Something about this time of year brings out the cranks. Last year at this time, Lubos Motl (along with a few others, some just confused, others just pure trolls) was disputing the simple but surprising answer to a little probability puzzle. (See first here, then here, then here, then here, then here, and finally, for an enlightening coda, here — and then for one more afterthought, here, with approximately 1000 comments altogether).
This was a tricky puzzle and of course you don’t have to be a crank to get it wrong. But the cranks distinguish themselves by a) repeating exactly the same arguments over and over and over and over and over, while ignoring the fact that those arguments have been clearly refuted; b) reacting with outrage when it’s suggested that if they make an argument with multiple implications, they don’t get to pick and choose which implications to accept; c) dismissing the relevance of definitive counterexamples (e.g. “You’ve made an argument that appears to apply to a country of any size. Let’s see if your argument works for a country with only one family.” “That’s totally beside the point! I never assumed the country had only one family!”), d) rejecting all arguments by analogy by observing that the analogy is imperfect, even when the imperfections of the analogy have no bearing on the argument; e) constantly changing the subject so as to deflect attention from arguments they can’t answer; f) constantly changing their definitions midstream so that everything they’ve been saying, even when it is self-contadictory, becomes true by definition; g) discerning a conspiracy when multiple people take the time to simplify the arguments in the (always vain) hope of penetrating the crank’s thick skull; h) substituting mockery for discourse; and i) repeating the same arguments over and over and over and over, while ignoring the fact that those arguments have been clearly refuted.
This year, instead of a small cadre of cranks, we’ve been visited by a single crank, one Yoram Bauman, who’s cluttered up a long comment thread with repeated instances of behaviors a) through i). It’s not just the flimsiness of his arguments that makes Yoram a crank; it’s the way he repeats those arguments while completely ignoring every objection, or, on those rare occasions when he takes note of those objections, dismissing them as coming from an “echo chamber”. It’s his habit of making two arguments that directly contradict each other within a single paragraph, and then getting miffed when someone points that out. It’s his substitution of mockery for debate. (Note to future commenters: It’s okay, now and then, to adopt a mocking tone when you’ve demolished someone’s argument. It’s not okay to adopt a mocking tone by way of ignoring an argument.) Above all, it’s his intense and total disdain for the process of intellectual discourse, as if this were all just a game and getting things right doesn’t matter.
Well, of course, this is just an online discussion, and whether we get things right probably doesn’t matter very much in the grand scheme of things. But most of us are here because we take pleasure in trying to understand something. Yoram’s entire purpose here seems to be to undermine that pleasure with his clownish (and possibly feigned) stupidity. He’s the guy at the party who pisses on the table for attention and then, when everyone edges away at the same time, accuses them of sheeplike subservience to social norms.
Enough of that! While the year was bookended by cranks, it was filled with other lively discussions worth remembering.
Here were the most-commented-upon posts of 2011:
- First, the rationality test that led off the year.
- Then, with close to 500 comments in all, there was The Man Who Can’t Be Taxed, with followups here and here and here. In retrospect I wish I’d written this one a little differently to put more emphasis on the main point: If you want to understand the burden of a tax (or of any other government policy), you must follow the goods and not the money. I illustrated this with the example of a man who hoards financial assets, but (by hypothesis) never consumes above a subsistence level, never plans to consume above a subsistence level, and has no heirs. Then if the government funds a spending program by taxing this man, the burden of the tax must fall on someone else, because government spending consumes physical resources, and he has no physical resources to sacrifice. It’s the same point I made in our end-of-the-year Christmas fable, and if you don’t think it’s a point worth making, just check out how confused some of the commenters on Bob Murphy’s blog seem to be. One writes (re Ebenezer Scrooge) that if Scrooge consumes goods, he deprives others of the use of those goods (correct!) whereas if Scrooge hoards money, he deprives others of the use of that money (false, because taking money out of circulation changes the price level and increases the value of everyone else’s money, so they lose nothing). At one level, this is basic monetary theory, but at an even deeper level, it’s just basic arithmetic. What matters are the goods we consume, and those are what you need to track. Many a poorly trained policy analyst has gone astray by losing sight of this simple truth.
- Another big thread began here, where I caught Paul Krugman in a whopping howler. (Followups are here and here.) Because he is not a crank, Krugman acknowledged the logic and backed off his argument, though he did so in a rather churlish tone.
- Then there was the thread where I trumpeted my ignorance of Keynesian business cycle theory and asked for help in understanding what seemed to me to be a difficult theoretical point. Over the course of two more posts (here and here), I figured out where I’d gone wrong. It now all seems blindingly obvious. In my defense, I initially (before the first post) consulted several very good macroeconomists, who seemed to be as confused as I was.
- A big thread that might have been bigger was Econ 101 for the Supercommittee, where many commenters (including the ever thoughtful and provocative Bob Murphy) took issue with aspects of my post, but, due to my travel schedule, I was mostly unable to respond. I expect that if I’d been online that week, the 136 comments might easily have grown to 300 or so. I regret missing out on that discussion because a lot of smart commenters jumped in, and I wish we could have hashed out the issues. Maybe I’ll raise the same issues again soon, and hope that all those smart commenters are willing to come back for another round.
Speaking of commenters, you guys are great. For the most part you do an amazing job of staying on topic, and when you stray it’s usually because you’ve got something tangential but interesting to say. You engage with each others’ arguments. You are merciless when you think I’m wrong, supportive when you think I’m right (though sometimes you point out that I could have been clearer), and incisive in either case. I am not aware of any other blogger who is blessed with such a great cadre of regular and occasional commenters. I’ll try my best to keep you entertained this year.
Heads up : broken link in “This year, instead of a small cadre of cranks, we’ve been visited by a single crank, one Yoram Bauman,”
Mike H: Fixing, thanks.
In your second paragraph you have two “(h)”s; of course your second “h” is “repeating the same arguments over and over”, so I just wanted to let you know someone got your meta-joke (since you don’t make errors).
You must be a really, really slow and weak thinker if one year wasn’t enough for you to understand your mistakes.
I’m glad you’ve brought this up again (your first link) because it gives me a chance to admit that the only comment I’ve left on your blog was a) wrong and b) slightly snarky. So: a) you were right and b) sorry.
Nice recap. This makes me think that most blogs don’t do a very good job of highlighting their interesting content.
Bennett: Fixing; thanks.
Guy:
So: a) you were right and b) sorry.
Thanks. But for God’s sake do not jump to the conclusion that I’m always right! (You’ll find plenty of counter-evidence in the past year’s posts.)
Regarding the cranks in the comments, you might find this list of rules helpful. Especially rules 1 and 5.
I took issue with Yoram’s article as well, but I suggest putting that aside and checking out his cartoon guide to macroeconomics that just came out. It’s quite good (and Bryan Caplan liked it too!).
SL: ‘h) substituting mockery for discourse’
Motl: ‘You must be a really, really slow and weak thinker if one year wasn’t enough for you to understand your mistakes.’
This was my favourite thread. I love arguing about when a number strictly less than 2 is equal to 2.
Me thinks Yoram is a very smart (plus funny!) economist. But being called a crank by some Austrian misanthrope — who seems to be pissed off that someone dares to question the enlightened selfishness of economists — is actually a badge of honor.
Since Lubos has reared his head again:
Reversed stupidity is not intelligence. If you don’t know anything, then you get 50% on a True-False test, not a zero. If you got a zero, you could just flip all your answers around and get a perfect…which suggests the truth is really encoded into you and are being willfully stupid when you get a zero.
For someone who is familiar with Lubos’ blog in general (and has the background to evaluate it), does it strike you that he is literally wrong more often than he is right? That is, I know everyone makes fun of him for picking idiotic fights, but are those just the ones that come to attention? Or can I actually learn more about the world by reading his blog and just reversing every conclusion he comes to?
That would be a sad state of affairs. It could be true for Lubos, though I wouldn’t worry about Yoram. They aren’t in the same category, whatever this post may suggest.
Dear Anonynom, I only have 4,555 items on my blog so given the tiny rate, the potential for mistakes has been very, very low. The people who managed to catch me as writing an erroneous thing, for example Tommaso Dorigo of CERN who found out that I misinterpreted a cross section in a (wrong) paper he co-authored by a factor of three, are (or “is”) so proud that he hasn’t been talking almost about anything else than about the claim that he is the only person in the world who has seen Lumo making a wrong statement. I was still right about the big issue – that their paper on lepton jets was wrong – but the single tiny small observation of my error is enough to bring him into the Heaven.
And of course, I have loudly acknowledged he was right and I was wrong on the technicality, something that Steve Burg – who isn’t able to see that one can’t change the 50%:50% proportion of girls and boys in a large enough population by any “stopping rules” and other superstitions – is very far from.
IMO, you are being a bit harsh on Yoram. I think he is being thick headed more than crankish, though sometimes it is hard to tell the difference.
In any case, I learned something from the whole discussion, besides the fact that Yoram is wrong, so it was clearly useful. Perhaps a better theory of interest groups could come of this.
Either way, I am sure Yoram is happy. He now has new material for his schtick.
seems to me that Yorams experiment has been poorely designed – namely there was no effort to neutralize the effects of ideologies, specific skills etc (economic insight?). The students should have been asked to dontate to a certain single sick child …
Lubos pops up again and sounds off, like a cross between an intermittent wiper and a foghorn.
Again, he is answering a different question.
“one can’t change the 50%:50% proportion of girls and boys in a large enough population”. He’s changed the puzzle yet again, now arguing that the limit being 2 — which no-one ever denied — is enough. As Thomas Zare succinctly put it, the actual on the ground ratio will be a biased estimator of the population parameter (the female birth ratio (by convention in puzzles but not in fact 50%)). Noticing the bias is what Steve’s original post was all about.
By the way, why would an economics student feel it’s better to focus on one charity, rather than spreading out their giving? Are they assuming that the efficient market hypothesis doesn’t apply to charties, or is it for soem other reason?
Oh Ken B, for the love of god don’t feed the Lubos more sex ratio stuff. That serves no purpose.
However, I’m happy to hear any meta-comments about Lubos’ error rate. I wasn’t expecting Lubos to chime in himself with such a damning display of overconfidence, but I guess neither am I surprised.
Score so far: Lubos is even less trustworthy than I would think he thinks he is, reporting an approximate error rate of 1 in 4555. This doesn’t help me much with my question about the true error rate, but it should serve to just about convince any passing rationalist that Lubos is wildly overconfident, without even having to wade through *any* of his writings. Gold.
Extreme confidence in one’s ability to judge the truth even despite other smart people persistently disagreeing…this is sheer folly. 1 in 4555 is impossibly tiny. For perspective, the lifetime prevalence of schizophrenia *alone* is something like 1 in 200…no one deserves to be all that confident that their window to the truth is undistorted.
Mike H: “why would an economics student feel it’s better to focus on one charity[?]”
I just found $100 in my couch and decide to give it to charity. I consider the entire list of charities and decide on charity X. But wait, I find another $100. Why wouldn’t I give it (and every additional $100 I find) to X? Is it still not the best charity? Now, if I were rich enough, I could contribute enough to X that causes them to slip down the list (they are less “needy” now). If Steve thinks the best charity is funding his daughter’s college tuition, one hopes he has sufficient resources to move that charity to his least worthy (i.e., he has filled her college fund). UW students are rich enough, I suspect, to change there rankings of the two “charities.”
I question why a student who can afford $6 wouldn’t give it all to one of the two UW checklist “charities,” if either (either through one check-off and a $3 contribution outside the tuition bill or $6 directly). Of course, the extra work involved with giving $6 to one might cause some to give $3 to each (a transaction cost argument).
David Wallin: Yes, as you might or might not know I’ve made this argument in print several times. When someone gives to multiple charities without giving enough to have the second order effect of changing the ranking of the charities, we are entitled to conclude that s/he is giving for some reason other than pure selflessness.
SL:” Yes, as you might or might not know I’ve made this argument in print several times.” I’ve read most of your available writing and file it in my mind as if I came up with it. It really impresses the ladies.
This issue is one that caused me some concern over Youram’s work (beyond the other very relevant issues). Why would a student with a “free” $6 not give it to her highest ranking charity? Assuming that charity would rarely be one of the two check-off groups, we should see rather low box checking. Importantly, this choice of contributing to only one charity would be expected (I imagine) to be more common amongst students of econ. So, how do we reject the notion that econ students contribute as much as others, but do so to their top ranking charity only (rarely one of the two check box ones)?
Anonynom: I suppose if we were taking bets ex ante on “will Lubos Motl get this right” then his error rate would help us handicap. But ex post we have seen his answer and it is wrong. At 1/4555 his error rate must soar each time he repeats it.
One wonders if there is some error rate R such that if your rate is below R we can trust everything you say. (The mathematician in me notices there is no such R … )
There is an engaging example over at CafeHayek of the your-argument-proves-too-much problem,
“You’ve made an argument that appears to apply to a country of any size. Let’s see if your argument works for a country with only one family.”
The transgressor is Paul Krugman.
Here is a taste.
The Keynesian advocates failed to see that, if their theory of debt burden is correct, the benefits of public spending are always available without cost merely by resort to borrowing, and without regard to the phase of the economic cycle. If there is no transfer of cost onto taxpayers in future periods (whether these be the same or different from current taxpayers), and if bond purchasers voluntarily transfer funds to government in exchange for promises of future interest and amortization payments, there is no cost to anyone in society at the time public spending is carried out. Only the benefits of such spending remain. The economic analogue to the perpetual motion machine would have been found.
http://cafehayek.com/2011/12/open-letter-to-paul-krugman-3.html
I disagree with the commentors who say that you are being too hard on Yoram Bauman: bad studies are painfully common, and pointing it out when researchers are being as misleading and incompetent as Bauman is downright laudable. If only everybody would hold them accountable for their research (taxpayer funded, in the case of University of Washington faculty like Bauman). Thanks, Landsburg!
I don’t have an economist’s vocabulary, so could someone explain, re Yoram’s article and the ensuing discussion, what’s meant by “selfish”? Should I read it with the ordinary, if normatively fuzzy, sense in mind (as Yoram’s use of such words as “greedy” and “Grinch”* would suggest)? Or is there some technical meaning that makes the determination of selfish/not-self more precise (i.e., is there a difference between terms like ‘selfishness,’ ‘self-interest,’ ‘preference maximization,’ etc.?)? While I surely could sort this out myself, I wouldn’t deny anyone the chance to exhibit publically his erudition. I’m selfless that way.
*I’m not sure the Grinch was particuarly greedy- more of a cross between Scrooge and Ted Kaczynski – and he probably had a state-law nuisance claim against Whoville for excessive noise pollution, and possibly tresspass.
CJohn: I think you’re asking exactly the right question. Part of why I can’t take Yoram seriously (which is a substantially stronger statement than saying I disagree with him) is that he has no model of what “grinchiness” or “selfishness” consists of. Presumably it has something to do with the way other people’s utility enters into your utility function, but beyond that there are many many different ways to model this, and the behavior that will count as “grinchy” according to one model will count as selfless according to another. I’ve actually been scribbling away at this a little, trying to write down a fairly general model with parameters that can be tweaked to reflect the philosophical preferences of the observer — nothing worth sharing right now, but it’s clear that if Yoram had taken this problem seriously, this is the sort of exercise he’d have started with.
I’m glad the expected ratio problem was reposted. Last year, I thoroughly enjoyed the “less than 50% result”, although I missed the fact that “the extra half boy” introduces a new surprise. More than the distinction between expectation of the ratio and ratio of the expectation is needed for the second part.
“One approach to the problem (our usual one) is used in sections 3 and 4 and gives E(G)=E(B). A different approach is used in section 5 and gives E(B)-E(G)=1. It’s a pleasantly spooky problem.” – Tom
I was going to ask why this isn’t a contradiction, except that by the time I finished phrasing the question, I figured it out.
Consider the set of countries of completed families. When partitioned by number of families, each subset has E(B-G)=0. When partitioned by number of children, each subset has E(B-G)=1.
Phrased in pure arithmetic, suppose we have a multi-set of integers. In one partition every subset have a sum of 0, while in another partition every subset has an average of 1. The fact that this is possible comes from the fact that addition is not “infinitely commutable”.
Jeffrey, what do you mean by infinitely commutable?
So therefore, this hypothetical econ student believes there is, in fact, a “best” charity, therefore that economic efficiency has not had its full sway amongst charities and their donors. Is that right?
@Keshav – he means (I believe) that if you add a bunch of numbers together, it doesn’t matter what order you add them – unless your bunch consists of an infinite number of numbers (eg, a series)
Mike H: I’d like to see SL’s response. If you care, here is mine. Each person would have, what for him is, his “best” charity (at least at a point in time—preferences change, charities change). Given we’ll never agree on our preferences amongst charities, we’d expect to simultaneously have thriving charities serving many (even opposed) goals. Certainly, there is competition for donors, and, for example, a new AIDS charity could drive others out of the “market” by convincing donors they are more efficient (more likely to find a cure, etc.). But, we’d never expect that charity to be able to drive out, say, Greenpeace or the USO.
@David, I get that, and I’d also like to see SL’s response (though he’s a busy man :-) but it strikes me that charitable giving differs from other ways I spend my money in that I, in theory, don’t get anything from it. In that sense, what’s “best for me” should not be an issue. This is different from, say, consumer spending, where I part with my hard-earned marginal dollars in order to maximise my marginal utility. So, either
a) efficiency fails amongst donors and charities, and there really is a “best” one, so I should concentrate my giving with the “best” charity, or at least with my best guess about which one is best.
b) efficiency doesn’t fail, and if I think there’s a “best” charity, I must be mistaken – and realising this, I should spread out my giving.
c) or, in fact, donors are not altruistic, and I should concentrate my giving on the few charities that maximise my utility.
My guess is that the real world is a mixture of (a) and (b). But I’m curious as to why the hypothetical econ student would reject (b).
Sorry, I means (a) and (c), not (a) and (b).
There are some parallels between the charity and the boys and girls problem.
When I saw the gender ratio problem, I picked a country of a particular size, and worked out that the answer was going to be about 50%, except that I could not “complete” the calculation. For a “country” of millions of people I thought 50% was a close enough answer, and didn’t bother to work out what the discrepancy was. For most practical purposes, 50% would be a satisfactory answer to this problem. After some thinking about the posts, I realised that although 50% may be satisfactory for most purposes, it is in fact the wrong answer. SL had elucidated the discrepancy to arrive at a correct answer, which for large countries was very close to (but never actually quite equal to) 50%. The problem seemed to arise because many people would not see the difference between a practical and a precise answer. Yes, 50% is a good enough answer for any practical purpose, so perhaps you could say you were not “wrong” if you said 50%, but the purpose of the post was not to work out policy for a real country, but to say something about expoected ratios and ratios in expectation.
The charities thing is similar. Logically, you cannot fault the “precise” answer provided by SL, but people sometimes find it unsatisfactory, and therefore answer a different question, including total contribution to charities, or assuming that the donation has reduced the neediness of the charity. I can think of an argument that “allows” donation to different charities. If we rank the charities according to “need”, then we should only give to the neediest. But if we include an uncertainty term, then donation to different charities would be statistically indistinguishable from donating to a single charity at any reasonable confidence level. It would only require a tiny contribution from non-charitable aspects of giving to more than one charity to tip the balance in favor of spreading your gifts. So again, the precise answer provided by SL is correct, but for most practical purposes, giving to several charities is no different. (I can’t see a way to make giving to several charities actually better.)
The fact that people find it so difficult to accept these arguments indicates that they do not behave like “economic man”. Even when our “errors” are pointed out clearly, we often persist in our irrational behaviours.
Yoram’s argument seems to rely on assumptions about how students think which is difficult to defend without some evidence.
Stephan, Landsburg isn’t an Austrian. A while back one of his Slate articles on escalators was highlighted at mises.org as emblematic of those silly neo-classicals.
RE: Scrooge. I was the one who claimed that his desire to hold money deprived others of its use. Perhaps I have crankiness tendencies but I stand-by this claim. At one level it is clearly trivially true to say that to hold onto something deprives others of its use. Steve’s point however seems to be based on the fact that the prices of other goods will fall if Scrooge holds additional money.
Perhaps if they fell enough Scrooge would stop being a miser and start spending. If so he would do so at the point where the money had less subjective value to him than the goods he could buy with them. He would exchange his money for goods provided by people who value money greater than the goods they are giving up. I see no reason to treat the subjective valuations given to money any different from the subjective valuation given to other goods. By hoarding money Scrooge is making money more expensive for everyone else as well as making other goods cheaper.
Would Steve say that by hoarding , say, Picasso paintings, that Scrooge was doing everyone a favor by increasing the value of all other goods that happen not to be Picasso painting. The logic seems the same.
(BTW: I think I specified the money in question was a commodity money)
Could it be that an individual merely has nontransitive preferences with respect to “does this charity do more good than that charity”?
Mike H: I think my thick skull has now absorbed your point, and I continue to think about it. It is a very interesting point (which I think makes us realize that charity is rarely so charitable).
Keshav: “Jeffrey, what do you mean by infinitely commutable?”
Ordinary commutability means that A + B = B + A. More generally, if you have a finite sequence, the terms have the same sum no matter what order you add them in.
“Infinite commutability” would mean that if you have an infinite number of real numbers, you get the same sum regardless of the order of the terms. Surprisingly, this is false. This is covered in a standard Calc II textbook, although it’s not necessarily emphasized in lecture or on tests.
Here’s the simplest example I’ve seen for why it is false. Consider the following array of integers:
0 +1 +1 +1 +1 +1 …
-1 0 +1 +1 +1 +1 …
-1 -1 0 +1 +1 +1 …
-1 -1 -1 0 +1 +1 …
-1 -1 -1 -1 0 +1 …
-1 -1 -1 -1 -1 0 …
…
The sum of each row is positive infinity, so surely the sum of all the numbers is infinity. But the sum of each column is negative infinity, so surely the entire sum is negative infinity. Finally, the sum of each diagonal (going from the bottom left to top right) is 0. So the sum of all the numbers should be 0.
The resolution of this paradox is simply that addition is not “infinitely commutable”, meaning that if you have an infinite sum, rearranging the terms could give you a different answer.
(If you wish to feel slightly less mathematically disturbed, take comfort in that fact that “infinite commutability” is true when the terms are nonnegative.)
—
Phrased more like the gender ratio problem, partitioning the array into rows leaves each part with an average of 1. Partitioning into columns leaves each part with an average of -1. While surprising, this isn’t a contradiction.
In the gender ratio problem, one partition leave each piece with E(B-G)=0, and the other piece with E(B-G)=1. While this sounds like a proof that one of those computations must have been wrong, it’s no different from the other paradox.
Jeffery: lets be clear that the only correct computation gives E(B-G)=0.
I was referring to section 5 of Tom’s post, which considers “The ensemble of completed countries for a fixed N.” Tom writes “In this case, by inspection of the ensemble, E(B) = E(G) + 1.”
I certainly agree that in any country, of any size, and with any stopping strategy, E(B-G)=0.
I meant to qualify “any country” with “any country where the country is selected before the births take place.” Countries with N children and usual stopping rule can only be selected after the fact.