This seminar probes how economic thinkers from the right and left view human behavior and the proper role of government in society. Each week, seminar participants read and discuss a brief, nontechnical, policy-oriented book by a prominent economist. Regular writing assignments are also required. Students should have some background in economics, such as an AP economics course in high school or simultaneous enrollment in Social Analysis 10.

The ten books on tap for this semester are:

• The Worldly Philosophers, by Robert Heilbroner
• Reinventing the Bazaar: A Natural History of Markets, by John McMillan
• Thinking Strategically, by Avinash Dixit and Barry Nalebuff
• Capitalism and Freedom, by Milton Friedman
• Equality and Efficiency: The Big Tradeoff, by Arthur Okun
• Nudge, by Richard Thaler and Cass Sunstein
• How the Economy Works, by Roger E.A. Farmer
• The Return of Depression Economics, by Paul Krugman
• The Road to Serfdom, Friedrich Hayek
• The Myth of the Rational Voter, by Bryan Caplan
• The Big Questions, by Steven Landsburg

What would your list have been?

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(For those who want more precision: We gather all those women in the world who have exactly two children, tell each of them to “go home unless you have a boy born on a Tuesday”, and select a woman randomly from those who remain. Assume that births are equally likely to occur on any day of the week, and that on any given day, boys and girls are equally likely.)

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Today’s question is: Do numbers exist? The answer is: Of course, and I don’t believe there’s much in the way of serious doubt about this. You were familiar with numbers when you were five years old, and you’ve been discovering their properties ever since. Extreme skepticism on this point is almost unheard of among mathematicians or philosophers, though it seems to be fairly common among denizens of the Internet who have gotten it into their head that extreme skepticism makes them look sophisticated.

Let me be clear that I am not (yet) asking in what sense the natural numbers exist — whether they have existed since the beginning of time, or whether they exist outside of time, or whether they exist only in our minds. Those are questions that reasonable people disagree about (and that other reasonable people find more or less meaningless.) We can — and will — come back to those questions in future posts. For now, the only question: Do the natural numbers exist? And the answer is yes. Or better yet — if you believe the answer is no, then there’s obviously no point in thinking about them, so why are you reading this post?

“Existence” here is used in the ordinary everyday sense of the word, according to which rocks and trees exist, you and I exist, your hopes and dreams exist, and the idea of a unicorn exists. Unicorns themselves do not exist and therefore it makes no sense to study their properties. (Though you can have fun inventing some properties for them.) By contrast, it makes perfect sense for geologists to study the properties of rocks, for botanists to study the properties of trees, for folklorists to study the properties of the idea of a unicorn, and for mathematicians to study the properties of the natural numbers.

An extreme skeptic might deny the existence of rocks. The only possible answers are: a) It’s hard to believe you’re serious, since you’ve been encountering rocks — just like you’ve been encountering numbers — your entire life. b) If you really are serious, I suppose your best strategy is to stop thinking about rocks, and leave them to those of us who find geology interesting. And c) Do not fool yourself into believing that your position is anywhere close to any mainstream school of thought.

Another extreme skeptic might deny the existence of numbers. I’ll leave it to my readers to replace rocks with numbers in the above retorts.

What else might one say to an extreme skeptic? Answer: One might attempt to acquaint him with Godel’s Completeness Theorem. (This is not the same as the far more famous Godel’s Incompleteness Theorem.) Here is (part of) what the Completeness Theorem says: First, without making any assumptions about existence, write down a list of axioms for the natural numbers. For example, write down the Peano Axioms. Then the Completeness Theorem tells you that as long as those axioms are consistent, there must be some mathematical structure that obeys those axioms. (Note that “be” is a synonym for “exist”.) The smallest of those structures (known as “models”) is our good old friend the natural numbers.

In other words, Godel’s Theorem tells you that if the Peano axioms are consistent, then the natural numbers must exist. (Don’t confuse the map with the territory! “Consistency” applies to the axioms; “existence” applies to the natural numbers themselves.)

On the other hand, we can also argue in the opposite direction: If the natural numbers exist, then the Peano axioms, being true statements about existing objects, must be consistent. An accurate map of an existing territory cannot contradict itself.

So — We know that the natural numbers exist because we know the Peano axioms are consistent. And we know that the Peano axioms are consistent because we know that the natural numbers exist. Does that sound circular? It’s not. Here’s the point: We have extremely good reasons for believing in the existence of the natural numbers (beginning with intuition, lifelong familiarity, and the fact that we seem to be able to discover their properties). We have (partly) separate extremely good reasons for believing in the consistency of the Peano axioms (beginning with intuition and the fact that they’ve never yet led us to a contradiction). The fact that our two beliefs reinforce each other — that if either is true, then so must be the other — should build up our confidence that the whole picture hangs together.

Now let’s get back to our extreme skeptic. He denies the existence of the natural numbers. We respond that Godel’s Completeness Theorem proves the existence of the natural numbers, as a consequence of the consistency of the Peano axioms. He now has only two recourses (other than to concede defeat). One is to deny the consistency of the Peano axioms, and the other is to deny the accuracy of Godel’s Completeness Theorem. Let’s see how those strategies are likely to work out for him.

Should he doubt the consistency of the axioms? The Peano Axioms lay out the rules of arithmetic that you’ve used your whole life; they say things like “Every number has exactly one immediate successor” and “x + (y+1) = (x+y) + 1”. People (and to some extent animals) have been applying these axioms, explicitly or implicitly, since long before the dawn of history and no contradiction has ever arisen; moreover, for what it’s worth, the consistency of these simple axioms is instantly clear to most people’s intuitions. If we were to jettison our belief that these axioms are consistent, then we’d pretty much have to give up all quantitative reasoning.

Well, then, should our skeptic doubt Godel’s Completeness Theorem? The theorem is proved using elementary notions about sets — the idea that it’s possible to talk about sets of things and about membership in a set, that it’s possible to form the union of two sets, and so on. This has nothing to do with the more esoteric subject of “axiomatic set theory”; instead, it uses only the most fundamental notions associated with forming collections of things. (These notions, in fact, are prerequisite for axiomatic set theory and therefore cannot depend on it.) Once again, if you were to abandon this sort of reasoning, you’d pretty much have to abandon reasoning altogether.

For anyone who accepts the simplest sorts of combinatorial reasoning, there is no longer an out. The natural numbers are real. Again, this says nothing about where they came from — be it Plato’s heaven, the minds of humans or the mind of God. We’ll get back to that in the next installment of this occasional series.

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Someday Google (or its successor) will be able to answer that question. It will understand what you’re asking, it will perform relevant searches for old newspaper items, it will sift through the results, it will know (or know how to find out) whether a vole is larger than a ferret, and it will give you an answer. We’ll call it the semantic web.

When the Chronicle of Higher Education asked me for a few hundred words on the defining idea of the next decade, this was the first thing that came to mind. Another was the partial conquest of cognitive bias through better understanding of the systematic ways our brains let us down, together with software designed to compensate for our own mental shortcomings.

What I really wanted to do was ask my blog readers to predict the defining idea of the next decade, with the prospect that I might write about the best of them. But the Chronicle editiors asked me not to do that.

In the end, I went with an old favorite — the beginning of the end of intellectual property law, which, thanks to our increasingly information-based economy (see “semantic web”), stands to hinder progress even more in the future than it has in the past. Readers of my book More Sex is Safer Sex will know that I am particularly enamored of Michael Kremer’s proposed solution to this problem, and that’s what I ended up writing about.

The other two dozen contributors to the forum had some pretty interesting things to say as well.

So now that this exercise is complete, tell me what we all missed. If I’d been able to ask you before I wrote this piece, what would you have told me to write about? What will be the defining idea of the coming decade?

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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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We moved on to the perils of interpreting data, in this case with regard to the ingredients of a happy marriage. Then a look back to what the world of 1985 thought would constitue a marvelous future; we seem to have met expectations pretty well. And finally, we came in a sense full circle — from lamenting those focus single-mindedly on energy costs to the exclusion of all else to lamenting those who fault others for failing to focus single-mindedly on one political issue to the exclusion of all others.

I’ll be back next week with some thoughts on why we should care about economic efficiency, a little more on the foundations of arithmetic, and some surprises.

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I missed the memo about the new criteria for hypocrisy, so I’d like a little clarification here. Are Catholics now required to vote solely on the basis of Catholic issues, and union workers solely on the basis of union issues, and billionaires solely on the basis of billionaire issues? Or is it only gays who are forbidden to prioritize, say, foreign affairs and tax policy? And what’s to become of the multifaceted? If you’re a gay Jewish small business owner, to which brand of parochialism are you now in thrall? Please advise.

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• Househould Robot. Does my Roomba count?
• Magnetic Train. Check.
• Flat-Screen TV. Check.
• Flat-Screen 3-D TV. Check.
• Two-Way Wrist Radio. We are so far past this.
• Two-Way Wrist TV. Ditto.
• Intelligent Computer. My computer’s a lot smarter than it looks, honest. It just acts dumb when it has to run Microsoft products.
• Instant Access to All Human Knowledge. Check!
• Human Clones. Getting there.
• First Woman President. Does Secretary of State count?
• First Black President. Check!!
• Universal Language. That would be English.
• X-Ray Specs. My infrared camera sees through clothes.
• World War III. By some accounts, we’re about 9 years into it.
• Access to Other Dimensions. Talk to the string theorists.
• Immortality. Check?
• Spelling Reform. OMG! I cn chk ths 1 off 2.

Some of the other entries, like “Home Holographs”, “Personal Rocket”, and “My Trip to Other Galaxy” might be a bit farther off. But things sure change in a hurry.

What else about your current life do you think would most surprise a time traveler from 25 years ago?

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Edited to add: The original version of this post misstated the result; I’ve changed a few words in the preceding paragraph so it’s accurate now.

From this, Robin concludes:

If you want a happy relationship, be a happy person and pick a happy partner; no need to worry about how well you match personality-wise.

NO!!!! That’s not the right conclusion at all, and it’s worth understanding why not. Suppose we lived in a world where personality matches had a huge effect on the success of marriages. In that world, why would two people with clashing personalities ever choose to marry? Presumably because there’s some special value in the match — like, say, an extraordinary mutual attraction — that overrides the personality clash.

So a survey of married couples — which is exactly the sort of evidence Robin is reporting on — is not at all a random sample of couples. Instead, it consists, for the most part, of couples with matched personalities on the one hand, and couples with mismatched personalities who are exceptionally well suited to each other for some other reason on the other hand. It’s not too surprising to find similar success rates in those two classes of couples. The third class — the couples with mismatched personalities and no redeeming match characteristics — never gets married and therefore never gets surveyed.

Conclusion: The results Robin quotes are perfectly consistent with a world where personality matching doesn’t matter — but also perfectly consistent with a world where it matters very much.

Now a more sophisticated analysis would account for the costs of search in the mating market, and the fact that people sometimes settle for imperfect mates because time is running out. My colleagues who know the search literature better than I do tell me that, depending on your assumptions about the distribution of personality traits, you might or might not be able to draw any inferences from the results Robin is quoting, but that in any event the inferences will be far less strong than you’d expect from a naive reading of the data. You’d probably want to start by thinking about a Roy model.

Moral: Never try to interpret data without thinking about how those data were selected. What’s your favorite example of a case where this moral was disastrously ignored?

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The article by Earl Cook, “Limits to exploitation of nonrenewable resources”, is extremely informative. In fact, I should like to assign it to my class except that it is marred by an egregious fallacy. Since this fallacy has been turning up repeatedly in writings about environmental and natural resource problems, I wish to call it to the attention of Science readers.

The mistake has to do with the nature of social cost. Cook, for example, writes “To society … the profit from mining (including oil and gas extraction) can be defined either as an energy surplus, as from the exploitation of fossil and nuclear fuel deposits, or as a work saving, as in the lessened expenditure of human energy and time when steel is used in place of wood … “. A number of other authors also equate social cost with the expenditure of energy.

For better or worse, neither kilocalories nor man-hours nor any other directly observable, unidimensional, physical input is an adequate measure of social cost. A moment’s thought should make this compelling. Consider a very simple self-contained economy where coal is extracted by surface mining and the coal seams lie under the only land suitable for growing hops. The greater the amount of coal that is surface-mined, the less the amount of beer that can be brewed. In these circumstances surface mining may be a loser, socially speaking, even though it requires the expenditure of far less than 12,000 BTUs per pound of coal; and subsurface mining may be advisable even though it requires more energy per pound extracted than surface mining, particularly if there is a beer shortage. The social cost of surface-mined coal includes the reduction in the availability of beer along with the expenditure of man-hours, capital investment, and other things too numerous to mention.

Clearly, then, social costs cannot be measured in simple physical units. The only adequate measure is what economists call “social opportunity costs”, meaning the social value of the alternative commodities that have to be forgone in order to obtain the commodity being produced. Under certain idealized conditions, this opportunity cost is measured by the dollars-and-cents cost of producing the commodity. Under realistic conditions the dollars-and-cents production cost is a fair approximation to the social cost. Under almost any conceivable conditions, the dollars-and-cents cost is a much better approximation to social cost than the amounts of energy expended or any other simple physical measure.

…

Energy is indeed a scarce and valuable resource, but it is only one of many, and there is a good deal more to life than British thermal units.

Robert Dorfman

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