Today, I will attack none of these questions. Instead, I will attack the meta-question of how to attack such questions. For economists evaluating alternative policies, the industry standard is the efficiency criterion, also known as the welfare criterion. (I’ll illustrate what that means as I go along.) But now comes Princeton Professor Uwe Reinhardt with a piece in the New York Times that questions the orthodox approach found in virtually all modern textbooks (including one in particular).

Let’s first dispense with the straw man. I’ve never heard of an economist who believes that every efficient policy is good, and I’ve heard of very few who believe that every inefficient policy is bad. It’s true that most economists do seem to believe that any good policy analysis should start by considering efficiency. That doesn’t mean it should end there.

I think economists are right to emphasize efficiency, and I think so for (at least) two reasons. First, emphasizing efficiency forces us to concentrate on the most important problems. Second, emphasizing efficiency forces us to be honest about our goals.

I’ll illustrate the first advantage with a stylized example adapted from Chapter 17 of The Big Questions. Suppose you live next door to Bill Gates. Bill likes to play loud music at night. You’re a light sleeper. Should he be forced to turn down the volume?

An efficiency analysis would begin, in principle (though it might not be so easy in practice) by asking how much Bill’s music is worth to him (let’s say we somehow know that the answer is $10,000) and how much your sleep is worth to you (let’s say $25). It is important to realize from the outset that no economist thinks those numbers in any way measure Bill’s subjective enjoyment of his music or your subjective annoyance. Only a crazy person would think such a thing, and I’ve never met anybody who’s that crazy in that particular way. Instead, these numbers primarily reflect the fact that Bill is a whole lot richer than you are. Nevertheless, the economist will surely declare it inefficient to take $10,000 worth of enjoyment from Bill in order to give you $25 worth of sleep. We call that a $9,975 deadweight loss.

Why is that an important calculation? Here’s why: It reminds us that there might be a better solution to this problem, such as allowing Bill to crank up his speakers and forcing him to pay you, say, $5000 in compensation. Compared to shutting down the music, that’s better for Bill and better for you. Maybe that’s an alternative we should consider. In fact, whenever a policy is inefficient, there’s always an alternative policy that, in principle, is better for everyone. That’s what inefficiency means.

Now in this case the proposed alternative policy might not be such a good idea. It might, for example, encourage Bill to lie about the value of his music, and encourage you to lie about the value of your sleep. It might even encourage you to move a little closer to Bill just so you can find more things to complain about and get compensated for. Or it might have negative long-term consequences for the way we think about wealth and social status. So maybe we don’t want to pursue this alternative policy after all. But, says the economist, we ought at least to consider it.

And — here’s the point — the bigger the deadweight loss, the greater the potential gains from an alternative policy. Therefore, the bigger the deadweight loss, the more it’s worth at least attempting to devise a good alternative policy. We calculate the deadweight loss as a rough but useful guide to how much effort we should put into this problem. (Calculating deadweight losses is the same thing as worrying about efficiency.)

Take a more realistic example: Should we spend, say, a billion dollars a year to subsidize end-of-life health care for poor people? It would be, I think, a terrible mistake to settle this question without at least asking whether the recipients might prefer that we spend our billion dollars some other way — say by subsidizing their groceries or just giving them cash. If so, the difference in value between what they’re getting and what they could be getting (as measured by the recipients) is a deadweight loss. The bigger that deadweight loss, the more we should reconsider our spending priorities.

Now once again, efficiency is not the be-all and end-all of policy analysis. Even if poor people prefer subsidized groceries to subsidized health care, we might still choose to give them health care if, for example, we believe that they are less likely to make wise decisions about their own health care than about their own groceries, or if we’re afraid that subsidizing groceries (or handing out cash) is somehow more likely to invite fraud. But the bigger the deadweight loss, the more we should probably rethink those concerns, because the bigger the deadweight loss, the more opportunity there is to improve life for the recipients. That’s the first reason we should care about efficiency.

The second reason we should care about efficiency is that efficiency analysis strikes down political smokescreens. Like this:

Politician: Here’s my program to make the health care system work better by subsidizing health care for the poor.

Economist: Your program costs a billion dollars and delivers half a billion dollars worth of benefits. That’s inefficient.

Politician: So what?

Economist: Well, the “so what” is that maybe you could take that billion dollars and deliver a full billion dollars worth of benefits instead if you spent it a little differently. Why not just hand the cash out to poor people?

Politician: Because I don’t want to help all poor people. I only want to help sick poor people — and this is the only way I can think of to do that.

Economist: Ah. So your goal here is not to make the health care system work better after all. Instead it’s to transfer resources to sick poor people.

Politician: I guess so.

Economist: That’s fine. Now we can have a healthy debate about whether that’s what we want to do.

And now, you see, thanks to the economist’s insistence on thinking about efficiency, we end up having an honest debate about the politician’s real goal instead of a dishonest debate about the politician’s feigned goal. However the debate turns out, that’s a useful exercise.

It’s not just politicians who sometimes hide their true goals behind smokescreens. Suppose, for example, that one of Professor Reinhardt’s colleagues were to write a series of columns in the New York Times calling for more fiscal stimulus, including higher unemployment benefits. On some days, he argues that these policies will increase GDP. Other days, he argues that they will reduce unemployment. Other days, he tells you that it’s cruel to deny benefits to suffering jobseekers.

Those are of course all different (though intertwined) arguments. You might accept some but not others. Even if you accept them all, you still can’t draw a policy conclusion until you weigh these benefits against the policies’ offsetting costs (including the opportunity cost of the expenditures, the effect on long run growth, and so forth). The advantage of an efficiency analysis (along, say, the lines suggested here) is that it would force Professor Reinhardt’s colleague to be clear about his priorities. Is he, for example, concerned primarily about increasing current output or about redistributing current output? Either might be a worthy goal, but we can’t have a useful debate with someone who won’t tell us what his goals are.

Usually, when economists take policy stands, they start with an efficiency analysis precisly in order to clarify their goals and so make it easier for opponents to identify the locus of their disagreement. They say things like “I support this policy because it’s efficient” or “This policy is inefficient — I estimate the deadweight loss at $X — but I think that much deadweight loss is worth tolerating for the following reasons.” That’s called intellectual honesty. I think it’s a good thing.

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Data from 9,785 users of the dating site OKCupid reveal that iPhone users have 50% to 100% more sex partners than Android users, at every age.

This graph combines men and women, but the same pattern holds for each gender separately.

Explain this to me!

More info here (if you scroll down a couple of screens).

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That central question is called the “P versus NP” problem, and for those who already know what that means, his claim (of course) is that P does not equal NP. For those who don’t already know what that means, “P versus NP” is a problem about the difficulty of solving problems. Here’s a very rough and imprecise summary of the problem, glossing over every technicality.

Deolalikar’s paper is 102 pages long and less than about 48 hours old, so nobody has yet read it carefully. (This is a preliminary draft and Deolalikar promises a more polished version soon.) The consensus among the experts who have at least skimmed the paper seems to be that it is a) not crazy (which already puts it in the top 1% of papers that have addressed this question), b) teeming with creative ideas that are likely to have broad applications, and c) quite likely wrong.

As far as I’m aware, people are betting on point c) not because of anything they’ve seen in the paper, but because of the notorious difficulty of the problem.

And when I say betting, I really mean betting. Scott Aaronson, whose judgment on this kind of thing I’d trust as much as anyone’s, has publicly declared his intention to send Deolalikar a check for $200,000 if this paper turns out to be correct. Says Aaronson: “I’m dead serious—and I can afford it about as well as you’d think I can.” His purpose in making this offer?

I could think of only one mechanism to communicate my hunch about Deolalikar’s paper in a way that everyone would agree is (more than) fair to him, without having to invest the hard work to back my hunch up.

On the one hand, this seems like quite an effective way for Scott to communicate the strength of his hunch, which is obviously something he very much wants to do. On the other hand, I’m a little baffled by Scott’s remark (in the comments to the linked post) that “If P≠NP has indeed been proved, my life will change so dramatically that having to pay $200,000 will be the least of it.” I’m sure that if P≠NP has indeed been proved, it will dramatically change the life of a complexity theorist like Scott Aaronson, but I’m not sure why it will change it in a way that makes $200,000 less valuable.

But that’s of course his call. I just wanted to share this and invite your comments.

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Here’s a data point: On Friday, Hewlett Packard’s CEO Mark Hurd resigned unexpectedly — and pretty much instantly the value of HP stock dropped by about $10 billion. If we assume Hurd would otherwise have been around for another 10 years or so, that means shareholders think his departure will cost the company about a billion dollars a year. Which, incidentally, makes his $30 million or so in annual compensation look like a hell of a bargain.

Now maybe some part of that $10 billion reflects expected short-term losses due to the turmoil of an unplanned transition. But even if that turmoil were to cost HP a full month of revenue (which seems like a pretty extreme assumption), that’s still less than a billion — leaving over $9 billion to represent the difference between what the market expected from Hurd and what it expects from his successor.

This doesn’t mean Hurd is that much better than anyone who could run HP, but it might mean he’s that much better than anyone HP is likely to hire. Most of the world’s best executives are already occupied. Hurd’s replacement will come from the second string. So (insofar as we are reckless enough to extrapolate from this one data point), it appears that there’s a huge gap between the very best and the almost-very-best. Like in baseball, where the 1000 or so major leaguers are, well, in an entirely different league from the 1000 best minor leaguers.

If this kind of gap is the norm, then there’s a huge cost to diversity-for-the-sake-of-diversity in positions that require extraordinary talent. Do you really want to settle for a distant second best just so you can fill your Albanian quota?

Coincidentally, the news from HP comes just as President Obama is seeking a replacement for departing economic advisor Christy Romer. It’s been reported that the President believes it’s important to hire a woman.

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Over at Overcoming Bias, Robin Hanson objects that if people really believed this argument, they’d want to criminalize lesbianism and extramarital affairs, both of which also contribute to the problem of men-without-partners.

But I think one could consistently take the position that while lesbianism contributes to the problem, it’s just not widespread enough to be worth stamping out, while polygamy (if legal) might well become so. And as far as extramarital affairs, I think Robin has it completely backward: When the wife of a 30 year old man (who is well past the prime age of violence) has an extramarital affair with an 18 year old, she is alleviating the problem, not contributing to it. Besides, most extramarital affairs do not deprive the husband of a long term sex partner.

I’m all for legalizing polygamy, because I’m all for legalizing almost everything. But I don’t think you can dismiss this argument—or the sincerity of its proponents—as easily as Robin seems to think you can.

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A colleague points out that it seems equally odd for a company with pockets the depth of BP’s to be engaged in as risky an activity as deep water oil drilling. Why wasn’t this project sold off to someone with a lot less to lose?

Maybe BP expected to be protected by laws limiting its liability, but surely it was foreseeable that those laws might be circumvented, as it appears they’re about to be. So if that’s part of the answer, it’s only a small part.

I’m not saying it would be a good thing for more of these risky ventures to end up in the hands of relatively judgment-proof firms. I’m just saying I don’t understand why we don’t see more of that. What am I missing?

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Both $10 billion and $300 billion are extremely rough guesses, but the $300 billion figure comes from the widely cited estimates of Harvard’s Martin Feldstein, according to which a one dollar tax increase triggers about 30 cents in deadweight losses. Since a trillion in new spending means a trillion in new taxes (either now or in the future), we get $300 billion in deadweight loss.

Of course $10 billion worth of oil-related damage is still big enough to be worth a goodly dollop of angst. But keep these things in mind:

• Occasional disasters are part of the cost of using fossil fuels. This might be a cost worth paying.
• On the other hand, even when a cost is worth paying, it’s still better to pay less. And this particular cost is likely to be excessive, both because limited liability inspires recklessness and because, in a sane world, we’d be drilling in the Arctic rather than a mile underwater near a population center. (Charles Krauthammer has made the latter point more elaborately.)
• On still another hand, excessive as the cost may be, it’s still piddling compared to the deadweight loss of taxation. Destroying $10 billion worth of what we’ve already got is not nearly as bad as destroying in advance $300 billion worth of what we could have had.

Now maybe $300 billion in deadweight loss is a price worth paying for the benefits of ObamaCare and the stimulus package—just as maybe $10 billion in damage is a price worth paying for the way we use energy. And maybe with wiser policies we could have slashed one or both of those costs. But one of them is thirty times the other, and if you’re looking to be justifiably angstful, that’s probably your better bet.

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Medpage Today reports that the revision has already been changed several times in response to these comments. These include several areas within the Sexual and Gender Identities categories, and modifications to the criteria for adjustment disorders and eating disorders.

By contrast, the American Physical Society is not asking the general public to weigh in on the prospects for supersymmetry, nor is the American Economic Association surveying the general public on the properties of dynamic stochastic general equilibria. So much for any pretense that psychiatry is a science.

Hat tip to Tom Amoroso, who called this to my attention though he might not endorse this commentary.

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First a recap of the problem, with a bit more detail than last week:

Each day, Albert leaves his office (at the bottom of the map), gets on the Main Highway and attempts to drive home to his house on Second Street. If he turns too soon (onto First Street) or if he overshoots (going all the way to the north end of the Main Highway), he is mauled by dinosaurs.

Obviously, Albert’s best strategy is to go straight at the first intersection and turn right at the second. Unfortunately, both intersections look identical. Doubly unfortunately, Albert can never remember whether he’s already passed the first intersection.

Since Albert can’t tell the intersections apart, he needs a single strategy for both of them. Strategy A is to turn at every intersection. This delivers him directly to the First Street dinosaur mob. Strategy B is to go straight at every intersection, putting him on a direct route to the North Side crew. Neither of these strategies has any chance of getting him home.

Therefore, Albert adopts Strategy C, which is to turn right with some probability p at every intersection. He wins if he goes straight at First Street (which happens with probability 1-p) and right at Second Street (which happens with probability p. His overall chance of making it home is (1-p)p, which is maximized when p=1/2. So he chooses p=1/2 and expects to make it home with probability 1/4.

Given this strategy, Albert is certain to make it as far as First Street, but has only a 1/2 chance of making it to Second Street. Thus when he pulls up at an intersection, the odds are 2 to 1 (i.e. the chances are 2 out of 3) that he’s at First Street. If he now revises his plan, turning right with some new probability q, then he reasons as follows:

• If I’m at First Street, I need to go straight and then right, which I’ll do with probability (1-q)q.
• If I’m at Second Street, I need to go right, which I’ll do with probability q.
• There’s a 2/3 chance I’m at First and a 1/3 chance I’m at Second.
• Therefore my chance of getting home is (2/3) x (1-q)q + (1/3) q.
• I can maximize this by choosing q=3/4.

Albert therefore switches to a strategy of turning right with probability 3/4. But we’ve already computed that he can do no better than turning right with probability 1/2. Should he switch strategies or shouldn’t he?

Some observations:

1) Suppose first that Albert can commit himself to turning at each intersection with some probability p. To get home, he must go straight at First Street (he gets this right with probability 1-p) and then turn at Second Street (with probability p). So his overall chance of making it home is (1-p)p, which is maximized when p=1/2. His chance of getting home is therefore 1/4.

However, when Albert pulls up to an intersection, he calculates his chance of getting home as 1/3, not 1/4. There are two ways to see this.

First way to see it: Albert’s strategy gets him as far as First Street every time but as far as Second Street only half the time. So the intersection he’s currently approaching has 2-to-1 odds (i.e. a 2/3 probability) of being First Street. If it’s First Street, his chance of getting home is 1/4, but if it’s Second Street, his chance of getting home is 1/2 (since now he only has to get one decision right, not two). His overall probability is therefore (2/3) x (1/4) + (1/3) x (1/2) = 1/3.

Second way to see it: There are eight states of the world. State One is [First coin says "straight", second says "straight", this is the first intersection] (call this SS1). State Two is [First coin says "straight", second says "straight", this is the second intersection]. Et cetera. Initially, all eight states are equally likely and only two (ST1 and ST2) get him home eventually, which is why Albert initially calculated his chances at 2/8 = 1/4. But now, the fact that Albert is approaching an intersection rather than cooking on a dinosaur stove rules out two of the bad possibilities (TS2 and TT2). So there are now six equally likely possibilities, two of which are good, and his chances are therefore 2/6 = 1/3.

In other words: The unconditional probability Albert will get home is 1/4. The probability conditional on the fact that the dinosaurs haven’t gotten him yet is 1/3. So far, no paradox.

2) Now we want to allow Albert to change strategies midstream. At the moment he’s approaching an intersection, there are three relevant probabilities:

• p is the probability he’s used in the past
• q is the probability he’s using now
• r is the probability he’ll use in the future

You are pretty sure to go astray unless you maintain a rigorous distinction between these three variables.

3) When Albert reaches an intersection, he can compute as follows:

• The probability that Albert is at First Street is 1/(2-p).
• The probability he’ll get home, conditional on being at First Street, is (1-q)r.
• The probability that Albert is at Second Street is (1-p)/(2-p).
• The probability he’ll get home, conditional on being at Second Street, is q.

Therefore the overall probability he’ll get home is [(1-q)r + (1-p)q]/(2-p).

Albert seeks to maximize this probability—or the expected value of this probability—by choosing q, taking as given both the value of p and the method he’ll use to choose r.

The solution to this problem depends both on Albert’s beliefs about p and Albert’s beliefs about r. Not surprisingly, different assumptions lead to different conclusions.

So we have several models to consider.

Mark I. Albert remembers p, and can commit himself to choosing r=q. (That is, he updates once and forever.) This leads him to maximize [(1-q)q + (1-p)q]/(2-p), which occurs at q = 1 – p/2. In particular, if p = 1/2, then q = 3/4. In the language of last week’s post, this is “Strategy D”. If Albert is to behave consistently, he must choose q=p, which requires p=2/3, yielding a 2/9 chance of getting home.

Criticism.It seems inconsistent to assume that Albert can lock himself into choosing r=q but was not able at the outset to lock himself into choosing q=p. [On second thought, what's really going on is that Albert believes at the outset that he's locked himself into choosing p, so it's not entirely inconsistent for him to believe at the intersection that he's locking himself into r=q.]

Mark IA. Mark I applies, but in order to trick his future self into choosing q=1/2, Albert “commits” at the outset to p=1. That is, he promises to always go straight. Then when he arrives at the first intersection, he believes he’s equally likely to be at either of the two intersections, leading him to choose q=1/2 and maximize his chance of getting home. This was nicely explained by Joeythepea in comments on the original post. Joeythepea, incidentally, is the same person as the standup comedian Joe Podwol whose YouTube clips are well worth a few minutes of your time.

Mark II. Albert always believes, perhaps incorrectly, that p=1/2, and can accurately predict that he’ll believe this in the future. This leads him to maximize (q + 2r – 2qr)/3, taking r as given. If he believes r is less than 1/2, this is maximized by taking q=1; if he believes r is greater than 1/2, this is maximized by taking q=0.

In either of these cases, Albert must believe that r differs from q, even though they are both solutions to the same problem. This seems implausible, so we can assume we’re in the only remaining case, namely r=1/2. Then Albert gets home with probability 1/3 independent of q, and so might as well choose q=1/2 also.

Comment. The Mark II model predicts that Albert never deviates from 1/2 and gets home 1/4 of the time. Thus according to this model there is no paradox.

Mark III. Albert remembers p, and expects to remember q in the future. He expects to choose r according to some rule r=f(q). This leads him to maximize

Offhand, I’m not sure what the general solution to this equation might look like.

There are also Marks IV, V, VI and onward. I’ve decided to omit them in a futile attempt at brevity.

Some Conclusions. First, to avoid confusion, I think it is quite important to make careful distinctions among the variables p, q and r. A quick web search turns up several “solutions” that ignore these distinctions. Second, it’s quite important to be clear about one’s assumptions (which in turn requires maintaining careful distinctions among p, q and r). Third, it’s not surprising that different assumptions can yield different conclusions.

Fourth, the case that really seems to be paradoxical at its core is the case where Albert commits at the outset to p=1/2, arrives at the first intersection remembering this commitment, and then abandons it. At first I thought that the assumptions in this case were self-contradictory, because Albert is initially 100% sure he can commit to p=1/2 and then gets a chance to de-commit. Nobody—at least nobody in a good economic model—is 100% sure of anything unless that thing *is* 100% certain. But I no longer believe we can dismiss this case so simply. Even if we hold Albert to his original commitment (thus justifying his 100% certainty) there’s still an apparent paradox in his desire to de-commit.

Fifth: Several very smart economists have written about this problem without reaching any conclusions that are widely recognized to be definitive. (For example, here, here and here.) This should give pause to those who think the whole problem is based on some kind of cheap trick.

And sixth, I suppose that at some level it’s not terribly surprising that absent-minded people, doing the best they can with their limited cognitive skills, might get mauled by dinosaurs a lot.

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Monday I insisted that all reasonable people should be at least mildly disturbed by the diminution of property rights implicit in a ban on whites-only lunch counters.

Tuesday I cited an excellent comment from Jonathan Pryor suggesting that a whites-only lunch counter is itself an indirect assault on property rights insofar as the owners expect taxpayers to foot the bill for enforcement of the whites-only policy (say, by calling the police when unwanted visitors show up).

There are circumstances in which I think Pryor’s argument clearly applies. I cited the case of the man who keeps a barrel of Hershey bars on his front lawn and expects the police to stop children from filching them. Surely this man is imposing a burden on the community over and above the assertion of his own property rights. But I also gave several other examples that gave me pause about the applicability to lunch counters.

This in turn brought forth an insightful comment from Ken B, who points out that the Civil Rights Act itself called for a lot of taxpayer-financed enforcement. The act was passed, blacks sat down at lunch counters, owners attempt to evict them, the police were called.

So if you base your case on Pryor’s argument, you’ve got an empirical question to face. In which regime do the police get called more often—the regime where owners can legally ban black customers, who nevertheless sometimes show up uninvited? Or the regime where blacks can legally eat at any lunch counter, but are nevertheless sometimes evicted? And depending on what the numbers show, you’ve got to be prepared to switch sides. (You might also conclude that the answer differs from community to community, so that it makes little sense to decide this issue on a federal level.)

And most importantly: Regardless of what the numbers actually show, you’ve got to concede that you would have switched sides if the numbers had been different. Which in turn should make you extremely hesitant about demonizing those who read the numbers differently than you do.

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