The Three-Sided Coin: Answers

The three-sided coin problem generated numerous responses. Virtually all the proposed solutions were correct, with most reporting “thinking time” of under 10 minutes. Some said it took them less than a minute, while others admitted longer times, but 5 minutes was about in the center. A couple of respondents thought the problem was so easy that maybe it was a joke, but most seemed to think it was a nice challenge. Of course, I have a biased sample here, since I don’t know how many people read the problem but couldn’t figure out the answer, or figured it out but didn’t email me.

The most common wrong answer was this:

Flip the coin twice. If you get two heads, go to the beach. If you get two tails, go to the mountains. If you get one heads and one tails, in whatever order, go to the desert.

This approach doesn’t work, because you can get one heads and one tails in two different ways (HT and TH), each one having 1/4 probability. So with this approach, you’d go to the desert 1/2 the time.

As I indicated in the first post, there are many acceptable answers. Here’s the simplest solution, first submitted by Mike Glover. This was also the most common solution, with about 15 people suggesting it (or something very similar):

Label the options A, B, and C. Flip two coins. If you get HH, choose option A. If you get HT, choose option B. If you get TH, choose option C. If you get TT, start over.

Here’s the answer I had in mind, some variant of which was submitted by 7 respondents:

Flip a coin for each pair (A vs. B., B vs. C, and A vs. C). If any option wins both of its head-to-head matches, choose that option. If no option wins both its matches, then start over.

The principle behind these two solutions is the same: attach A, B, and C to equally probable outcomes, and repeat the procedure if any other outcome comes up. Mike’s solution uses two coin flips to generate four outcomes, and then repeats on one of those outcomes. My solution uses three coin flips to produce eight outcomes, and then repeats on two of them.

But I was mistaken to think every solution would have to rely on this principle. Lauren Fisher submitted a very clever solution:

Flip a coin until heads comes up. There is a one-third chance that the first head will come up on an even-numbered flip.

Doubt it? The math works. The probability of the first head occurring on an even-numbered flip is:

(1/2)^2 + (1/2)^4 + (1/2)^6 + (1/2)^8 + …
= (1/4) + (1/4)^2 + (1/4)^3 + (1/4)^4 + …
= (1/4)/(1 - 1/4) = 1/3

This solution does not, like the prior solutions, rely on repeating the procedure for certain outcomes. If you’re concerned that this procedure only generates the 1/3 probability, without choosing among the three options, that’s easily remedied: if the first heads comes up on an even-numbered flip, choose A; if the first heads comes up on an odd-numbered flip, then flip the coin one more time to decide between B and C.

Lauren’s answer does share one thing with Mike’s and my answers: it could in principle require you to flip the coin an infinite number of times. Some respondents suggested procedures that would avoid that problem. For instance, two respondents suggested using the positioning of the coin when it falls – e.g., treating the word “LIBERTY” as one-third of the quarter’s circumference, and choosing option A when LIBERTY is closest to your body. Another couple of respondents suggested something like dividing a piece of paper into three sections, then setting it on the floor and flipping the coin onto it. Although these approaches could work as a practical matter, I think they run counter to the spirit of the puzzle. Glen Raphael defends these approaches, saying:

You might criticize my proposals to make use of rotational or positional info on the grounds that they don't produce exactly a 1/3rd probability. However, any proposal involving merely flipping the coin fails the same test - coins aren't perfect. Flip a quarter and you don't get an exactly 50% chance of heads; it'll be off by a few hundredths of a percent.

Agreed. But in keeping with the conventions of puzzles like these, I wish to assume that we have a “perfect” quarter. Given a perfect quarter, the algorithms discussed earlier will generate a probability of exactly 1/3. (BTW, Glen R. came up with Mike’s algorithm in addition to his position/rotational proposals.)

So, of the three mathematical solutions – mine, Mike’s, and Lauren’s – which is best? All three produce the correct outcome, so the question is which one will get you to a decision fastest. Mike’s clearly dominates mine, because the probability of getting a decision on any given round is 3/4 for both, but his involves only two flips per round while mine requires three. So it’s down to Mike’s and Lauren’s solutions. For Mike’s solution, the average number of rounds it takes to reach a decision is 4/3 (which results from a guaranteed first round, a 1/4 chance of a second round, a 1/16 chance of a third round, etc.). Since each round requires two coin flips, the average number of coin flips is 8/3. For Lauren’s solution, the average number of rounds it takes to for the first head to come up is 2 (which results from a guaranteed first flip, a 1/2 chance of a second flip, a 1/4 chance of a third flip, etc.). But 2/3 of the time, it will be necessary to flip one more coin to decide between options B and C. This adds another 2/3 of a round to her average, for a total of 8/3, which exactly ties Mike’s algorithm. I’m sure this is no coincidence, but I’m not going to try explaining why.

Thank you all for playing!

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My Bias; My Slur; My Bad

Please allow me to apologize for my use, in a recent post, of a slur that I’m afraid reveals an unfair bias. The phrase results from my over-generalization of a few unfortunate personal experiences, and risks offending millions of my fellow Americans. I’ve caught myself saying it in the past and resolved to stop. Nonetheless, once again, I unfortunately called part of the U.S. the “Boring Coast.”

I initially coined that term, together with “the Fun Coast,” in an attempt to come up with a pairing more evocative than “East Coast/West Coast” or “Right Coast/Left Coast.” I’m sticking with “the Fun Coast,” which I think fairly captures much of what I love about my adopted home. But I pretty quickly realized that, even if I often find some aspects of the other side of the U.S. less interesting than this side, I can not fairly call it “boring.” I’ve thus since opted for “the Respectable Coast,” a usage that I think captures something of the essence of the East, that usefully contrasts it with the West, and that casts no unfair cloud on the glory of the former Colonies.

Again, I apologize to everyone from those Respectable parts. Please understand that I was just having some Fun.

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Some AALS Data Documenting Preferential Treatment

In earlier posts I’ve described how the American Association of Law Schools facilitates sexual and racial discrimination against candidates for law school teaching, suggested that in so doing it disadvantages law schools that have mostly minority faculty, also argued against affording preferential treatment on the basis of mere genes, and offered outreach and education reform as an alternative policy. But I’m not done! I still plan to write about whom properly bears the most blame for discriminating against pale-skinned males who want to become law professors (hint: neither women nor minorities) and who such discrimination hurts the most (hint: not those self-same males). Here, though, I’d like to follow up on my earlier claim to have detailed data indicating, contrary to what some people believe, that law schools in fact do tend to disfavor pale-skinned males in hiring.

The AALS itself very helpfully provides that data. It has for many years tracked how often the various sorts of candidates listed in its Faculty Appointments Register actually land law school teaching jobs. Its Statistical Report on Law School Faculty And Candidates for Law Faculty Positions (2002-03), compares the success rates of men and women from the 1990-91 hiring season to the 2001-02 one (go here and scroll down to Table 7B). In brief, that data shows that in all but one (1995-96) of those twelve hiring seasons, women candidates fared better than men ones did. Averaging over the twelve years, women candidates got hired 13.9 % of the time, whereas men candidates got hired only 11.3 % of the time.

The effect of preferential treatment really jumps out in the data comparing the relative success of minority and non-minority candidates from 1990-91 to 2001-02 (go here and scroll down to Table 7C). In all but one (1997-98) of those twelve hiring seasons, minority candidates fared better than non-minority ones. Averaging over the twelve years, minority candidates got hired 17.2 % of the time, whereas men candidates got hired only 11.8 % of the time.

Uh, oh. The kids need breakfast! I’ll try to follow up later with more data and analysis. There’s interesting data specifically about the success (or, more properly, failure) of non-minority males candidates, and I really need to talk about the prospects of a regression analysis. That ought to be enough to get your started on your own number-crunching, and consequent ruminations, however.

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The Brighter Side of Hurricanes

The hurricanes afflicting the Boring Coast have recently attracted a great deal of attention, and for good reason. Those hurricanes threaten terrible losses to lives and property. Without discounting their salient costs, however, I’d like to point out that we on the Fun Coast feel the effects of hurricanes, too—and that we often love it.

As explained here, the eighteen or so hurricanes to hit the Eastern Pacific each year seldom do much damage. They usually drift to the west, out to sea, where they harmlessly dissipate. We have no record of any of them coming ashore in California, though they sometimes do strike Mexico’s comparatively lightly populated western shore.

So what’s the upside of a hurricane hereabouts? Surf. Great surf. Great long swells of head-high and better surf.

But wait, it gets better! Hurricane season falls during the best time of year to surf in SoCal. The June Gloom has long disappeared, the water has finally warmed up, the summer tourists have left, and the kids have gone back to school. Thanks to a hurricane, a very fortunate surfer (see, e.g., me) might thus find himself standing on a warm, sunny, Orange County beach staring agog as macking sets pump through a nearly empty line-up. Rest assured, though, that he won’t (and didn’t) stand long; he will (and did) grab his board and run, grinning, to the water.

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The Three-Sided Coin

I thought up the following puzzle today. Since I came up with it myself, I don’t know whether it’s difficult or not, so I’m posting it here to find out. My solution is not the only solution, but I suspect that all viable solutions will rely on the same basic principle. Here goes:

Using only a coin, how can you generate a probability equal to exactly one-third?

Here’s more context, if you feel the need for it:

Suppose you want to vacation at the beach, mountains, or desert. You want to choose your destination randomly, with equal chances for all three outcomes. Your only randomization device is a coin. What should you do?

If you think you have the answer, please email it to me at the address listed in the right-hand column. Also, give me an estimate of how long you had to think about it (be honest!). PLEASE DON’T POST YOUR ANSWER IN THE COMMENTS SECTION. I will post an update later with the (or a) solution, along with the name of the first person who got it. I’ll post multiple solutions if they rely on different principles, though I don’t think that will happen.

Let me head off one obvious, but incorrect, solution. “Flip one coin. If it comes up heads, go to the beach. If it comes up tails, flip the coin again, and go to the mountains if it’s heads and the desert if it’s tails.” This solution fails, because it generates one-half probability of beach, and one-quarter probability (each) for mountains and desert.

UPDATE: I've made a new post with the answers. Thanks to everyone for their responses. Please, no more emails!

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Curious Georgist, Part 2

As promised, I have some further thoughts on the Georgist land-tax proposal.

Basic tax theory says the best tax, from an efficiency perspective, is one that has the least impact on people’s actual choices. Thus, some economists have argued that sin taxes are desirable precisely because so many people will not be induced to refrain from sin – they’ll drink and smoke just as much as they always did. As a result, it’s possible to extract tax dollars from them without causing much deadweight loss from deterring activities that people clearly consider valuable. Of course, some people do reduce their activity levels in response to sin taxes, which means these taxes aren’t free from inefficiency. An even more efficient tax is the head tax, which you must pay just for living. This tax can only be avoided by suicide, an option that few people will choose to exercise on the margin (that is, very few people would get pushed off the ledge by the imposition of the head tax who would not have jumped anyway). (Okay, emigration would also allow one to escape a head tax.)

The problem with efficient taxes is they tend to be highly inequitable, or at least regarded as such. Sin taxes fall solely on those who engage in socially disapproved behavior. A head tax imposes the same burden on everyone, regardless of ability to pay. (If the tax is calibrated to your income or wealth, then it’s not a true head tax – it’s a form of income tax dependent on yours or your ancestors’ productive behavior.)

So we come to the Georgist proposal to impose a tax on land. Since the quantity of land is fixed, the Georgists argue, the land tax does not reduce incentives to create anything. As with other efficient taxes, the burden will – as I argued in my previous post – fall disproportionately on those who own land at the time of the tax’s imposition (not on subsequent owners, even though they will be responsible for sending the checks). But, the Georgists argue, such expropriation is justified because the land rightly belongs to the public – not the “owner” – anyway. I responded to that claim as well, noting that many current owners have purchased their land with the fruits of their labor. In this post, I’ll focus on the incentive issue.

David Youngberg has already anticipated one point I wished to make: while land is fixed, space is not. Space can be created, as when taller apartment buildings expand available living areas. Micha Gertner, commenting on Julian’s post, made a different point: not all land is currently known to us, and discovering land creates value. Taxing the value of land reduces the return to investments in discovery.

But there’s another objection I consider more important: that a tax on land can discourage the development and improvement of land. Anything that improves the land increases its market value, causing the tax to rise as well. Some efficient improvements on the margin, ones for which the added value is greater than the cost, will be forgone because the tax reduces the perceived value.

Georgists anticipate this argument, and say that the tax should not be on the whole property value, but on the “ground rent,” meaning the value of the land net of any improvements. The problem, however, is that the ground rent is essentially impossible to calculate, because it cannot be meaningfully separated from the value of improvements. To establish the ground rent, you have to find the value of “unimproved” land that is similar to the property in question in all other respects. In most (or at least very many) realistic cases, that is impossible because similar land will tend to be used similarly.

More importantly, plots of land tend to be highly unique. Rarely is any piece of land is exactly like another in all respects, including location, view, amenities, soil quality, ad infinitum. Even if there exist some types of property that are effectively identical – say, all the plots in a line of tract houses – many others differ substantially. Consider, for instance, a plot of land at the top of a mountain with a glorious ocean view. This plot is distinct from all the other nearby plots of land that are not at the peak. (And all those within a stone’s throw of the peak differ from those a little further down.) Suppose that someone has built a glorious mansion on this plot. The market price of this property will exceed that of all nearby properties for two reasons: first, because of the better location, and second, because of the nice house. The key point is that the two sources of value cannot be distinguished. And while this is an extreme example, what’s true here is true to a lesser extent for most properties in the developed world.

Even if it were in principle possible to calculate the “ground rent” on land and tax only that, politically it’s a dead letter. In reality, no jurisdiction I know of has ever implemented a ground-rent tax instead of a standard property tax, and the reasons are obvious enough: too large a share of the value of property comes from the improvements, not the land. It’s both easier and more remunerative to tax the market value of land, which is much more readily available. And even with this sort of tax, as property owners know well, government assessors have a strong incentive to overestimate the value of land in order to maximize tax receipts.

In reality, then, land taxes are property taxes, and property taxes do create some negative incentives. It might be true that they are less pernicious than those created by some other taxes, such as income taxes and tariffs. But let’s not pretend that land taxes are indifferent or, as the Georgists suggest, benign sources of government revenue.

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Britney Takes a Vow

Britney Spears attracts much well-deserved criticism, but I agree with her on this one. Some people are claiming that Britney is not really married, despite Sunday night’s surprise ceremony in a private home in Studio City (where I live!), because she and her intended haven’t filed a marriage license yet. Britney’s response?

“I know we're not completely legal until we file the license, which we’ll do next week,” the 22-year-old pop star said. “But in a real sense, a spiritual sense, we're married.”

And she’s right. Marriage does not depend for its existence on the recognition of the state. Marriage is, at its fundament, an ethical commitment between two (or more if you swing that way) individuals. If the parties choose, they may wish to make a legal commitment as well, but the acts are in principle distinguishable. To say that Britney and her beau are unmarried simply because they haven’t filed a license with the state is to confuse the promise with the enforcement mechanism.

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Curious Georgist, Part One

A couple of days ago, Julian made a post on Hit & Run inspired by an email discussion we’d had (with some other libertarian friends), inspiring a lengthy comments thread. Commenter Jason Ligon’s take on the matter is darn close to mine, so I won’t expand on it. However, another commenter (Scatalogicus) raised a different topic of interest: the Georgist proposal to fund government entirely via land and property taxes. I have a few comments to make on the subject.

1. Georgists are correct to claim that a tax on land differs from other taxes. Specifically, whereas taxes on other things (such as goods or labor) increase their price to the buyer, a tax on land decreases the price of land to the buyer. Why? While taxes are often regarded as taxes on specific people, they are really taxes on transactions. A cigarette tax only gets paid if cigarettes get sold, for instance. But a tax on land is different because no transaction is required – if you own land, you pay the tax. When you sell the land, the tax burden is transferred along with the title to the buyer. Realizing this, the buyer won’t pay as much as he would have for land unencumbered by the tax. Suppose the present discounted value of the land is V, and the present discounted value of the tax attached to it is T. Then the buyer won’t willingly pay more than V – T. Thus, the tax liability is capitalized into the value of the land. The Georgists are therefore correct to claim that land taxes drive down land prices.

2. What Georgists often fail to realize is that the entire burden of the tax is carried by the owners at the time of the tax’s imposition. This is not obvious, because current land owners pay taxes each year, despite the tax having been imposed years ago. But the capitalization logic above shows that the current owners were compensated for the tax burden by having been enabled to pay a lower price to acquire the land in the first place. This means that creating a new land tax (or increasing the rate of an old one) effectively confiscates a portion of the wealth of those who own land at the time the tax is enacted (or increased). It is as though the government had claimed part ownership in the land for itself.

Also, some Georgists claim the lower land prices as a benefit of the land tax. The fallacy here is the mirror image of the fallacy that current owners carry the burden of the tax. In general, the tax liability exactly balances the reduction in price, for a net effect of zero on those who acquire land after the tax’s imposition.

3. Smart Georgists recognize the two points above. At this point in the discussion, they will usually claim that it is fair and just for “society” (i.e., the state) to claim partial ownership of the land, because nobody creates land – it just exists. They argue that the owners of land have expropriated the public by removing land from the commons and taking it for their own use. For reasons I will discuss in my next post, the notion that land is never created is misleading – but for now, suppose it's true. It is nonetheless false to assume that current land owners (at the time of the tax's imposition) did the expropriation. In general, current owners have acquired the land in some other way – either through inheritance or purchase. If they inherited it, their ancestor either inherited or purchased it. Keep going back in time, and in general you’ll find a purchaser at some point in the land’s history. Rarely has a parcel of land been removed from the commons and delivered in an unbroken chain of pure inheritance through multiple generations all the way to the present. (The best examples I can think of are lands claimed by conquest and still owned by the government.)

So what? Well, if the owner of land at the time of the tax’s creation purchased it from someone else, then the wealth expropriated by the tax most likely did not derive from the removal of land from the commons. It could just as easily have resulted from labor. Suppose, for instance, that a school teacher works for many years to accumulate enough money to buy a home. Then the property tax rises. That tax takes a portion of the teacher’s labor-created wealth.

The irony here is that other taxes (income, sales, etc.) are typically regarded as taxes on people, whereas the property taxes are regarded as taxes on things. The truth is nearly the opposite. Income and sales taxes can in principle be avoided, even after their imposition, by avoiding the transactions to which they attach. Admittedly, it’s not always easy – few people could live without a job. But a property tax falls on the owners of land at the time of the tax’s creation, who have no prospect of escaping it. They can sell the land, but only at a reduced price, so the tax loss travels with them. The land tax can only be dodged by anticipating it and selling the land early. And even then, the dodge will only be successful if others don’t expect it (otherwise, the expected tax liability will be capitalized into the land), and it only succeeds by shifting the burden to the less-foresighted person who buys the land.

Lest I be misunderstood, I’m not claiming that land taxes are necessarily worse than other taxes. In comparison, land taxes might be the least of all evils (taking as given that the state will raise revenue one way or another). But even the advantages relative to other taxes are exaggerated by the Georgists – as I’ll discuss in my next post (in which I’ll also attempt to work in a Man in the Yellow Hat reference).

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Newcomb's Paradox: Being and Doing

I just encountered a decision problem that I’d never heard before, though I’m guessing philosophers probably know all about it. I found it in a book by psychologist George Ainslie, who quotes it from philosopher Robert Nozick, who credits it to physicist William Newcomb. Here is my paraphrasing of the problem:

A Powerful Being with the perfect ability to predict your choices sets two boxes in front of you. In Box A, there is $1000. In Box B, there is either $1 million or nothing. You have two options: either (1) collect the contents of both boxes, or (2) collect the contents of Box B only. If the Being predicts that you’ll choose (1), he puts nothing in Box B. If he predicts you’ll choose (2), he puts $1 million in Box B. The Being fills the boxes before you make your choice, but again, he can perfectly predict what you’ll do. So what do you do?

I won’t try to discuss everything that’s brain-twisting about this story, such as its implications for free will and determinism. I’ll just point out the paradoxical part. In choosing, you have to ask yourself, “What kind of person am I?” And no matter what you answer, you’ll want the answer to be something else at some point in the process. If you are a Box-B-Chooser, then the Being will put money in both boxes, and then you’ll wish you could become a Both-Boxes-Chooser after the Being fills the boxes (because $1 million + $1000 is better than $1 million). If you are a Both-Boxes-Chooser, then the Being will put money only in Box A, and then you’ll wish you could become a Box-B-Chooser before the Being fills the boxes (because that will cause the Being to put $1 million in Box B after all).

As fun as that problem is, I also like this simpler variation, which is actually my original (mistaken) interpretation of the story. (I don't know if Nozick or Newcomb considered it; Ainslie did not.) In this version, the Being is somewhat more malevolent:

A Powerful Being with the perfect ability to predict your choices sets two boxes in front of you. In Box A, there is $1000. In Box B, there is either $1 million or nothing. You can choose Box A or Box B, but not both. If he predicts you’ll choose Box A, he puts $1 million in Box B. If he predicts you’ll choose Box B, he’ll put nothing in Box B. The Being fills the boxes before you make your choice, but again, he can perfectly predict what you’ll do. So what do you do?

Here, the paradox is more straightforward, because there’s no difference in when (before or after the Being fills the boxes) you want to change who you are. If you are Box-A-Chooser, the Being puts $1 million in Box B, and you’ll therefore want to become a Box-B-Chooser after the boxes are filled (to get $1 million instead of $1000). If you are a Box-B-Chooser, the Being puts nothing in Box B, and you’ll want to become a Box-A-Chooser after the boxes are filled (to get $1000 instead of nothing).

My brain hurts.

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The AALS v. Howard Law School

What does the AALS have against Howard Law School? As I related below, the AALS has configured its search engine to allow law schools to search only for female or minority job candidates. Granted, I question whether a law school could use that feature without violating anti-discrimination laws. But let us generously suppose that a law school might legally search for candidates having certain genes in an effort to increase the diversity of its faculty. Why, then, does the AALS stack the deck against Howard Law School?

Judging from this photo directory, Howard might want to diversify its faculty by hiring some pale-skinned professors. On a rather cautious accounting, at least 22 of Howard’s 36 faculty—61%—tout relatively recent African ancestors. (By most accounts, of course, all our family trees ultimately take root in Africa.) Only about 6 of Howard’s 36 faculty members obviously descend from mainly Northern European stock. The inherent uncertainties of racial and ethnic classifications make these mere guesses, of course. It nonetheless seems quite clear that if Howard, like many schools, aspires to have its faculty reflect the racial and ethnic make-up of the whole of the U.S., it has to hire a good many more light-skinned people. Why, then, does the AALS make it so hard for Howard to do so?

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Preferred Preferences Policies

That worthy pseudonymous commentator, Trumpit, again asks a question worth answering, this time in response to my recent post about achieving diversity without discrimination. Although I began to answer his comment with one of my own, I found myself writing enough for a blog post proper—namely, this one.

Trumpit read my prior posts on the topic to indicate that I am “de facto opposed to affirmative action.” I wouldn’t put it that way. I take “affirmative action” to include both outreach, which I ardently support, and preferential treatment, which I generally oppose. Why “generally”? Because I am against preferential treatment only: 1) by state actors (taking that term broadly, as anti-discrimination law does); and 2) by private actors if the state allows preferences to be afforded only to certain categories.

I am against preferential treatment by state actors for a variety of reasons, both on grounds of rights (e.g., those protected by the 14th Amendment) and prudent public policy (e.g., the dangers of encouraging race-based politics). On the other hand, I think private parties should have the right to associate with whomsoever they choose, for reasons good, bad, or indifferent. It follows that they should have the right to discriminate on the basis of race or sex, whether for or against currently favored classes.

Taking me to oppose all preferential treatment, Trumpit asks, “How then do we get black/brown kids out of the Ghetto then?” I share his concern about the opportunities afforded to certain minorities in the U.S. But I do not think it appropriate to mask the harms inflicted by other causes--most notably by monopolistic government education--by violating the rights of third parties who did not cause those harms. Nor, as my use of "mask" indicates, do I think it constitutes good policy in the long run.

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"Heads Will Roll"

While driving home, I heard on the radio that Dan Rather and CBS News had apologized for relying on the clearly forged National Guard memos. CBS will be performing an internal investigation, and one CBS official was quoted (or maybe paraphrased) as having said “heads would roll” over the incident. As I drove, I thought idly about how glad I am to live in a country civilized enough that a grisly expression like “heads will roll” has come to mean people getting fired – and “head-hunting” actually refers to people getting hired.

As if to punctuate my thoughts, I came home to find this ghastly story on the news.

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Diversity Without Discrimination

In the comments to my earlier post about how the AALS allows law schools to search only for women or minority job candidates, the pseudonymous “Trumpit” asks, “Suppose I want to hire a female or minority law professor (I know I'm in the minority for wanting that!), then how do I go about it without stepping on any(white)bodies toes?” That excellent question deserves an answer, one different from this: “You go out looking for a female or minority law professor, anti-discrimination laws to the contrary notwithstanding, and feel pretty damned lucky if you manage to hire the one you want!”

Contrary to Trumpit’s assumption, women and minority law professors are very much in demand. Law schools want to hire them so much that they favor them over pale-skinned male candidates. Perhaps I'll follow up later with a post offering detailed proof of that claim. For now, though, I'll focus on Trumpit’s question.

In the first place, I would say that if you set out specifically intending to hire a woman or minority, you are engaging in sexual or racial discrmination. In that event, you could not honestly say that you are an equal opportunity employer. You would have already ruled out, or at least ruled against, certain employees because you are discriminating (i.e., "choosing") against them on the basis of sex or race.

In the second place, supposing that you set out intending only to diversify your faculty, I would say that: a) you can properly aim only to increase the diversity of viewpoints held by your faculty as a whole; and b) you cannot properly use sex, race, or ethnicity as a proxy for diversity of viewpoints. Only viewpoint diversity helps education. Building a superficially diverse faculty that, in fact, uniformly grew up in upper middle class U.S. households, attended top-notch educational institutions, and holds moderately left-wing political views does not add a whit to your students’ education. To assume that a faculty member will have interestingly different views solely because of his or her particular genes, moreover, demonstrates exactly the sort of prejudgement that anti-discrimination laws aim to correct.

What to do, then? First, engage in outreach, making sure that a variety of candidates learn about your job search. Next, search for viewpoint diversity, whether or not it lines up with sex or race. Lastly, work for educational reform to liberate those minority communities now held in the thrall of the teachers' unions, so that you might someday discover that paler folks are not overrepresented among those who boast the best credentials for going into law school teaching.

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Relationship Cycles

[Apologies in advance to anyone who finds this post sexist. I'm just having a bit of fun here.]

Recently, I casually mentioned to a group of guy friends that I thought many guys would be happiest with a 3-day-a-week girlfriend. Everyone present agreed. Some also expressed the suspicion that most women want a 7-day-a-week boyfriend. I bought this at first, until I realized women couldn’t possibly like us that much. Naturally, I have another theory.

I figure that everyone, men and women alike, derives diminishing marginal utility (MU) from relationship time. But the MU diminishes more quickly for men than for women. The figure below illustrates the difference.

For men, the MU of relationship time is given by MU(RM). It crosses the MU of alternative activities, MU(A), at 3 days per week. For women, the MU of relationship time is given by MU(RW), and it crosses MU(A) at 5 days per week. Thus, women’s optimal number of relationship days exceeds that for men, but it’s still less than 7. (Slightly different assumptions could generate essentially the same conclusion. For instance, men and women could have the same MU of relationships, but men could have a higher MU of alternative activities, thus generating the same qualitative result – a lower optimal number of relationship days per week.)

But what explains the perception that women want 7-day-a-week boyfriends? Now we come to my theory of relationship cycles. When two parties to a relationship have different preferences about timing, even a small divergence can create the illusion of a much larger one. Say that Harvey and Matilda have spent three days straight together. At this point, Harvey requests some alone time. If Matilda agrees (despite her desire to continue another couple of days), both parties get to reset their relationship clocks. Once Harvey and Matilda reconvene, say, four days later, Harvey’s and Matilda’s relationship-time MU’s have both risen back to their initial levels. But in another three days, Harvey will be asking for alone time again. Matilda never has to ask for alone time, because Harvey is always satiated sooner. Thus, the pattern of interactions creates the appearance of one-sidedness: Harvey keeps asking for alone time, while Matilda always want more together time.

The pattern would emerge even for a smaller difference; e.g., if Matilda’s optimum were 4 days per week, Harvey would still always want alone time earlier. And if the pause in between meetings is shorter, the effect gets stronger: since Harvey hasn’t had enough time to “decompress,” his MU of relationship time hasn’t risen all the way back to its start value, and so he reaches the saturation point even sooner.

The phenomenon of relationship cycles occurs in other interactions as well. Take phone call frequency. Say Ted would like to talk on the phone every two days, whereas Sheila would like to talk every day. You might think Sheila would call Ted about two-thirds of the time – but in fact, she will call him every time. If they talk on Monday, Ted plans to call on Wednesday; but then Sheila calls him Tuesday. His clock reset, Ted plans to call on Thursday. And then Sheila calls on Wednesday. Eventually, Sheila decides Ted doesn’t care about her, because he never calls.

Or consider sex frequency. Terry would like sex every other day, whereas Pat would like sex about twice a week. If they were separated for a week, Pat might initiate sex. But when they are in regular contact, Terry will always initiate before Pat does. Each time they have sex, both sex clocks get reset, and Terry’s fuse burns faster. At some point, Terry begins to doubt Pat’s affection, because Pat never initiates sex.

At this point, it seems natural to discuss the need for communication and compromise in a healthy relationship. But I’ll leave that to the experts.

UPDATE: I described the basic theory. Alex Tabarrok provides the empirics. And Eric Rasmusen extends the theory with a little Bayesian updating.

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