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The Kitty Genovese Equation

Someone's in trouble. You can hear them from your apartment, but you can't tell if any of your neighbors are already rushing down, or already calling the police. It's time sensitive, and you've got to decide now: is it worth spending those precious minutes, or not?

Let's define our variables:

Cost to victim of nobody helping:

cost to each bystander of intervening:

Number of bystanders: (Since , for it's always right to intervene.)


Suppose the bystanders all simultaneously decide whether to intervene or not, with probability p. Then expected world-utility is

Utility is maximized when ; In other words, when . Let . Then we have the optimal probability of not helping, .

One interesting implication of our solution is that the probability that the victim isn't helped, , equals . Since , this means P(not helped) starts small at for and rapidly rises to .


Suppose intervening would cost a minute, and the victim would live 2 years longer on average if you intervened. Then is about one in a million, . Once you get to seven bystanders, it's optimal to not intervene 10% of the time. is about a million, so with 21 bystanders it's optimal for each to take a 50-50 shot at helping.

If is a mere , you get there six times as fast: a 10% chance to not help at N=2, 50% around N = 4-5, and a whopping 75% chance around N=9.


This was inspired by friends' varied willingness to intervene in public disputes, and my own experience worrying about how to respond to potential crises around me. Of course, in real life we have a lot of uncertainty around and around other people's , and we can often wait and observe if someone goes to help. For situations where decisions are pretty simultaneous, though, it would be interesting to see how well people's responses line up with the curve.

The LessWrongy framework I'm familiar with would say that value = expected utility, so it takes potential downsides into account. You're not risk-averse wrt your VNM utility function, but computing that utility function is hard in practice, and EV calculations can benefit from some consideration of the tail-risks.

Schelling's The Strategy of Conflict seems very relevant here; a major focus is precommitment as a bargaining tool. See here for an old review by cousin_it.

Iterated chicken seems fine to test, just as a spinoff of the IPD that maps to slightly different situations. (I believe that the iterated game of mutually modeling each other's single-shot strategy is different from iterating the game itself, so I don't think Abram's post necessarily implies that iterated chicken is relevant to ASI blackmail solutions.)

Speaking of iterated games, one natural form of blackmail is for the blackmailee to pay an income stream to the blackmailer; that way, at each time-step they're paying their fair price for the good of [not having their secret revealed between time t and time t+1]. Here's a well-cited paper that discusses this idea in the context of nuclear brinksmanship: Schwarz & Sonin 2007.

It's true the net effect is low to first order, but you're neglecting second-order effects. If premia are important enough, people will feel compelled to Goodhart proxies used for them until those proxies have less meaning.

Given the linked siderea post, maybe this is not very true for insurance in particular. I agree that wasn't a great example.

Slack-wise, uh, choices are bad. really bad. Keep the sabbath. These are some intuitions I suspect are at play here. I'm not interested in a detailed argument hashing out whether we should believe that these outweigh other factors in practice across whatever range of scenarios, because it seems like it would take a lot of time/effort for me to actually build good models here, and opportunity costs are a thing. I just want to point out that these ideas seem relevant for correctly interpreting Zvi's position.

The post implies it is bad to be judged. I could have misinterpreted why, but that implication is there. If judge just meant "make inferences about" why would it be bad?

As Raemon says, knowing that others are making correct inferences about your behavior means you can't relax. No, idk, watching soap operas, because that's an indicator of being less likely to repay your loans, and your premia go up. There's an ethos of slack, decisionmaking-has-costs, strategizing-has-costs that Zvi's explored in his previous posts, and that's part of how I'm interpreting what he's saying here.

But it also helps in knowing who's exploiting them! Why does it give more advantages to the "bad" side?

Sure, but doesn't it help me against them too?

You don't want to spend your precious time on blackmailing random jerks, probably. So at best, now some of your income goes toward paying a white-hat blackmailer to fend off the black-hats. (Unclear what the market for that looks like. Also, black-hatters can afford to specialize in unblackmailability; it comes up much more often for them than the average person.) You're right, though, that it's possible to have an equilibrium where deterrence dominates and the black-hatting incentives are low, in which case maybe the white-hat fees are low and now you have a white-hat deterrent. So this isn't strictly bad, though my instinct is that it's bad in most plausible cases.

Why would you expect the terrorists to be miscalibrated about this before the reduction in privacy, to the point where they think people won't negotiate with them when they actually will, and less privacy predictably changes this opinion?

That's a fair point! A couple of counterpoints: I think risk-aversion of 'terrorists' helps. There's also a point about second-order effects again; the easier it is to blackmail/extort/etc., the more people can afford to specialize in it and reap economies of scale.

Perhaps the optimal set of norms for these people is "there are no rules, do what you want". If you can improve on that, than that would constitute a norm-set that is more just than normlessness. Capturing true ethical law in the norms most people follow isn't necessary.

Eh, sure. My guess is that Zvi is making a statement about norms as they are likely to exist in human societies with some level of intuitive-similarity to our own. I think the useful question here is like "is it possible to instantiate norms s.t. norm-violations are ~all ethical-violations". (we're still discussing the value of less privacy/more blackmail, right?) No-rule or few-rule communities could work for this, but I expect it to be pretty hard to instantiate them at large scale. So sure, this does mean you could maybe build a small local community where blackmail is easy. That's even kind of just what social groups are, as Zvi notes; places where you can share sensitive info because you won't be judged much, nor attacked as a norm-violator. Having that work at super-Dunbar level seems tough.

I found this pretty useful--Zvi's definitely reflecting a particular, pretty negative view of society and strategy here. But I disagree with some of your inferences, and I think you're somewhat exaggerating the level of gloom-and-doom implicit in the post.

>Implication: "judge" means to use information against someone. Linguistic norms related to the word "judgment" are thoroughly corrupt enough that it's worth ceding to these, linguistically, and using "judge" to mean (usually unjustly!) using information against people.

No, this isn't bare repetition. I agree with Raemon that "judge" here means something closer to one of its standard usages, "to make inferences about". Though it also fits with the colloquial "deem unworthy for baring [understandable] flaws", which is also a thing that would happen with blackmail and could be bad.

>Implication: more generally available information about what strategies people are using helps "our" enemies more than it helps "us". (This seems false to me, for notions of "us" that I usually use in strategy)

I can imagine a couple things going on here? One, if the world is a place where may more vulnerabilities are more known, this incentivizes more people to specialize in exploiting those vulnerabilities. Two, as a flawed human there are probably some stressors against which you can't credibly play the "won't negotiate with terrorists" card.

>Implication: even in the most just possible system of norms, it would be good to sometimes violate those norms and hide the fact that you violated them. (This seems incorrect to me!)

I think the assumption is these are ~baseline humans we're talking about, and most human brains can't hold norms of sufficient sophistication to capture true ethical law, and are also biased in ways that will sometimes strain against reflectively-endorsed ethics (e.g. they're prone to using constrained circles of moral concern rather than universality).

>Implication: the bad guys won; we have rule by gangsters, who aren't concerned with sustainable production, and just take as much stuff as possible in the short term. (This seems on the right track but partially false; the top marginal tax rate isn't 100%)

This part of the post reminded me of (the SSC review of) Seeing Like a State, which makes a similar point; surveying and 'rationalizing' farmland, taking a census, etc. = legibility = taxability. "all of them" does seem like hyperbole here. I guess you can imagine the maximally inconvenient case where motivated people with low cost of time and few compunctions know your resources and full utility function, and can proceed to extract ~all liquid value from you.

The CHAI reading list is also fairly out of date (last updated april 2017) but has a few more papers, especially if you go to the top and select [3] or [4] so it shows lower-priority ones.

(And in case others haven't seen it, here's the MIRI reading guide for learning agent foundations.)

Oh wait, yeah, this is just an example of the general principle "when you're optimizing for xy, and you have a limited budget with linear costs on x and y, the optimal allocation is to spend equal amounts on both."

Formally, you can show this via Lagrange-multiplier optimization, using the Lagrangian . Setting the partials equal to zero gets you , and you recover the linear constraint function . So . (Alternatively, just optimizing works, but I like Lagrange multipliers.)

In this case, we want to maximize , which is equivalent to optimizing . Let's define , so we're optimizing .

Our constraint function is defined by the tradeoff between and . , so . , so .

Rearranging gives the constraint function . This is indeed linear, with a total 'budget' of .5 and a p-coefficient of 1. So by the above theorem we should have .

I think your solution to "reckless rivals" might be wrong? I think you mistakenly put a multiplier of q instead of a p on the left-hand side of the inequality. (The derivation of the general inequality checks out, though, and I like your point about discontinuous effects of capacity investment when you assume that the opponent plays a known pure strategy.)

I'll use slightly different notation from yours, to avoid overloading p and q. (This ends up not mattering because of linearity, but eh.) Let be the initial probabilities for winning and safety|winning. Let be the capacity variable, and without loss of generality let start at and end at . Then and . So , so . And , so .

Therefore, the left-hand side of the inequality, , equals . At the initial point , this simplifies to .

Let's assume . The relative safety of the other project is , which at simplifies to .

Thus we should commit more to capacity when , or , or . This is a little weird, but makes a bit more intuitive sense to me than or mattering.

Yeah, I worry that competitive pressure could convince people to push for unsafe systems. Military AI seems like an especially risky case. Military goals are harder to specify than "maximize portfolio value", but there are probably reasonable proxies, and as AI gets more capable and more widely used there's a strong incentive to get ahead of the competition.

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