If you happen to be in the Rochester, New York area, you’ll want to know that the esteemed Robin Hanson, proprietor of the endlessly fascinating Overcoming Bias blog will be delivering the Lawrence Goldberg Memorial lecture, based on his new book The Age of Em this Monday, April 18, at 7:30 PM in Dewey 1-101 on the University of Rochester campus. The general public is warmly welcome.
(Click poster to enlarge.)
Have at it:
Click on the image to solve the puzzle. You’ll see a “save” button in the upper left in case you want to save your work and return to it later, and a “Submit” button if you want to submit your solution for judging. The three closest-to-perfect solutions will be acknowledged in this space and will receive appropriate rewards after the passage of a decent time interval (the length of which will be determined partly by the speed at which solutions arrive, but ought to be about a week).
Please try to keep spoilers out of the comments.
The rules are basically London Times rules:
A 2006 study by Matthew Salganik and his co-researchers at Princeton suggests that a huge amount of effort is wasted in many different areas of human endeavor, and the resulting outcomes are far less than optimal — but that there is a simple algorithm that could fix both problems.
In Salganik’s experiment, users of a music-rating site were divided at random into eight artificial “worlds”. All of the users in all eight worlds had access to the same library of songs, which they could download or recommend to their peers, but they could only recommend songs to other users in the same world. Also, each user could view the number of times that a song had been downloaded, but only by other users in the same world.
The goal was to see whether certain songs could become popular in some worlds while languishing in others, despite the fact that all groups consisted of randomly assigned populations that all had equal access to the same songs. The experiment also attempted to measure the “merit” of individual songs by assigning some users to an “independent” group, where they could listen to songs and choose whether to download them, but without seeing the number of times the song had been downloaded by anyone else; the merit of the song was defined as the number of times that users in the independent group decided to download the song after listening to it. Experimenters looked at whether the merit of the song had any effect on the popularity levels it achieved in the eight other “worlds”.
Continue reading ‘An Algorithm For An Automated Meritocracy’
It now seems likely that:
Given that, it seems like one of the following two things should happen at tonight’s debate:
Either:
or
This gives each of them only a 50% chance of survival. But if they’ve already each got only a 50% chance of survival, that’s no loss. And it substantially increases the value of survival, because it gets things over with now instead of a month from now.
If I’m wrong in saying that each currently has a 50% chance — if instead, say, Cruz has a 60% chance and Rubio a 40% chance or vice versa — then they can flip an appropriately weighted coin.
Continue reading ‘Political Strategy’
My favorite Scalia story is from Ted Cruz’s book A Time for Truth. This took place in 1986, when the departure of Warren Burger had created a vacancy on the Supreme Court, and it was clear that attorney general Ed Meese would be President Reagan’s most influential advisor on choosing a nominee. According to Cruz:
Everyone knew that two of the stars on the conservative side, and thus possible nominees, were Robert Bork and Scalia, both on the D.C. Circuit. So one day Scalia was walking in a parking garage at the appellate court when two U.S. marshals stopped him. “Sorry, sir,” one of them said. “We’re holding this elevator for the attorney general of the United States.”
Scalia pushed past them, entered the elevator, and pressed a button. As the doors closed, Scalia shouted out, “You tell Ed Meese that Bob Bork doesn’t wait for anyone!”
Listening to Season One of NPR’s podcast Serial, which is the story of a real-life murder case, I came away about 80% sure that the defendant was guilty and 100% sure that I’d vote to convict him. This got me to pondering whether my standards for reasonable doubt (apparently less than 80% in this case) are in fact reasonable.
So I wrote down the simplest model I could think of — a model too simple to give useful numerical cutoffs, but still a starting point — and I learned something surprising. Namely (at least in this very simple model), the harsher the prospective punishment, the laxer you should be about reasonable doubt. Or to say this another way: When the penalty is a year in jail, you should vote to convict only when the evidence is very strong. When the penalty is 50 years, you should vote to convict even when it’s pretty weak.
(The standard here for what you “should” do is this: When you lower your standards, you increase the chance that Mr. or Ms. Average will be convicted of a crime, and lower the chance that the same Mr. or Ms. Average will become a crime victim. The right standard is the one that balances those risks in the way that Mr. or Ms. Average finds the least distasteful.)
Here (I think) is what’s going on: A weak penalty has very little deterrent effect — so little that it’s not worth convicting an innocent person over. But a strong penalty can have such a large deterrent effect that it’s worth tolerating a lot of false convictions to get a few true ones.
In case I’ve made any mistakes (and it wouldn’t be the first time), you can check this for yourself. (Trigger warning: This might get slightly geeky.) I assumed each crime has a fixed cost C to the victim and a random benefit B to the perpetrator. For concreteness, we can take C=2 and take Log(B) to be a standard normal distribution, though the results are pretty robust to these particulars. (Or, much more simply and probably more sensibly, take B to be uniformly distributed from 0 to C — the qualitative results are unchanged by this.)
Continue reading ‘How to Be Reasonable’
I’m typing this a few hours before the Iowa Republican Debate. By the time you read it, you might know whether Ted Cruz chose to ignore this advice.
Cruz’s opposition to ethanol subsidies is apparently a problem for him in Iowa. It shouldn’t have to be. The whole point of opposing inefficient subsidies is that if we eliminate enough of them, we can all be better off.
So what Cruz ought to do is introduce a bill eliminating a long list of subsidies, ethanol among them — together with Planned Parenthood, NPR, the National Endowments for the Arts and Humanities and I’m sure it wouldn’t be hard to find another hundred or so — and then emphasize to Iowans that the net effect of the entire package, which takes away their ethanol subidies but also relieves their tax burden, will be to make them richer. A collateral benefit is that he can then argue that the same bill makes New Hampshirites, Nevadans and South Carolinians richer, and if he succeeds in getting the nomination, that it makes Americans generally richer.
As a general rule, I do not understand why politicians take politically risky stands without this kind of bundling. It seems like good politics, and I’m sure it’s good policy.
Ethanol and NPR are of course small potatoes. One could of course do the same sort of bundling with big issues, and politicians of course sometimes do this. But why don’t they do it with both the small stuff and the big stuff?
Scott Adams (the Dilbert guy) offers a Voter’s Guide to Thinking that is so good I am going to reproduce it in its entirety:
Wasn’t there this idea going around that we could explain business cycles through intertemporal substitution of labor supply? (Without the jargon, this means that people work less in times when they are less productive and more in times when they are more productive, so small shocks to productivity — due to random things like weather — tend to have much bigger effects on output.)
Well, it rained here on Wednesday and Thursday of last week, so my roofers spent most of the day pressed up against the garage door trying to stay dry and waiting for little breaks in the rain so they could get something done. On Saturday and Sunday, the weather was beautiful and they didn’t show up. Now it’s Monday and they’re back to work.
Here, in honor of the hundredth anniversary of the General Theory of Relativity, is a very nice visualization:
Followup to last night’s debate:
Didn’t Rubio essentially disqualify himself when he said he’d prioritize his job as a parent over his job as President of the United States?
Heard only a little of the undercard, but I do have some comments on it. But I’ll add those later.
Re the main debate (I’ll add to this every twenty minutes or so till the debate is over): (Note this is live-blogging, hence not always carefully thought through).
Continue reading ‘Debate Blog’
Sometimes you just have to take matters into your own hands.
After posting about the difficulty of finding a modern source for choosing a random city or a random river, I went ahead and created:
I took the data from Maxmind’s free world cities database, but there are odd gaps in it. Although the database lists about 3.3 million cities, the population field is blank for all but about 50,000. (Most notably, that field is blank for all but two of the thousands of cities in the Republic of Korea.) My server offers up a random city from among those 50,000. I’m sure I can probably find a list of Korean cities with populations and manually tack them on to the list at some point. [Edited to add: I’ve just done that.]
Now I want to do something similar for river lengths. Does anyone know where to get the data? (No, pawing through Wikipedia’s hundreds of separate lists, for each part of the world and each letter of the alphabet, is not an option.)
Suppose you want, for some reason, to find the length of a randomly chosen river or the population of a randomly chosen city.
In the old days, we all had things called “reference books”, with long lists of river lengths, city populations, etc. You could open to a random page, close your eyes, put down your finger, and there you’d have it.
But now many of us no longer own reference books. We own smartphones instead. This raises two issues:
1) I’m not sure there are online lists of river lengths or city populations that are as extensive as what you used to find in reference books. Why should there be? Nowadays, if you want to know the population of Des Moines, you just Google for Des Moines; you don’t need a site that lists the populations of thousands or tens of thousands of cities.
2) Even if there were such lists, what would be the modern equivalent of opening to a random page, closing your eyes and pointing? Scrolling for a random amount of time seems less random somehow.
So what do you do?
My friend and former colleague (and our occasional commenter), James Kahn, weighs in on Federal Reserve policy in a thoughtful piece over at Fox Business.
Some highlights:
Proponents of the Fed’s ZIRP (zero-interest rate policy) will quickly point out that the low inflation numbers in recent years belie any claim that policy has been too loose. In a sense they are right: Policy has not been as loose as interest rates suggest, because the Fed has been pushing forward on one lever (asset purchases) while pulling back on another (paying interest on bank reserves). With the economy’s mediocre fundamentals (those supply factors mentioned above), banks are happy to hold large reserves of cash, thus blunting the impact of the Fed’s enormous balance sheet increase.
Bernanke’s gloating about the lack of inflation is thus somewhat misplaced. The concern about losing control of inflation (in one direction or the other), has always been (or should have been), on the Fed’s ability to manage the transition back to normalcy, i.e. the unwinding of its balance sheet, the raising of interest rates, and the drawing down of bank reserves. The Fed may be able to manage all this, but so far it is just lots of rhetoric – it brags about the ability to do so while postponing actually doing it.
In other words, thoughtful critics have said all along that there’s an inflation risk associated with the (future) transition back to normal monetary policy. Less thoughtful counter-critics have claimed to refute that observation with the counter-observation that right now, inflation doesn’t seem to be a problem. Like the optimist in free fall, they figure we’re doing alright so far.
Another highlight:
Continue reading ‘Overprotective Parents, Falling Optimists, and Other Dangers’
I did not watch the debate. I chose to go to my aerial silks lesson instead.
When I got home, the debate was half over. I turned it on for about a minute, during which Marco Rubio managed to turn my stomach to the point where I just couldn’t go on.
Apparently he’s all worried about American tech companies “taking advantage” of relaxed immigration laws to hire foreigners who can work more efficiently than Americans. Any firm that does this should be subjected to strict regulations on who they can hire going forward, etc. etc. And there should be a 180 day waiting period before they can hire that foreigner in the first place, etc. etc.
So let’s be clear about this: Rubio cares enormously more about American engineers than about American consumers, American investors, and low-skilled American workers, all of whom benefit from more efficient engineering. Who do you suppose is richer to begin with — the average engineer, or the average consumer/investor/low-skilled worker?
I cannot stand this stuff.
This is a post about hot hands in basketball. But first, some relevant history:
The single most controversial topic ever broached here on The Big Questions was not Obamacare, or tax policy, or the advantages of genocide, or the policy treatment of psychic harms. It was this:
The answer, of course, is that you can’t know for sure, because (for example) by some extraordinary coincidence, the last 100,000 families in a row might have gotten boys on the first try. But in expectation, what fraction of the population is female? In other words, if there were many such countries, what fraction would you expect to observe on average?
The “official” answer — the answer, for example, that Google was apparently looking for when they posed this as an interview question — is that no stopping rule can change the fact that each birth has a 50% chance of being either male or female. Therefore the expected fraction of girls in the population is 50%.
That turns out to be wrong. It’s true that no stopping rule can change the fact that each birth has a 50% chance of being either male or female. From this it does follow that the expected number of girls is equal to the expected number of boys. But it does not follow that the expected fraction of girls in the population is 50%. Instead, that expected fraction depends on the country size, but is always less than 50%.
If you don’t see why, I encourage you to browse the archive of relevant blog posts. If you still don’t get it, I encourage you to keep browsing. Whatever your objections might be, you’ll find them addressed somewhere in the archive. I’m not interested in relitigating this. I will, however, happily renew my offer to take $5000 bets on the matter, on the terms described here. Last time around, all takers changed their minds before putting any money on the table.
Now let’s get to the hot hands.
Continue reading ‘Boys, Girls and Hot Hands’
The frontispiece from Differentiable Germs and Catastrophes by Theodore Brocker:
There are about a million reasons why I hate my iPhone, but this one pretty much sums it all up.
On my phone, I’ve got quite a few files that were not downloaded from any of my other devices. These include pictures I’ve taken with the phone itself, pdfs I’ve downloaded through the phone’s browser, etc.
Of course, I’d like to have backups of all these files. And of course Apple makes this as difficult as possible by pushing me to use its abysmal iTunes software for creating the backup.
Now here is what iTunes does: I have photo files with names like IMG_0840.jpg — which, if not terribly descriptive, is at least immediately recognizable as a photo. I have pdfs with names like Dirac.QuantumMechanics.pdf, which is a nice, easily recognizable name. I download everything to my computer via iTunes, and here is a partial directory listing of what I get:
Continue reading ‘Poison Apple’
In a bid for ongoing taxpayer support, Planned Parenthood president Cecile Richards will be appearing before Congress today. It’s reported that as part of her testimony, she will admit that only 1 percent of Planned Parenthood’s affiliates currently harvest fetal tissue, and that even those affiliates charge only modest fees of $60 per tissue specimen.
Which raises the question: Why should we give money to an organization that has access to a valuable resource but can’t be bothered to sell it to the highest bidder?
When your brother-in-law is out of work, you might be inclined to help him out. When your brother-in-law is out of work, deluged with job offers, and refusing even to consider them, you’ll probably be less inclined. Planned Parenthood is that brother-in-law.
Continue reading ‘Bad Planning’
For an upcoming Festschrift, I was recently asked to write an account of Dee (then Don) McCloskey‘s years as a brilliant teacher at the University of Chicago, her influence on a generation of economists, and my own enormous debts to her. This was a great pleasure to write. A draft is here.
Pope Francis is coming to New York, and Cardinal Timothy Dolan is disturbed about ticket-scalping:
“Tickets for events with Pope Francis are distributed free [via lottery] for a reason — to enable as many New Yorkers as possible, including those of modest means, to be able to participate in the Holy Father’s visit to New York,” Cardinal Dolan, the archbishop of New York, said in a statement. “To attempt to resell the tickets and profit from his time in New York goes against everything Pope Francis stands for.”
So according to Cardinal Dolan, “everything Pope Francis stands for” consists of the proposition that for New Yorkers of modest means, nothing should take precedence over turning out to see Pope Francis — not groceries, not medicine, not car repairs, not any of the other things that people can buy with the proceeds from selling their tickets.
I doubt that Pope Francis is quite as egomaniacal as the Cardinal paints him. But apparently the Cardinal himself would rather see poor people cheering for the Pope than improving their lives.
My sister snapped this picture of my Dad and me sitting on a couch:
No, this wasn’t posed. It’s just how we happened to be sitting.
To review the bidding:
Two days ago I posed a puzzle about 10 pirates dividing 100 coins.
Yesterday, I presented what appears to be an airtight argument that the coins must be divided 96-0-1-0-1-0-1-0-1-0.
But yesterday I also told you that the “airtight argument” is in fact not airtight, and that other outcomes are possible. I challenged you to find another possible outcome, and to pinpoint the gap in the “airtight argument”.
Our commenter Xan rose to the occasion. (Incidentally, his website looks pretty interesting.) Here’s his solution:
Continue reading ‘Are You Smarter Than Google? — Part Three’
Today I’ll offer the “official” solution to yesterday’s puzzle — that is, the solution that Google has apparently expected from its job candidates. This is also the solution I gave when I first saw the puzzle, and the solution I usually get from my best students, and the solution given yesterday by some astute commenters.
But this solution has a gaping hole in it. Can you find it?
Continue reading ‘Are You Smarter Than Google? — Part Two’
I’m not sure where this problem originated. I heard it first from John Conley, and have often assigned it to my classes. Google has used it to weed out job candidates. The answer that Google expects is the same answer I gave John Conley, and the answer I usually get from my best students. That answer is wrong. (Long time readers might feel a sense of deja vu.)
Can you get it right?
Here’s the problem:
Continue reading ‘Are You Smarter Than Google?’
Yesterday’s post touched on several related points, and I’m afraid the most important one got buried near the end, so I want to repeat it:
1) In the presence of an effective minimum wage, all benefits of the earned income tax credit are transferred to employers. This is, as they say, a matter of Economics 101. (Edited to add: As Bennett Haselton points out in comments, I should have said “dissipated”, not “transferred to employers”. The point remains that the benefits don’t go to the workers, which, for this discussion, is what matters.)
2) Paul Krugman argues that we should have an effective minimum wage in order to prevent some of the benefits of the earned income tax credit from being transferred to employers.
In this context, it should be remembered that Krugman ordinarily reserves his deepest scorn for those who, according to Krugman, willfully ignore the lessons of Economics 101.
Let’s review the argument for 1), with reference to the graph below. In the presence of, say, a $5-an-hour minimum wage, employers will hire 1000 workers. Because more than 1000 people want to work, employers can extract extra concessions in the form of reduced on-the-job-training, shorter breaks, and harsher working conditions. They can get away with exactly $1-an-hour’s worth of this, because even at an effective wage of $4, there are still 1000 people willing to work.
Edited to add: I am assuming that these concessions are of relatively little value to employers (otherwise they wouldn’t have waited for the EITC to demand them!), so that the quantity of labor demanded does not change.
Now let’s add a $3-an-hour earned income tax credit, which shifts the labor supply curve to the dashed position. Ordinarily, this would lead to a lower equilibrium wage, transferring some of the benefits of the EITC to employers. But in the presence of the $5 minimum, wages can’t drop, and employment remains fixed at 1000, though now even more people want to work, allowing employers to impose even harsher conditions until the effective wage drops to $1 an hour (the wage at which there are still 1000 people willing to work). This process transfers all the benefits of the EITC away from the workers.
Continue reading ‘Minimum Logic, Part 2’
The question is often raised: “Why would you ever want to raise the minimum wage when you could raise the earned income tax credit instead?”. In other words, if you’ve got a choice between two ways to increase the effective wage rate, why would you choose the one that reduces employment over the one that increases employment?
Paul Krugman has an answer. He’s argued on numerous occasions that the EITC and the minimum wage are complements, not substitutes — that is, each makes the other more effective. So, according to Krugman, once you’ve raised the EITC, the case for a minimum wage hike becomes stronger, not weaker.
Here’s his argument: When you raise the EITC, more people enter the labor market. The increased supply of labor tends to drive wages down, which transfers some of the benefit from the workers you intended to help to the employers and/or consumers who you presumably care about less. To prevent this perverse consequence, one needs a hike in the minimum wage.
The other day, a colleague (who I’m not naming because I’m not sure whether he’d want to be quoted) pointed out that this argument makes not a shred of sense. Here’s why: Any effective minimum wage (that is, any minimum wage set above the wage rate that would prevail in an unregulated market) suffices to do the job Krugman wants it to do. At best, then, Krugman has made an argument for having some minimum wage, not a case for raising it.
Here’s the picture:
Continue reading ‘Minimum Logic’
Did Stanford university surgeons fail first grade arithmetic? Or do they just assume the rest of us did?
Shortly before I started Kindergarten, my mother purchased a book called “Steven’s School Years”, with pockets to store my report cards and school projects, and questionnaires for me to fill out at the end of each school year.
I was not diligent about filling in the questionnaires, and they remain mostly blank. But had I been forced to, I wonder how I would have answered the following question, which was to be answered annually at the end of Grades 1,2,3,4,5, and 6:
(According to my mother, my ambition at age three was to be an electric drill, and sometime after that a rabbit. No other records of my early career inclinations seem to have survived.)
Continue reading ‘Dear Old Golden Rule Days’
