Koestler says a bunch of contradictory things about Plato. He recognizes that there are a bunch of different time periods to explain, so he seems to recognize that his explanations don't fit together.
One place he says that it's not Plato's fault, but the fault of the Neoplatonists. Maybe that could explain the decline after Ptolemy and the lack of interest of the Byzantines in science, but in the quote above he's talking about decline before Ptolemy, so Plato proper. He specifically notes a gap between Hipparchus and Ptolemy, so he is talking about a fast fall, not decay past Ptolemy.
He recognizes that the Western Dark Age didn't have Plato or Aristotle. He specifically mentions that the West got Aristotle before Plato. In between it got Archimedes and science exploded. Aristotle is generally seen as promoting medieval science (Roger Bacon was a fan), but at the very least he didn't interfere with reading Archimedes. There was a decline of science and civilization generally when Petrarch translated Plato, but I think that's a coincidence, really the fault of the Black Death.
Apollonius introduced epicycles and proved a theorem of the commutativity of addition: a small epicycle about a large orbit appears the same as a large epicycle about a small orbit. This makes it seems like he was using them to represent heliocentrism, not just fitting data.
The Ptolemaic model has an epicycle and an equant for each planet. One of them corresponds to heliocentrism and the other to the non-circularity of an orbit. (That's very vague because the correspondence is different for the inner planets vs the outer planets. The role of epicycle vs deferant gets switched and (thus) which orbit, the planet or the earth's has its non-circularity approximated differs.)
“in the year 1500 Europe knew less than Archimedes who died in the year 212 BC.” In short, the answer seems to be Plato and Aristotle (OP)
But Plato and Aristotle came before Archimedes! How is this an answer? Bad ideas can retard progress, but they didn’t hurt Archimedes.
By the end of the third century BC, the heroic period of Greek science was over. From Plato and Aristotle onward, natural science begins to fall into disrepute and decay (Koestler)
This is complete garbage. The Hellenistic period after Aristotle was much better than the “heroic” period before him. Aristotle appears to have created science. While there were some scientific Presocratics (Thales, Democritus), Koestler’s Pythagoras is a fantasy. Aside from inflating the achievements of the Pythagoreans, relying too much on Simplicius a thousand years later, he also gerrymanders the real achievements of real people, arbitrarily crediting the Pythagoreans. Maybe Herakleides was a Pythagorean, but he was also a student of Plato, as Koestler mentions in passing, but fails to credit. Classifying Aristarchus as Pythagorean rather than Hellenistic is crazy.
Hellenistic science didn't decay, but abruptly collapsed, with civil war in Alexandria in 144BC and, more mysteriously, with the peaceful Roman annexation of Pergamon in 133BC.
That's a quote from Wealthfront. Here's the fine print:
The cash balance in the Cash Account is swept to one or more banks (the “program banks”) where it earns a variable rate of interest and is eligible for FDIC insurance. FDIC insurance is not provided until the funds arrive at the program banks. FDIC insurance coverage is limited to $250,000 per qualified customer account per banking institution. Wealthfront Brokerage uses more than one program bank to ensure FDIC coverage of up to $1 million for your cash deposits.
You phrased your thought experiments in terms of good and bad lives. But what about the good and bad parts of a life? When you imagine a lot of good lives, you say that the value doesn't add up. But what about the bad parts of those lives? Do you imagine that still accumulates and wipes out the value in the good parts?
Maybe this is just nitpicking, but I found this passage confusing:
On the level of corporations doing this direct from the top, often these actions are a response to the incentives the corporation faces. In those cases, there is no reason to expect such actions to be out-competed.
In other cases, the incentives of the CEO and top management are twisted but the corporation’s incentives are not. One would certainly expect those corporations that avoid this to do better. But these mismatches are the natural consequence of putting someone in charge who does not permanently own the company. Thus, dual class share structures becoming popular to restore skin in the correct game.
Is that last sentence in the wrong paragraph?
Before I get to my reading that suggests that change, a couple things that I found confusing that could have caused me to misread it: What does "in charge" mean? The CEO or the owners? How do corporations face incentives, rather than individuals?
I read the first paragraph about Wall Street and quarterly reports giving bad incentives to the CEO. Dual class shares exist to protect founders from outside investors. So doesn't that sentence belong in the first paragraph, not the second...? (It's a little weird to say that outside investors don't have skin in the game. Maybe you mean that money managers investing other people's money don't have skin in the game. Also, it's more that super shares remove control, rather than add skin. I think that it may be more important that the founders have demonstrated ability to make long-term plans than their incentives. Consider Steve Jobs returning to Apple as a hired-gun CEO.)
What is the other case, the case of the second paragraph? When Wall Street or other owners understands the company, but has to install a hired manager? Then, yes, the misalignment of incentives makes it difficult for the board to hire a CEO. But super shares don't seem relevant to that problem.
I think that you mixed them up. When I use the markdown syntax, I get full-width, presumably inline images, not block. Whereas when I follow your other instructions...I can't follow them. When I select text, I don't get an image button, just (Bold, Italic, Underline, Link | Title, Blockquote). Is image supposed to be on that list? If so, that's a simple explanation of the bug.
Sorry if I'm belaboring the obvious, but aiming for secrets is an extreme form of comparative advantage. Maybe the framing is important, either by focusing on the tail or on risk or by some purely psychological effect, but the argument is exactly the same.
What's up with images? I stumbled on advanced image features. I don't mean badly discoverable, but really clearly a UI bug. The features let me resize them and choose between left- and right-justification (and text flowing around them?) and it's a pity that they're not widely available. Specifically, I made this comment. First I switched my account to markdown (is there a way to switch a single comment?). I made the comment with the image. I switched my account to wysiwyg. I edited the comment and accepted the option to switch the comment to wysiwyg. At this point I had the resizing ability, but only for the old markdown image and not for new images I added in wysiwyg, either that comment or a comment that started as wysiwyg (the test comment below).
I replicated this procedure with this comment. It started as markdown and I can resize this image:
In other words, regression to the mean. The predictions form a line, with a positive slope. Less than 1, but only perfect predictions would have slope 1. The intercept is high, which is overconfidence. But the intercept is a statement about the whole population, not about the lowest bin.
Here are the graphs. A lot of information has been destroyed by binning them, but it doesn't sound like DK thought that information was relevant or made use of it:
The second is different. That better matches the cartoons one finds for an image search for Dunning-Kruger. But I'm not sure it matches this post. (The third could be described as yet another shape, but I'd classify it as a line with a very low positive slope.)
The fourth graph is of a more complicated intervention. It seems like it has the opposite message of this post, namely it finds that the 4th quartile is better calibrated than the 3rd.
I don't think he's saying that error is good. He's saying that ignoring error is bad. And there's a valley of bad rationality in which the error level is low enough that people ignore it, but it still matters. Specifically, he says that black box models that don't include error are bad. You should model error of components and error propagation and design circuits that are robust to error. I'm not sure what this would mean in practice, though. Today we design systems that recover from computers crashing, but recovering from wrong computation is harder.
But this is 1948. In 1956, he showed how to take digital gates with known error rates and build from them digital gates with lower error rates. This opens up the possibility of getting the error low enough that you can ignore it and embrace digital logic. I'm guessing that he changed his mind and rejected the earlier paper, but it would be nice to have an explicit statement.
Eliezer's post is quite compatible with Sabine's. They may have additional positions that are not compatible, and maybe you know that from their other posts. Eliezer claims a very weak version of realism, while Sabine rejects a strong version. Eliezer claims QCD is true because it predicts reality; whereas Sabine says that she doesn't know what it means for quarks to be real. Sabine does not address truth or reality of theories and Eliezer does not address the reality of objects.
I think that your second quote is misleading. She does not claim to reject the truth of theories, only the truth of objects. That seems like an odd word choice, but the third time she uses "true" it is explicitly about constituent objects.
Scientific progress is not at all continuous and not systematically forward. There have been many periods of scientific regress. The most famous is the Dark Ages between Antiquity and Modernity, hence Luke's example of Hero.
But regress is all over the place, even in well-known examples of progress, like the Italian Renaissance. People often say that Renaissance art began with Giotto or maybe even so specifically with his invention of perspective. But, actually, most accounts of Renaissance art skip ahead a century from Giotto's death in 1337. In particular, perspective regressed and was reinvented in 1413 by Brunelleschi. And this wasn't even an independent discovery: Brunelleschi could see Giotto's work and knew that better was possible. *
Going back to Hero, "ancient Greece" is a bad category. Hero isn't the pinnacle of ancient Greek science, but a figure of a Roman era of rebirth after a dark age 150 BC – 50 AD during which we know the names of no scientists. In fact, almost everything Hero writes about he attributes to Ctesibius (d. 222 BC). If he is truthful about his sources, then there was a either a 250 year pause in pneumatics or there was more progress that was lost in the interim. In general, a controversial question is whether the rebirth in Roman Alexandria reconstructed and surpassed Hellenistic Alexandria or whether it was only able to understand a few books.
* Lorenzetti (d. 1348) seems to have been pretty good at single buildings, but bad at putting them together. Compare the only city I can find by Giotto.
That sounds like a totally normal coup, openly seizing power and thus creating a Schelling point for everyone to fall in line behind them. Maybe they lied about having written earlier manifestos that also acted as a Schelling point, but that would just be a single lie; and just a bald assertion, not backed up by the authority of some "info-processing apparatus."
I think it would be clearer if you said who "they" is, men or women. Having read the post and found that it's all about men, it's pretty clear that it is men, but when I first read it I found it pretty ambiguous and in fact assumed that it was women. On a slightly different note, my failure to understand the relation between the two statements seems like a good example of the writing advice that you should repeat your thesis at the end, because it may be incomprehensible on the first pass. You do have a kind of thesis at the end, but it seems backwards, the more easily comprehended version at the end, rather than the beginning.
What do you mean by "modern experience"? If you mean things happening at new scales, like twitter mobs, probably game theory is not the right way to describe it, but accidental consequences of psychology adapted for smaller settings. Whereas I think Benquo is talking about smaller scales, like office politics, where the resources are near enough to seize. That may well explain irrational behavior at broader scales. (Although I think twitter mobs aren't that asymmetric.)
OK, if praise-gangs don't actually do anything, while destruction gangs actually destroy, then praise-gangs are cheap talk. But that sounds to me like it's just pushing it back another level. Benquo claimed that there was an asymmetry in joining putatively effective gangs. If destruction is 10x as effective as creation, then maybe a pebble promoting creation should get 1/10 as much credit as a pebble promoting destruction.
If that's what people are getting out of it, it's symmetric, and they might as well join praise-gangs, so this fails to explain the asymmetry. You are disagreeing with Benquo just as much as Jimrandomh is.
In the original series of articles by Eilenberg and Mac Lane, they wrote something like:
"Category" has been defined in order to be able to define "functor" and "functor" has been defined in order to be able to define "natural transformation."
The word "natural" has a long history in mathematics. Category theory is a rigorous interpretation of what it means (neither stronger nor weaker than the more obvious notion of canonical). The first example of a natural transformation is the determinant. What does it mean that it is "natural," that is compatible across rings of coefficients?
This (especially Huff) seems like a very fine-grained question, as if you already know the answers to coarser questions, like why not Rome or the Song dynasty or Roger Bacon? If you see history as a long arc of progress with China a little ahead, then it is natural to ask what happened at the end, a sudden sprint or a stumble. But do you understand history well enough to justify such a question?
History is not monotone. There are definite dips, such as the Western Dark Ages and the chaos between Chinese dynasties. But is each dynasty better than the last? You should try to plot a rough curve, rather than asking the binary of science being invented or not. Trying to explain more bits of information is usually easier.
Progress is not uni-dimensional. The Song was the most commercial dynasty. But should we expect it to be the most scientific? People usually say that the Greeks were better at science, the Romans at engineering. Instead of asking why China failed to progress, ask why Roman regressed, without the obvious cause of a collapse. How is uneven progress possible?
There are a handful of SNPs (mainly in Cytochrome P450) that predict how fast you metabolize drugs. This is a shortcut to dosing drugs. But the big problem is that people don't adjust their doses at all. The much more basic personalized medicine is to experiment with doses. If you aren't doing that, using the SNPs as a shortcut to predict where to start isn't much of an improvement.
It might be useful to make such requests more explicit.
It might be useful to make explicit how much progress has been made. Most of the discussion has anchored on Baudrillard and the number 4, but it's not clear that you wanted that. Is this even supposed to be a discrete qualitative model, or is it continuous and the stages are just for verbal convenience? ("The system wireheads itself" vs "the system wireheads employees" is the only thing that jumped out at me as object-level qualitatively distinct.)
If you start with bullet points and then add filler, it's probably worthless filler and the worst of both worlds. I don't trust the people who say that they want complete sentences. They're probably just praising people for going through the motions, not paying attention to whether it's actually easier to read.
There have been a lot of such manifestos, so it will be pretty hard to isolate the effects of any particular one.
Such manifestos can be divided into two classes: those which set p-values in opposition to confidence intervals and those that describe them as the same. The first class has a positive suggestion: use confidence intervals. It seems to me that positive manifestos are more likely to be adopted than those which merely condemn p-values, but offer no alternative. This manifesto seems to condemn confidence intervals, but makes the very vague suggestion to pay attention to effect sizes. In the end, maybe that amounts to the same thing.
There are lots of examples where the optimal state has some kind of consistency property (eg, lack of hypocrisy). It's probably always possible to use the failure of consistency of the current state to improve, but I think that there are lots of examples where naively trying to improve consistency makes things worse, not better.
I argue in the last piece that it is common even now for people to engineer blackmail material against others and often also against themselves, to allow it to be used as collateral and leverage. That a large part of job interviews is proving that you are vulnerable in these ways.
I don't see anything about existing practices for job interviews in the previous piece.
This is all so abstract. Does it match how the world works?
Why are we talking about this? Because the National Enquirer knows how to get away with blackmail? What do you think of the hypothesis that blackmail is legal if lawyers get a cut? That sounds to me like the worst of both worlds.
I recently learned that UK politics is openly described in terms of blackmail. There is some equivocation and I'm not sure it's actually true, but it isn't a norm violation.
Usually this comes up in the context of financing education, where they are sometimes called human capital contracts. This was previously discussed on LW. I left a comment there giving several of education (England, France, Yale) and another example more like this post: "360 deals" in the music industry, where instead of touring existing to promote the album or vice versa, the record label owns a proportion of everything musician does, so that their interests are more aligned. I think that the most famous example is Lady Gaga, who signed such a deal fairly early in her career. (The wikipedia article I link gives as examples even more famous musicians Madonna and Jay-Z, but those were late in their careers and, I guess, maybe in the opposite direction, where the tour promoter buys a chunk of the record.)
Yes, you should draw calibration curves without binning.
The calibration curve lives in a plane where the x-axis is the probability of the prediction and the y-axis is the actual proportion of outcomes. We can make each prediction live in this plane. A scored prediction is a pair of an outcome, b, either 0 or 1, and the earlier prediction p. The value p belongs on the x-axis. The value b is sort of like a value on the y-axis. Thus (p,b) makes sense on the x-y-plane. It is valuable to plot the scatterplot of this representation of the predictions. The calibration curve is a curve attempting to approximate this scatterplot. A technique for turning a scatter plot into the graph of a function is called a smoother. Every smoother yields a different notion of calibration curve. The most popular general-purpose smoother is loess and it is also the most popular smoother for the specific task of calibration curves without bins. Frank Harrell (2-28) suggests tweaking the algorithm, setting α=1.
I've asserted a lot of things. Should you believe me? You don't know that I'm disinterested (though you should damn well know that 300 pages of advertising copy is very, very interested). But I can provide a different perspective; you can't imagine that anything good is going on, but I can try to widen your imagination.
More broadly and aside from allegations of specific wrongdoing, the claim is that HFT is just shaving the margins of everyone who makes trades more slowly.
The main difference in perspective I want to promote is how you carve up the market. You're carving it into HFT and Everyone. I say that you should carve it into market makers and investors. HFT makes money. It makes money by shaving the margins off of someone. But why think that it's shaving "everyone"? It's competing with market makers and shaving their margins. The market makers are mad about that. That's enough to explain everything that is observed. Maybe something bad is going on beyond that, but no one says what, no one except liars.
I could say more, but I think it would distract from that one point. (Indeed, I think my prior comments made that mistake.)
I haven't read it, but Vanguard wrote about how it loves HFT. A lot of what I know is from Matt Levine, but he is such a fragmentary blogger that he probably doesn't say much in one place and it's hard to find any particular thing he's written.
Your abstractions like "benefit" seem confused to me. Where is money flowing? How?
By the biggest players, I mean investment firms. I thought that the biggest investors are bigger than the exchanges, but maybe they're only equally big. For example, BATS and Fidelity both have a market cap of $60 billion (NASDAQ $14B, NYSE $6B).* HFT firm Virtu has a market cap of $5B. That is, the net present value of the profits Fidelity extracts from its retirement accounts is $60B, while the NPV of the profits BATS extracts from all retirement accounts in the US is about the same. BATS allows (and subsidizes) HFT because it thinks that Fidelity wants it. That's what BATS says and that's what Fidelity says. Maybe they're lying and actually BATS has market power to extract money from Fidelity, but I'll get to that later. [And why would Fidelity go along with such a lie?] [* looking up these numbers again, I find completely different numbers. But they're roughly right if we swap NYSE and BATS.]
Transaction costs are way down. This is easily and objectively measured in terms of bid-ask spreads and trading fees. This is money that is not going to the middlemen, neither exchanges nor market makers, but is saved by the investment firms, which is why they love HFT. There is a more subtle argument that market liquidity is an illusion that will go away "when it matters" and produce flash crashes. I think that this is also false, both painting too rosy a view of the past and exaggerating the damage caused by flash crashes, but it is much harder to argue about rare events.
HFT and running exchanges are not terribly lucrative businesses, not by the standards of Wall Street. HFT makes orders of magnitude less money than market makers made (in aggregate) even 20 years ago. Individual HFT firms make a lot of money, but there used to be a huge number of market makers who specialized in very small numbers of stocks. When HFT first appeared and drove out these people, they reduced the aggregate money going to market makers and the small number of HFT firms have continued to compete away their own profit. This is a pretty simple metric that is exactly opposed to many common stories. It's not that simple because many of the market makers were vertically integrated into firms that did other things, so it's not that easy to aggregate the market makers. In particular, I claim that's what Brad K's old job was (understanding market structure and making money off of the difference between markets, allowing the rest of the firm to think in terms of stocks, not markets). If you buy that, it makes the old market makers look even more bloated and thus the new HFT look even more efficient, but I don't claim that it is obvious.
But are you saying that Lewis is saying that the exchanges are sucking all the profits out of the HFT? I don't think that exchanges are very lucrative (see numbers in beginning). Does he give any numbers? I think that there are only about 4 companies running exchanges in the US (including IEX), which doesn't sound very competitive. But that's because they keep buying out new exchanges, so it can't be that hard to enter the market. And they keep the exchanges around, so they do see value in diversity. IEX being the 12th exchange and the 4th company does make the market more diverse and competitive, but they're probably only fill a small niche. Whereas the dozens of dark pools are already very competitive.
Everything I've ever heard attributed to Michael Lewis on this topic was false. Good ideas shouldn't require lies to sell them. And I can tell it's false because I carefully read the quoted passages. In particular, you conclude from his claim that "the richest people on Wall Street" are angry that they employ HFT algorithms. But that's not at all true. HFT is tiny. If the biggest players on Wall Street are angry, it's because they'd rather trade with HFT than with Brad Katsuyama.*
Is IEX listing a stock a significant milestone? I doubt it. IEX has been selling other stocks for 4 years, first as a dark pool and then for 2 years as an exchange. (But aren't "dark pools" evil incarnate?) IEX claims to be 2.7% of the total volume. I never looked at that number before today. I've previously claimed that IEX was a failure, and I was surprised to see that the number was so high. I welcome experimentation and I'm happy that they've found a niche. But if you thought it was a much better product that would quickly win in the marketplace, maybe you should reconsider this, 2-4 years on.** But the future is long. Maybe IEX listing individual stocks will matter, though you should be suspicious if no one can explain why. And it's hard to rule out the possibility that's it's a much better product that will take a long time to win.
* It was probably a bad idea to use Brad K as metonymy, because he plays two roles. I meant the kind of trader he was at the beginning of the book, who was outcompeted by HFT. I don't mean IEX, the market he now runs. In as much as IEX exists as a place to trade with people like him, it seems like most people wouldn't want to trade there, either, but it has a lot of room to evolve.
** To put the 2.7% in context, there are 12 exchanges, so I think IEX is the smallest, but I don't know. There are dozens of dark pools, so the 1.5+% market share IEX had when it transitioned to exchange was pretty big for a dark pool.
Is there no middle ground? You say that Kegan paints it as a binary ("nothing inside the range of what we think of as a normal workplace"). But you suggest that kaizen is an intermediate. Your summary as two phrases suggests that they are separable ("everyone talks about mistakes and improvements, and where the personal/professional boundaries are broken down").
Also, the negative book is about how things actually work, while the positive book is about the system working as promised. But this could be cherry-picking successes. Is there any reason to believe that DDO is self-correcting? Why shouldn't we expect the worst of both worlds, implementations with the face of a DDO that actually work as describe in Moral Mazes? (which is probably what people insinuate with the word "cult") Does the book make an argument, or does it just profile success stories?
Added: Indeed, "The Western Elite from a Chinese Perspective" talks about the discussion of emotion at business school and implies that people are faking it.
To add a little on different terminologies being a feature: if you ultimately want to apply linear algebra, you'll have to build a bridge from the theory to the particular application that is probably even more difficult than the bridge between two presentations of the theory. So it's probably good to practice building bridges.
(I'm also suspicious of people who say that the last book that they read on a subject was the best book, because that's when it clicked. How much did the first books prepare them?)
I don't know. My claim was based on reasoning from first principles. It was intended as an illustrative example that there could be positive externalities, not to measure them. If you have to triage nets, it's probably the way to go, but if you're triaging nets, you've probably made a bad decision. I can think of so many reasons to concentrate nets in one village, rather than spreading them out and micro-managing the deployments in the villages. One reason is habit formation. Another is the cost of distribution, which is probably low for marginal nets and high for a new village. A third is that there positive externalities compound, at least if you cross over the threshold of locally wiping out malaria. (Under that threshold, I'm not sure.)
Parasites in general and malaria in particular are pretty specific. For example, humans developed immunity shortly after speciation from chimps and malaria only jumped back 30kya (but probably did so multiple times to produce the several species of malaria). It's pretty clear that it doesn't have other hosts in the New World because the strategy of treating all humans in an area for 3 weeks wipes it out. But it's hard to rule out the possibility that it has other hosts in Africa.
Ewald has written lots of great papers. Here (ungated) is a paper summarizing his career. Mostly it's about explaining the past, but he goes on to say that we should design interventions to shape the evolution of infectious agents. His main claim about the past is that malaria is debilitating because it can be passed on from someone who can't move. Thus if we keep the mosquitoes out of beds or out of homes, then malaria will evolve to be less debilitating. But I'm not sure where he says this. Scientific American? TED?
Between rational and irrational is PD: individually rational, collectively irrational. Lanrian gave two reasons that nets benefit people other than they person paying. One is that they are most valuable for children. The other is that they protect people not using the nets. Probably the most valuable nets are those deployed on people who already have malaria, to prevent it from spreading to mosquitoes, and thus to more people. (See also Paul Ewald.)
If you regularly get sunburn, you should use sunscreen, because sunburn is unpleasant. Death isn't the only thing that matters. If you haven't noticed that you get sunburn or haven't thought about the possibility of using sunscreen or making simple interventions, like buying sunscreen, or putting it near sports gear as a reminder, there are great opportunities for improvement.
Whether to use sunscreen in situations where you won't get sunburn is controversial. But these situations are intermediate and it's probably less important to get them right than the extremes.
Added: maybe this sounds like trivial advice, but it's important to figure out what the typical advice actually means in terms of who it's aimed at (confer).
Classical antiquity definitely has plagues in the modern sense, like the Antonine plague. Indeed, in your paper you endorse the fairly standard claim that it was smallpox. That seems to me worth mentioning here, more than the negative claim about Hippocrates.
Yes, if the game has many opportunities for betting, you should focus on the instrumental use of the money, which is via compounding, thus the instrumental value is geometric, and so you should use the Kelly criterion. In particular, if your edge is small (but can be repeated), the only way you can make a lot of money is by compounding, so you should use the Kelly criterion.
France does this, at least in mathematics. Many people go straight from PhD to a permanent CNRS research position with no responsibilities. Short term postdoctoral funding was only introduced in 2005, but before that a lot of people did foreign postdocs. Alain Connes talks about this here.
But mathematicians are cheap. What can you do in other fields? What does CNRS do?
You seem to believe that people who engage in Tall Poppy Syndrome would engage in anti-social punishment in this game. But they don't. They engage in the least anti-social punishment and, by a large margin, the most pro-social punishment.