Muggings, Nuclear Devices, Probability & Decision

Somehow I ended up on the curious site, directed by somebody with the nickname Yud (from Eliezer Yudkowsky). Odd isn’t in it. Investigating it led me to Reddit and this explanation of the strange views at LessWrong.

Yud’s main issue in terms of his ‘personal philosophy’ is a slavish adherence to the idea of ‘Bayesianism’ and his view of ‘rationality’, even when it does not actually make sense. Yud rejects the idea of anything having absolutely 0% or absolutely 100% probablity, which leads to some very odd opinions and conclusions. In one of Yud’s own essays, he points out that if you’re mugged and asked for $50 or the mugger will detonate a nuclear bomb in the city (but he doesn’t have a gun pointed at you), then you should give the mugger the money – after all, there’s a nonzero chance of the city blowing up!

Now whether this Yud fellow holds these views, or whether this is a fair summary of his mugger problem, it’s good enough for us to demonstrate two important truths: that all probability is conditional, and that probability is not decision. (This is not Pascal’s Mugger, which we’ll do another day.)

Would you give the mugger the fifty bucks? If you’re a guy who makes a living writing a blog to drum up business, you wouldn’t have it. You’d have to negotiate and see if he’d take twenty. Or ten. (Note to certain readers: I initially wrote this post before Thanksgiving.)

But suppose instead you were a government employee with a guaranteed pension. You’d probably laugh in the mugger’s face.


First, our proposition of interest runs something like, Y = “The mugger has a nuclear device and it will work and he will use it to murder millions if I don’t give him fifty bucks.” The probability of that is what we want. What is it?

It doesn’t exist. There is no Pr(Y), i.e. there is no probability of Y. Yet it seems to us there is and that it is low, even negligible, and even zero. Why is that? Because we are each of us supplying premises, evidence and observations, from which we can form a probability. That is each of us is arguing (with each of our own selves) something like this:

E = “This guy is a nut. Nuts don’t have access to nuclear devices. How could he have got one? I suppose it’s possible, but there are so many safeguards and security precautions that I can’t see how he could. Besides, nutty people say things like this. And, anyway, even if he had it, would he really kill millions for a mere fifty bucks? At best, he’s got some wires strung together that he’s calling a bomb.”

And from those not-too-coherent but genuine premises, we form Pr(Y | E) = minuscule or, for most of us, Pr(Y | E) = 0; i.e. the probability that Y is so given our internal argument is tiny, negligible, close to zero as you like. Maybe even zero depending on the precise form of the evidence.

It’s not that we form this E is some systematic way. It, or some thing like it, appears in chaotic fashion to each of us. Those that consider Y, at any rate. Not everybody will understand Y. That the mugger made himself plain is another premise we assume. Many people, in Manhattan, would hear the mugger say, “Do you have a minute for…” and pass right on by.

Importantly, if Pr(Y | E) = minuscule, minuscule is not a number. Our E is far too fuzzy for us to deduce an quantity for the probability. If one came to a number, it is because, and only because, one has included in E a way for a deduction from E to a quantity for Y. E.g. E includes “It’s impossible for a mugger to have such a device”, then Pr(Y | E) = 0.

Now it’s clear enough there will be two many camps, based on two general forms of evidence. There will be a group which says Pr(Y | E) = minuscule, and other which says Pr(Y | E) = 0. The second predominates. For those who hold Pr(Y | E) = 0, it’s also clear which decision is best. Walk on; ignore the mugger; or consider reporting him to the police so that he might be tossed into the loony bin.

What about the Pr(Y | E) = minuscule crowd? What decision should they make? First, and by now obvious, the decision is not the probability. No part of the decision formed any part of the evidence for Y. And even if it had, by accident or through faulty reason, put the decision and its consequences as part of E, this would merely be a mistake.

Understand, the probability is not the thing. If you judge Pr(Y | E) = minuscule and it turns out the mugger was lying or telling the truth, “Pr(Y | E)” was still true, or correct.

What decision to make then depends on some rule which takes the probability as (if you like) input. This isn’t the space to investigate all the different proposed rules (minimax, maximin, expected value, and others), except to say that these rules all take consideration of what happens once you make a decision (hand over your money or walk on) and what happens with the mugger (he has or hasn’t a bomb).

None of those pairs (there are four) will be quantifiable, though many would fake it by, for instance, assigning so many dollars or “utiles” (fictional quantums of feeling), and then fixing a number on the probability and solving the equation given by the rule. That works when infinities don’t crop up, as they sometimes do.

Anyway, there are surely awful consequences if you decide to walk away and the mugger has (and uses) the bomb. But too awful to contemplate, for most of us, especially on the street in front of what might be a nut. Best most of us would do in the “heat” of that moment is to say, fleetingly, to ourselves, “Gosh.” The allure of continuing is much easier to contemplate, and would overwhelm the vague harm of millions. So even with the decision rules, given crude quantifications, we would make the “optimal” decision to pass on by.

Like I said above, we’ll do Pascal’s Mugging another day (soon).

Update Just in time for Christmas, a book which explains all of probability and statistics: Uncertainty: The Soul of Modeling, Probability & Statistics.


  1. Sheri

    I’d give the $50 bucks for his creative approach.

  2. Gary

    Why not demand $50 from the mugger for not turning him over to the police? His game is extortion; why not turn the tables? Now he’s got to figure the probability of your threat based on premises of his past experience with the law, your familiarity with local authorities, your unexpected brazenness, etc. At least this wrinkle might give him pause and allow time to escape any personal violence (sans gun) against you.

  3. Joy

    Gary, that would be playing games.
    Why not just turn him over to the police? It’s not even a matter of choice.
    To be confused by speech of parting with fifty Dollars is to have a peculiar notion of what is right and what is wrong.
    It isn’t mugging. It’s demanding money with menaces. A form of blackmail. White collar crime. Mugging is blue collar crime.
    Both are common activities of organised criminals, aka gangsters.

  4. DAV

    Well, you need to determine the cost of giving $50 vs. nothing, which means you need to assess the probability of the threat. Whether one should or not you will bring what you already know to the table and insert them into the propositions

    Frankly, considering how expensive it is to build a nuclear device, I would wonder why he only wants $50 when it would seem the Iranians would eagerly buy it for $75; conclude he doesn’t have one; and decline the offer. Similarly, if the threat were different, say, releasing ricin in the subway, I’d wonder why he wants to slowly extort in $50 increments instead of going to the city and demanding millions.

    This is an example where one is forced to make a decision with little information. The only rational approach means assessing the probable cost of the decision. Like voting for action to prevent Global Warming or, more recently,voting for when all of the choices look bad. All the same problem but different circumstances. Not everyone is going to see the costs the same way. Yes, there are irrational folk whose decisions seem based on lunar phases. An argument for not encouraging voting by those who don’t care; can’t decide; or are uninformed.

  5. Sander van der Wal

    If he was any smart, he would be selling the rights to press the button. ISIS would pay a good lot for the possibility to blow up an entiere American city, and they would have no shortage of volunteers.

  6. Joy

    Would that some people just answer in the fashion of the argument presented?
    That would be normal and decent. If I hang around this blog much longer I shall have no convictions left, to quote a favourite character.

    However, mugging is robbery which occurs in a public place with use of force or threat of violence on a person.

  7. DAV

    If I hang around this blog much longer I shall have no convictions left

    Having a lot of convictions may indicate poor legal representation. If so, how would you lose them? Or did you mean left to obtain?

  8. Ken

    I’m surprised that Briggs didn’t dismiss the whole thing on semantics — that there’s no such thing as a “mugging”! U.S. laws center on “robbery” and “extortion” and the like, rarely ever mentioning “mugging” (or any variant of that slang).

    Like here in New York:

    Pascal’s Wager — the gist of which being that very unlikely negative outcomes that are extraordinarily severe should be addressed, and addressing [rather than dismissing] the unlikely is rational.

    We do this sort of thing all the time and there are lots of wonderful examples — TSA comes to mind with its consistently proven ineffectual security measures, described as “security theater” by security experts.

    Christopher Hitchens applied the same basic logic when he spoke for much of a generation [or two or three] with this bit:

    “The argument about global warming is not whether there is any warming but whether or not and to what extent human activity is responsible for it. My line on that is that we should act as if it is…The Fate of the Earth: We don’t have another planet on which to run the experiment. … So if it turned out to be that there was no severe global warming threat or that it wasn’t man-made, then all we would have done would be make a mistake in analysis – which we could correct from. But if it turned out that there was and we didn’t do anything about it, then it would be too late to do anything at all. And that would lead to disaster.”

    Note Hitchens’ rationale — he stops just short of noting that the credible science is ambiguous, and claims we should proceed anyway, just in case. No scientism there!

  9. Joy

    The word in the same sense as ‘Courage of conviction’ or moral conviction.
    Judgement or discernment.
    As for having a lot of those? That is a vital part of integrity.

  10. Joy

    While I’m here and see the Christopher quote:

    That is the precautionary principle which is murderous and does have negative consequences with the use of biofuels altering the price of grain and availability of food. It asks Africa, for example not to pursue fossil fuels. Africa is rich in coal and oil.
    Furthermore the first sentence is so over said that it is impossible to say who said it first. I’ve heard that about a thousand times.
    By the same logic any made up sky is falling threat can be used to hold the world ransom.

  11. Joy

    The man I quoted was Colonel Peacock, to Higgins.

    “we’re not Humpty Dumpty”. No…Sir, but
    one doesn’t have to throw out beautiful language to tell the truth and to express what you think believe or feel in any order sequence or mixture. Even in Alice’s world it is what is meant which is important not what is only received. Once reasonable effort is made to clarify any ambiguity that is the end of the discussion unless you’re in an odd rigid system of special language of the type which is set in ice.

    Sod them to Hades, says Steven Fry.

  12. Joy

    It was Higgins on Alfred P Doolittle.
    £5. is given in exchange for Eliza.
    “£10. Is a lot of money, makes a man feel all prudent like and then, goodbye to happiness.”
    (Had he thought his intentions weren’t honourable he would have asked £50!)

    Higgins to Colonel Pickering:
    “If we listen to this man for a minute longer we shall have no convictions left”

  13. JH

    Many summers ago, when we all are yoinger, Mr. JH was mugged in a washroom in DC, he fought the mugger and ended up going to ER for stiches. He thought he did the right thing, but to me, I’d rather loose the money than to have my families seeing me hurt in anyway.

    So if I were mugged, no thought of probability would come to my mind, and I would give the mugger $50 regardless of whether the mugger has an any weapons or makes any threat. $50 or $1,000 or any material thing that I carry with me is nothing compare to the worries I would have incurred upon my families. And chances are someone or public cameras would have taken a photo of the mugger. And, you know, God would punish bad people.

    Raise your hand if you think probability is decision.

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