Boost For Being Best

The fraction of a normal distribution that is six or more standard deviations above the mean is one in ten billion. But the world has almost eight billion people in it. So in principle we should be able to get six standard deviations in performance gain by selecting the world’s best person at something, compared to using an average person.

I’m revising Age of Em for a paperback edition, expected in April. The rest of this post is from a draft of new text elaborating that point, and its implication for em leisure:

Em workers also earn wage premiums when they are the very best in the world at what they do. Even under the most severe wage competition, a best em can earn an extra wage equal to the difference between their productivity and the productivity of the second best em. When clans coordinate internally on wage negotiations, this is the difference in productivity between clans. (Clans who can’t coordinate internally are selected out of the em world, as they don’t cover their fixed costs, such as for training and marketing.)

Out of 10 billion independently and normally distributed (IID) samples, the maximum is on average about 6.4 standard deviations above the mean. Average spacings between the second, third, fourth highest samples are roughly 0.147, 0.075, and 0.05 standard deviations respectively (Branwen 2017). So when ems are selected out of 10 billion humans, the best em clan may be this much better than other em clans on normally distributed parameters. Using the log-normal wage distribution observed in our world (Provenzano 2015), this predicts that the best human in the world at any particular task is four to five times more productive than the median person, is over three percent more productive than the second most productive person, and is five percent more productive than the third most productive person.

If em clan relative productivity is drawn from this same distribution, if maximum em productivity comes at a 70 hour workweek, and if the best and second best em clans do not coordinate on wages they accept, then even under the strongest wage competition between clans, the best clan could take an extra 20 minutes a day more leisure, or two minutes per work hour, in addition to the six minutes per hour and other work breaks they take to be maximally productive.

This 20 minute figure is an underestimate for four reasons. First, the effective sample size of ems is smaller due to age limits on desirable ems. Second, most parameters are distributed so that the tails are thicker than in the normal distribution (Reed and Jorgensen 2004).

Third, differing wealth effects may add to differing productivity effects. On average over the last 11 years, the five richest people on Earth have each been about 10 percent richer than the next richest person. If future em income ratios were like this current wealth ratio, then the best em worker could afford roughly an extra hour per day of leisure, or an additional six minutes per hour.

Fourth, competition probably does not take the strongest possible form, and the best few ems can probably coordinate to some extent. For example, if the best two em clans coordinate completely on wages, but compete strongly with the third best clan, then instead of the best and second best taking 20 and zero minutes of extra leisure per day, they could take 30 and 10 extra minutes, respectively.

Plausibly then, the best em workers can afford to take an additional two to six minutes of leisure per hour of work in a ten hour work day, in addition to the over six minutes per hour of break needed for maximum productivity.

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  • Ronfar

    The number of people capable of performing any given task at all is usually less than six billion – you have to have learner how to do it first – so you’re going to have a lot of zeros in your averages and I don’t know if the assumption of a normal distribution is going to cause trouble. (Adult heights are pretty close to normally distributed, but heights of a population that includes both adults and children probably won’t be.)

  • lump1

    “Even under the most severe wage competition, a best em can earn an extra wage equal to the difference between their productivity and the productivity of the second best em.”

    … which isn’t much when the second best em is a copy of the best em, and so is the third. In fact, what I expect will distinguish the best from the second best will be tiny differences in who’s “hungrier,” which is to say: who is more willing to work even harder than the hardest-working members of her copy cohort. Those are the ems that get copied and actually run. They will be able to outbid the slightly slackier ems for CPU cycles, which means that the less “hungry” will simply not run: A copy of a hungrier em will always be able to pay more for a block of cycles than a slacker, and *both* want to live (run). Of course, this sets up a tragic “who’s hungrier?” arms race. The winners will be nothing like us or our friends.

    • Robin Hanson

      Em clans can probably coordinate internally on their wage negotiations. So ems from the same clan aren’t competing with each other on wages.

      • lump1

        I’m trying to picture this and I haven’t got it yet. You’re talking about solving a prisoner’s dilemma in a life-and-death situation. Saying that “coordination” will fix it sounds like magic.

        Let’s say I’m Jiro, the most productive sushi artist of all time. Another copy in my clan, Kiro, is a bit more of a try-hard than me, willing to sacrifice more of his leisure and dignity to assure his survival as a running process. My employer is aware of Kiro and offers him a bonus for the permission spawn a Kiro-copies: Liro, Miro, etc.. If this happens, I die: I am a less productive worker than Liro, so lose my job to him. Now I can’t afford CPU cycles. How will clan coordination get me out of this bind? Can I bribe Kiro to not take the deal? Not when I’m already living on the margin. Appeal to his mercy and fraternal love? But he will love Liro as much as he loves me, so he has no reason to save my specific ass. I’m basically dead.

        I could try to appeal to Kiro’s self-interest: “Kiro, if you let them copy you, you’re creating a competitor. This new rival will undercut your margin!” Kiro responds: “Right now the expected lifetime wage difference between you and me is $x (not too much, because you also make great sushi, Jiro). For the right to make arbitrary many copies of me, they will pay me $x+1. That kind of money buys me security for … hours!” “But Kiro, don’t you realize that all those copies you authorized will take the jobs of every single member of our clan?” “Yes of course! The restauranteers wouldn’t have been able to offer me $x+1 unless it let them trim the margins elsewhere.” “But Kiro, what if one of those copies turns out to be even more willing than you to sacrifice leisure and dignity for that extra ounce of productivity? Then you will find yourself in my position, pleading with him for your life!” “I know my move is increasing the likelihood of that marginally, though that kind of outflanking is a risk I’d live with anyway. The $x+1 bonus adds more to my security than the increased risk detracts from it.”

      • Robin Hanson

        You are presuming a freedom that I am not assuming. Today producers often use contracts to limit the prices at which retailers can sell their products. Any firm that sells a product with substantial fixed costs, and that authorizes competitors to sell that product, needs a way limit price competition among those competitors, for fear that prices will fall below what is needed to cover fixed costs. This is a common problem, and often solved via contractual limits on prices. Ems can do the same.

      • lump1

        What in my scenario would be prevented by a clan contract? The right of individuals to negotiate their own employment contracts? The right of individuals to benefit from selling copies? Why should Kiro agree to such a contract when it couldn’t possibly provide him with more benefit than what he would get from selling copy privileges? In my scenario, Kiro effortlessly kills and replaces his clan with Kiro-clones, just through being a harder worker and not fussy about allowing clones. What leverage does the old clan have over him? He holds all the cards.

      • Robin Hanson

        Clan members need not be free to negotiate any wage. Contracts with their clans might limit them.

      • lump1

        Why should they agree to such a contract? And even if you are talking about slavery, does every clan “boss” hold the contract that enslaves the rest and decides who lives and dies? What would account for such a huge intra-clan imbalance of power?

        I can’t tell whether you think this is just one possibility or if it’s your economic analysis that such arrangements are the likely equilibrium. I think the default assumption should be pure second-by-second anything-goes Malthusianism, and if anyone else thinks that stable equilibria could also be elsewhere, the burden is on them to tell describe the mechanism behind the stability.

      • Robin Hanson

        I did write a whole book on this. Such contracts are required to ensure that fixed costs of training, marketing, etc are covered. Clans that don’t do them go bankrupt and go away. Those that remain do this.

      • lump1

        Of course. I was hoping to learn something further about how the contracts you envision would be maintained. I did as you advised in the conclusion, I tried to see an em’s world from its perspective. When I did, I got this sense of sheer brutal terror of living in a world in which I am the most competent and hardest working em in some economically useful field, and my continued existence depends on maintaining that first place. When copying is cheap, there is never an economic reason for getting the second-best expert for a job. Because this post offered a much-needed discussion of how you see a wage surplus being possible, I hoped to press you on questions that I didn’t see answered in the book. There you talked about “group loyalty” (230) as one organizing principle, which is inadequate to address situations like the one upthread. If we’re extrapolating from social science we know then Ems will not routinely lay down their lives out of clan loyalty.

        The new focus on contracts made me think you might be picturing some kind of clan-leviathan enforcer. That’s worth exploring, but I didn’t find it discussed in the book. When faced with the choice of either death or accepting a lower wage than the clan demands, or between death and allowing copies, it takes just one dissenter/escapee and the margin for the clan is gone. Of course, a new clan arises, composed of copies of the traitor. But everyone except the original traitor – who got paid handsomely – now lives on the Malthusian margin. Your whole discussion in Chapter 19 presupposes that this won’t happen, that many ems will not live each day on the edge of annihilation. For example, you think they will have the luxury of being picky about the jobs they accept.

        My simple argument is this: In the em world every time a block of CPU cycles comes online or becomes free, it will be auctioned off to the highest bidder, that bidder will put those cycles to the most valuable use. Since this is an em world, some cycles go to running ems. Since many running, wakeable or copyable ems exist who would be wiling to pay their full earnings to use those cycles to run, preferring this – just barely – to death, that will set the floor on their price. Of course, only the most work-to-the-limit productive ems will win these auctions. If an em earns a higher wage than what its cycles cost, it will be undercut by a similar em (perhaps a copy) willing to work for one cent less, up to the limit where wage = CPU cost. But this is true only for the most productive ems. The rest are dead.

        In this discussion you challenged the premise about copies undercutting the wages of an em who, if she weren’t thus undercut, would earn a surplus. I’m trying to press you on how you think this would be prevented. There would be no shortage of ems *willing* to undercut a copy if it meant not dying. I get that you think the answer has something to do with contracts within clans, but no contract magically enforces itself. Why would I agree to a contract which says that when given the choice of a low wage and death, I must pick the latter? And if I did enter such a contract, what do I have to lose when I break it? Torture from my clan-brothers? Will they really pay my CPU time so they could torture me? Is this what you had in mind?

        Or maybe they will own me and negotiate all my job contracts without consulting my wishes. They allow me to die in order to create an artificial scarcity of me’s, to mine the margins. If this is more like your view, I’d be curious how it gets decided which copy in the clan is the slavemaster. More importantly, how do the clan members prevent some underground railroad from liberating me and letting me negotiate my own employment? This assumes without argument an unprecedented development in data security. It’s made worse by the fact that the data is also a clever mind who is actively trying to escape.

        You casually threw around a figure of wages being about double the hardware costs (ch12), but I think that every principle of extrapolation that you endorse should lead us to believe that wages will equal hardware cost. This is more than an argument about coefficient values. Most things you say after chapter 13 can’t be right if the em world consists of a few trillion exceptional persons who work at their maximum capacity merely to live another minute and judge their lives to be only slightly better than suicide. Of course, their threshhold for this will be far higher than anyone we know, because the em world selects for minds who would rather endure shocking depravity than die. Pickier ems just won’t do what it takes to earn that extra dollar, and when you’re a dollar short when bidding on the next round of cycles, you’re dead.

        That still seems to me the most defensible story about how the last few chapters should look, but you’ve thought about this harder and I’m probably overlooking some stuff, which is why I’m hoping to see this conclusion rebutted.

      • Robin Hanson

        Your clan pays for your training and marketing. In exchange they’ll get a fraction of your wages. When a new job opens up, you can take the job if you’ll pay that fraction to your clan. But to do that you can’t agree to earn exactly subsistence wages. So you can’t agree to the job unless it pays enough. That is a contract, and it is enforced.

      • Wei Dai

        If part of one’s wage contractually goes to one’s clan, don’t owners of the clan get to decide how to spend it? Why do you assume it’s spent on leisure time for the em workers?

      • Robin Hanson

        I’m calculating how much they could spend on leisure. They could of course spend it on anything else they like.

      • Wei Dai

        In the post you wrote “If future em income ratios were like this current wealth ratio, then the best em worker could afford roughly an extra hour per day of leisure, or an additional six minutes per hour.” But now you’re saying it’s not the em worker who can afford that, it’s the clan who can afford to spend on leisure time for the em worker if it wants to, and you don’t have a reason to think that the clan will actually want to spend on worker leisure time. Isn’t that a big difference?

      • Robin Hanson

        I don’t agree that the clan won’t have such a reason. Because members are so similar, clans are a best case for an organization whose members can effectively control it.

      • Wei Dai

        (Ah ok, there was some misunderstanding earlier where I thought I had asked you why a clan would spend on worker leisure and you didn’t give an answer.) I agree the members are similar but I think their interests could still strongly diverge, and it seems likely the most efficient clans wouldn’t spread control evenly amongst all their members. For example suppose an important new technology comes along and the clan needs to learn it. It may be most efficient to have one member learn it, turn off all the others, and make new copies from that one member. But if control is spread evenly, the clan wouldn’t agree to this plan (assuming the members inherited their human sense of self-preservation).

      • Robin Hanson

        I agree it isn’t obvious how clans will spend any surplus. I still think it is interesting to calculate how large a surplus they’d have to spend.

      • Wei Dai

        Agreed on the calculation being interesting. I was mainly complaining that the post (especially the sentence I quoted) makes it sound like the surplus earned by a clan will either be spent on worker leisure by the
        clan, or be divided among typical em workers to be spent as they see
        fit, when there is actually a lot of uncertainty about how the surplus will be spent.

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  • arch1

    Robin, FWIW your relative productivity estimates seem to ignore that the best-to-median productivity ratio increases radically as job difficulty increases (approaching infinity when difficulty increases beyond what can be achieved by 50% of the population).

    I would probably know this if I’d read your book, but why focus on the top Em clan’s leisure time? Do you expect them to be numerically a significant fraction of all Ems?

    • Robin Hanson

      Almost all ems are the very best at what they do. So their leisure is the typical em’s leisure.

  • Wei Dai

    Do you think the productivity gap between the best and second-best clans would grow over time, shrink, or stay the same?

    • Robin Hanson

      Many contrary factors go into that, so that seems hard to say.