itself. However I would argue that the definition of complexity does not allow for random calculations. To make such calculations, a pseudo random input is required, the length of which is added to the complexity. AIXI would certainly not be able to function otherwise.

The mugger requires more than just a sufficiently large universe. They require a universe which can simulate 3^^^^3 people. A low complexity universe might be able to be large by some measures, but because it is locked in a low complexity symmetry, it cannot be used simulate 3^^^^3 unique people. For example the memory required (remember I mean the memory within the mugger's universe itself, not the memory used by the hypothetical program used to evaluate that universe's complexity) would need to be of the order of 3^^^^3, however while the universe may have 3^^^^3 particles if those particles are locked in a low-complexity symmetry then they cannot possibly hold 3^^^^3 bits of data.

In short, a machine of complexity of 3^^^^3 is fundamentally required to simulate 3^^^^3 different people. My error was to argue about the complexity of the mugger's universe, when what matters is the complexity of the mugger's computing resources.

I already explained why this is incorrect, and you responded by defending your separate point about action guidance while appearing to believe that you had made a rebuttal.

No, all of your arguments relate to random sensory inputs, which are alternative theories 'C' not the 'A' or 'B' that I referred to. To formalise:

I claim there exists theories A and B along with evidence E, such that: p(B) > 3^^^^3p(A) p(A|E) > p(B|E) complexity(E) << 3^^^^3 (or more to the point it's within our sensory bandwidth.

You have only demonstrated that there exists theory C (random input) such that C != B for any B satisfying the above, which I also tentatively agree with.

So the reason I switch to a separate point is because I don't consider my original statement disproven, but I accept that theories like C may limit the relevance of it. Thus I argue about the relevance of it, with this business about whether it affects your action or not. To be clear, I do agree (and I have said this) that C-like theories can influence action (as you argue). I am trying to argue though that in many cases they do not. It's hard to resolve since we don't actually have a specific case we're considering here, this whole issue is off on a tangent from the mugging itself.

I admit that the text of mine you quoted implies I meant it for any two theories A and B, which would be wrong. What I really meant was that there exist such (pairs of) theories. The cases where it can be true need to be very limited anyway because most theories do not admit evidence E as described, since it requires this extremely inefficiently encoded input.

If you're saying that the extent to which an individual cares about the desires of an unbounded number of agents is unbounded, then you are contradicting yourself. If you aren't saying that, then I don't see why you wouldn't accept boundedness of your utility function as a solution to Pascal's mugging.

I'm not saying the first thing. I do accept bounded utility as a solution to the mugging for me (or any other agent) as an individual, as I said in the original post. If I was mugged I would not pay for this reason.

However, I am motivated (by a bounded amount) to make moral decisions correctly, especially when they don't otherwise impact me directly. Thus if you modify the mugging to be an entirely moral question (i.e. someone else is paying), I am motivated to answer it correctly. To answer it correctly, I need to consider moral calculations, which I still believe to be unbounded. So for me there is still a problem to be solved here.


Well, you'd need a method of handling infinite values in your calculations. Some methods exist, such as taking limits of finite cases (though much care needs to be taken), using a number system like the Hyperreals or the Surreals if appropriate, or comparing infinite cardinals, it would depend a little on the details of how such an infinite threat was made plausible. I think in most cases my argument about the threat being dominated by other factors would not hold in this case.

While my point about specific other actions dominating may not hold in this case, I think the overall point that infinite resources cause problems far more fundamental than the mugging is if anything strengthened by your example. As is the general point that large numbers on their own are not the problem.


Sorry, but I don't know which section of my reply this is addressing and I can't make complete sense of it.

an explicit assumption of finite resources - an assumption which would ordinarily have a probability far less than 1 - (1/3^^^^3)

The OP is broken into two main sections, one assuming finite resources and one assuming infinite.

Our universe has finite resources, why would an assumption of finite resources in an alternative universe be vanishingly unlikely? Personally I would expect finite resources with probability ~=1. I'm not including time as a "resource" here by the way, because infinite future time can be dealt with by geometric discounting and so isn't interesting.

What you have now almost seems like a quick disclaimer added when you realized the OP had failed.

It would especially help to know which quote you are referring to here.

Overall I endeavoured to show that the mugging fails in the finite case, and is nothing particularly special in the infinite case. The mugging as I see it is intended as a demonstration that large, low complexity numbers are a problem. I argue that infinite resources are a problem, but large, low complexity numbers on their own are not.

I still don't consider my arguments to have failed (though it's becoming clear that at least my presentation of them has since no-one seems to have appreciated it), I do disclaim that the mugging still raises the question of infinite resources, but reducing it to just that issue is not a failure.

I also remain firmly convinced that expected utilities (both personal and moral) can and should converge, it's just that the correct means of dealing with infinity needs to be applied, and I leave a few options open in that regard.


This argument relies on a misunderstanding of what Kolmogorov complexity is. The complexity of an object is the length of the source code of the shortest program that generates it, not the amount of memory used by that program.

I know that.

The point about memory is the memory required to store the program data, not the memory required to run the program. The program data is part of the program, thus part of the complexity. A mistake I maybe made though was to talk about the current state rather than the initial conditions, since the initial conditions are what give the complexity of the program (though initialising with the current state is possible and equivalent). In my defence though talking about the memory was only meant to be illustrative.

To elaborate, you could simulate the laws of physics with a relatively small program, but you could not simulate the universe itself without a program as complex as the universe. You might think of it as a small "laws of physics" simulator and a large input file, but the complexity measure must include this input file. If it did not the program would not be deterministicly linked to its output.


Ok let me spell it out.

you cannot be 100% certain of its correctness. You should assign some nonzero probability to the hypothesis that the probability does not decrease fast enough for the correct expected utilities to be bounded. Then, taking this uncertainty into account, your expected utilities are unbounded.

A person comes up to you and says "arglebargle 3^^^^3 banana". This appears to you to be gibberish. However, you cannot be 100% certain of the correctness of this assertion. It could be that they're trying to perform Pascal's Mugging, but your ears are blocked and you didn't hear them right. You should assign some nonzero probability to this hypothesis, and that value will be greater than 3^^^^3. Thus the risk is sufficient that you should pay them $5 just in case.

This is what I mean by calling your argument too general. Now obviously neither you nor I would consider "arglebargle 3^^^^3 banana" a mugging, but I do not see a meaningful difference between your counterargument and the argument I present above.

You've changed the claim you're defending

No, I'm just making a multi-faceted point. Maybe if I break it up it would help:

  • Given two alternatives A and B, where A is initially considered 3^^^^3 times less likely than the B, it is possible, even with limited sensory bandwidth, to receive evidence to convince you that B is more likely than A. This is a point which I believe was not considered correctly in Pascal's Muggle.
  • Separate to this are other catch-all theories (C, D, etc.) which are impossible to disprove and potentially much more likely than 3^^^^3.
  • However, catch-all theories may not influence a decision relating to A and B because they do not generally reward the corresponding actions differently.
  • When they do influence a decision, it is most likely for the better. The best way to handle this is in my opinion still unsolved.

Pascal's Muggle was a scenario where the protagonist belligerently stuck to B because they felt it was impossible to generate sufficient evidence to support A. There's a lot of other discussion in that post, and it's quite sensible on the whole, but this is the aspect I was focusing on.

I'm confused because it sounds like you're conceding here that bounded utility is correct, but elsewhere you say otherwise.

I'm saying bounded utility is correct for an individual or agent. But I'm also saying bounds are not justified for the aggregation of the desires of an unbounded number of agents. These statements are not inconsistent.

No, that does not give you a well-defined utility function. You can see this if you try to use it to compare three or more different outcomes.

Well ok you're right here, the case of three or more outcomes did make me rethink how I consider this problem.

It actually highlights that the impact of morals on my personal utility is indirect. I couldn't express my utility as some kind of weighted sum of personal and (nonlinearly mapped) moral outcomes, since if I did I'd have the same problem getting off the couch as I argued you would. I think in this case it's the sense of having saved the 1000 people that I would value, which only exists by comparison with the known alternative. Adding more options to the picture would definitely complicate the problem and unless I found a shortcut I might honestly be stuck evaluating the whole combinatorial explosion of pairs of options.

But, exploring my own utility aside, the value of treating morality linearly is still there. If I bounded the morals themselves I would never act because I would honestly think there was as good as no difference between the outcomes at all, even when compared directly. Whereas by treating morals linearly I can at least pin that sense of satisfaction in having saved them on a real quantitative difference.


No, it isn't. It can't be used against agents with bounded utility functions.

Ok fully general counterargument is probably an exaggeration but it does have some similar undesirable properties:

  • Your argument does not actually address the argument it's countering in any way. If 1/n is the correct prior to assign to this scenario surely that's something we want to know? Surely I'm adding value by showing this?

  • If your argument is accepted then it makes too broad a class of statements into muggings. In fact I can't see why "arglebargle 3^^^^3 banana" isn't a mugging according to your argument. If I've reduced the risk of factual uncertainty in the original problem to a logical uncertainty, this is progress. If I've shown the mugging is equivalent to gibberish, this is progress.

I do think it raises a relevant point though that until we've resolved how to handle logical uncertainty we can't say we've fully resolved this scenario. But reducing the scenario from a risk of factual uncertainty to the more general problem of logical uncertainty is still worthwhile.

I was trying to point out that it actually is an impossible burden.

Only if you go about it the wrong way. The "my sensory system is receiving random noise" theory does not generally compel us to act in any particular way, so the balance can still be influenced by small probabilities. Maybe you'd be "going along with it" rather than believing it but the result is the same. Don't get me wrong, I think there are modifications to behaviour which should be made in response to dreaming/crazy/random theories, but this is essentially the same unsolved problem of acting with logical uncertainty as discussed above.

In any case all I was trying to do with that section was undermine the ridicule given to assigning suitably low probabilities to things. The presence of alternative theories may affect how we act, and the dominance of them over superexponentially low probabilities may smother the relevance of choices that depend on them, but none of this makes assigning those values incorrect. And I support this by demonstrating that at least in the absence of alternative catch-all theories, by assigning those probabilities you are not making it impossible to believe these things, despite the bandwidth of your sensory system. Which is far from a proof that their correct in itself, but does undermine the point being made in the Pascal's Muggle article.

It's not like there is some True Ethical Utility Function, and your utility function is some combination of that with your personal preferences.

Well we have a different take on meta-ethics is all. Personally I think Coherent Extrapolated Volition applied to morality leads to a unique limit, which, while in all likelihood is not just unfindable but also unverifiable, still exists as the "One True Ethical Function" in a philosophical sense.

I agree that the amount to which a person cares about others is and should be bounded. But I separate the scale of a moral tragedy itself from the extent to which I or anyone else is physically capable of caring about it. I think nonlinearly mapping theoretically unbounded moral measurements into my own bounded utility is more correct than making the moral measurements nonlinearly to begin with.

Consider for example the following scenario: 3^^^^3 people are being tortured. You could save 1000 of them by pressing a button, but you'd have to get off a very comfy couch to do it.

With bounded moral values the difference between 3^^^^3 people and 3^^^^3-1000 is necessarily insignificant. But with my approach, I can take the difference between the two values in an unbounded, linear moral space, then map the difference into my utility to make the decision. I don't believe this can be done without having a linear space to work in at some point.

Which is the core of my problem with your preferred resolution using bounded moral utility. I agree that bounding moral utility would resolve the paradox but I still don't think you've made a case that it's correct.

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