An Athenian Puzzle

The ancient Athenians had a very straightforward approach to the problem of funding government expenditures. If you were one of the richest Athenians, every other year you had to pay for something—sponsor Athens' team at the Olympics, pay all (later part) of the cost of the one of the triremes in the Athenian fleet, or the like.

If you were selected for such a task—called a liturgy—there were two ways of getting out of it. One was to show that you had already been assigned a liturgy for this year or had done one in the previous year. The other was to show that there was another Athenian, richer than you, who had not been assigned a liturgy either this year or last—and who should therefore do yours.

That raised an obvious problem. In a society without an IRS, without accounting, without modern banking and financial records, how do you prove that another Athenian is richer than you are?

I will give one hint to the answer: It was obviously invented, not by an accountant, but by an economist. Possibly a mad economist.

Plus Ca Change

A summary of Richard Posner's Recent comments on the Summers case.

In other universities the teacher is prohibited from receiving any honorary or fee from his pupils, and his salary constitutes the whole of the revenue which he derives from his office. His interest is, in this case, set as directly in opposition to his duty as it is possible to set it. ...

If the authority to which he is subject resides in the body corporate, the college, or university, of which he himself is a member, and which the greater part of the other members are, like himself, persons who either are or ought to be teachers, they are likely to make a common cause, to be all very indulgent to one another, and every man to consent that his neighbour may neglect his duty, provided he himself is allowed to neglect his own. In the university of Oxford, the greater part of the public professors have, for these many years, given up altogether even the pretence of teaching.

(from Adam Smith, The Wealth of Nations, Bk V Chapter 1 Part 3 Article II "Of the Expense of the Institutions for the Education of Youth")

Athenian Wisdom

In classical Athens, the victim of theft was entitled to search the home of the accused; if he found his property he could recover it and receive a damage payment of twice its value. This provided an obvious opportunity for fraud—plant the supposedly stolen property while pretending to search for it. The Athenians came up with a simple and elegant solution to that problem.

The accuser was entitled to search—but he had to do it naked.

We have our own version of the same problem—the risk that police officers may plant drugs while pretending to search for them. Perhaps we should take a lesson from the ancient Athenians.

[Readers sufficiently interested in ancient Athenian law may want to look at the web page of my current seminar, which contains a link to my outline of an excellent book on the subject]

Announcement

This day there arrived at my door a cardboard box full of printed copies of my novel Harald. Amazon still lists it as not yet available, so I don't know how soon other people will be able to get it.

It's beautiful.

I now return you to your (ir)regularly scheduled programming.

Rational Bigotry?

One of the puzzling things about certain political and cultural conflicts is how strongly people feel about them. I can understand why some people would prefer that homosexuals not be permitted to marry. It is harder to understand why they regard the issue as enormously important. Similarly for same sex couples adopting. Similarly for polygamy. And similarly—I think the most interesting case of all—for attitudes towards transsexuals, individuals who have undergone a sex change operation. In each case, the obvious question is why A cares so much about what B, or B and C, or even B, C, D, and E are doing.

I have a conjecture about part of the answer.

The world is a complicated place. One way in which we deal with that complication, in law and thought, is by representing a complicated reality with a much simpler model. There are lots of examples:

Some people are more mature than others, in one or another dimension. For many purposes we lump all those differences, along with the continuous range of ages, into two categories—children and adults. Doing it that way makes it a lot easier, in law and in conversation, to deal with issues where maturity matters—at the cost, as with any simplification, of sometimes getting the wrong answer.

If we define gender by genitals, hermaphrodites are both male and female, eunuchs in some sense neither. If we define it by DNA, some apparent males are female, some females male. Some are neither XX nor XY, some both. Nonetheless, we continue to classify people, in the law and inside our heads, as either men or women. Most of the time the simplification fits the reality, occasionally it doesn't.

Someone who does not fit our categories is a problem, not because he is doing anything to us but because his existence makes it harder for us to use our simplified models to make sense of the world. The problem only exists if we are aware of it—XXY genetics existed a century ago, but nobody knew about them. Hermaphrodites existed, and were known to exist, but nobody you knew was a hermaphrodite, or if someone was you didn't know about it, so there was no problem for your day to day attempt to use a simplified map to navigate social space.

The biggest example of this problem, one now more or less over among the people I know, was the breakdown of marriage. It used to be that people could be usefully classified as married or not married, which simplified a good deal of social calculation. As it became increasingly common for couples to openly live together without being married, the classification began to break down. That made it harder to figure out whether you had to invite A to dinner if you invited B, whether you were free to court A, and how to briefly sum up your knowledge of the status of A and B when talking with C.

Transsexuals provide a particularly striking example of the problem. If you knew him as a male and now know her as a female, there is a real problem fitting him/her into your mental picture of the world—a problem that shows up in, among other places, my discomfort with using either gendered adjective. I can see how other people might find similar difficulties in fitting into their heads polygamous families, same sex married couples, children with two mommies, and much else.

I am not, of course, arguing that other people have any obligation to make their lives fit my picture. Maintaining my map of the world is my problem, not theirs—reality has no obligation to conform. But I think the discomfort which comes when reality changes in ways that make obsolete what used to be an adequate set of simplifications provide at least a partial explanation for the strength of the response.

Christmas Books: 2

In an earlier post, I mentioned books I liked enough to buy multiple copies as Christmas gifts and gave one example. Here is another.

Chimpanzee Politics by Frans de Waal is based on a close study, over a period of years, of a chimp colony. The chimps come across as more like dumb people than smart animals. My favorite anecdote:

While the chimps were in their indoor habitat, the experimenters buried some grapefruit in a patch of sand in their outdoor habitat. The chimps saw the experimenters go by with the grapefruit, so knew something was up.

When released outdoors, they made an apparently unsuccessful search for the grapefruit. Then it was naptime. When the rest of the chimps were asleep, one of the low status males got up, went straight to the buried graperfuit, dug them up and ate them. To me, at least, that is striking evidence not only of rational behavior but of rational thought behind the behavior.

The other interesting observation was reflected in the title. The dominant male might or might not be the biggest and strongest—because the political struggle that determined dominance involved an elaborate pattern of shifting alliances.

The FISA Puzzle

NSA spokesmen have been understandably reticent about the details of their warrantless wiretapping, leaving the rest of us with the puzzle of figuring out just what they are doing in order, among other things, to know whether they should be thanked or arrested--or perhaps both.

A useful starting point is the Foreign Intelligence Surveillance Act, the law they appear to be breaking. FISA sets up procedures for getting warrants to intercept communications between terrorists and Americans. The NSA is intercepting communications without such warrants. The obvious question is why--not why they intercept but why they don't get warrants to do it, either before or, as the act permits, after.

I can only think of two plausible explanations. One is that the wiretapping is on an enormous scale, perhaps of all phone conversations with one end in the U.S. and one end outside, using computers to convert speech into text, search the text for keywords and suspicious patterns, and forward the recorded conversation to a human being only on the rare occasions when that search reveals evidence that it may have something to do with terrorism. I think it would be technologically straightforward to apply that approach to, say, a million conversations a day--but I doubt the FISA court would be willing or able to issue search warrants on that scale.

The other possiblity is that the searches do not come close to reaching the probable cause requirement of both the Fourth Amendment and FISA. Checking every phone call might be a sensible tactic, but it would be hard to justify it under that standard. The same might be true of a much less ambitious program of interceptions, targetting conversations that there was some very weak reason to think might be of interest--say all phone conversations between the U.S. and any Muslim country, or all phone conversations involving a party who had been called by someone under suspicion, or by someone called in the past by someone under suspicion, or by … . The fact that someone has talked to someone who has talked to someone who has talked to an Al Quaeda member does not qualify as probable cause for tapping his phone--but it still might be worth doing, if the only cost is a few cents worth of computer time.

As I pointed out in a previous post, quoting a book manuscript that I webbed a few years ago, wire tapping by computer raises an interesting legal problem: If only a computer has listened to your phone call, have you been searched? One could argue that the search only occurs when a human being listens to the recorded conversation--at which point the key words found by the computer provide probable cause. If that is the Administration's unstated argument, it explains one part of the controversy--the issue of whether the NSA was using information from warrantless interceptions to get warrants for further interceptions.

I do not know if my conjectures are correct. What is clear is that any explanation of what the NSA is doing must explain why they chose not to follow the procedures laid down in the law. I do not see how any explanation that comes down to "wiretapping people we have good reason to think are terrorists" can satisfy that requirement.

Metaphors and the Constitution: Wiretapping as Search

The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated; and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized. (US Constitution, Amendment IV)

The controversy over NSA wiretapping involves two different legal issues. One is whether the actions are illegal, the other whether they are unconstitutional--whether a statute permitting them would be in violation of the Fourth Amendment. A group of legal professionals ranging from Richard Epstein to Lawrence Tribe have produced a summary of the arguments against the administration's position on both issues. In my view and theirs, the illegality of the actions is clear. They think the actions are also unconstitutional; I am less sure.

The Constitution says nothing at all about wiretapping. It says nothing about eavesdropping on conversations, which might seem the closest equivalent given 18th century technology. What it regulates are searches. Past court decisions have treated wiretaps as searches and so required warrants for them. But a wiretap is only a metaphorical search--it differs from a literal search in important ways, some of which raise problems for interpreting the Consitutional restrictions.

Suppose George has been having a possibly criminal correspondence with Thomas. The government gets evidence against George, obtains a search warrant, searches his house and finds letters from Thomas and drafts of letters to Thomas. They have obtained information about both George and Thomas, but they only needed a warrant against George, since only his house was searched.

Now fast forward a few hundred years. The government gets a warrant to tap Bill's phone--but what they are actually "searching" is not Bill's house but his conversations with George. Still legal--but the distinction between searching Bill and searching George has vanished.

Finally, consider a conversation between George and Usamah. Usamah is not an American, so the government is, constitutionally speaking, free to tap his phone without a warrant. But George is an American person--and they are listening to his conversation too. Do they need a warrant? Under the terms of FISA they do--but is that a constitutional requirement, or only a statutory one? Is the wiretap equivalent to searching both houses, or to searching Usamah's house and finding letters from George?

Why is Tort Law like Accounting?

Because in both, all probabilities are either zero or one.

I have suffered a million dollar loss for which I think you should be liable. I sue you. If the court concludes that there is a .4 chance that I am right, I get nothing. If it thinks there is a .6 chance, I get a million dollars. All probabilities less than .5 are treated as zero, greater than .5 as one.

Accountants do the same thing. If your accountant thinks the probability of your losing the suit is .4, he doesn't list your expected loss of $400,000 as a liability. He leaves it out entirely, aside from a footnote mentioning the existence of the lawsuit. If he thinks the probability is .6, he puts it in as a million dollar liability.

I suspect the underlying reason is the same in both cases. Both tort law and accounting depend on low quality decision making mechanisms. Nobody designing an automobile or diagnosing an illness would do it by putting the question to 12 laymen. So instead of asking the hard question--what is the probability that the defendant was negligent--we ask a simpler question: Was he probably negligent? If you are not competent to answer a comlicated question, there is much to be said for limiting yourself to simple ones.

An accountant is a more sophisticated decision maker than a jury, but he knows much less about a business than the people running it. And those people frequently have an interest in having the accounts turn out one way instead of another--high equity to boost stock prices or low profit to hold down taxes. One way of making it harder for them to fudge the accounts by the information they give their accountant is to have accountants use simple rules wherever possible. That explains many of the ways in which accounting substitutes a simple answer for a correct one--with the treatment of probability only one example. Other biggies are the preference for cost price over market price and the reluctance to take account of intangibles, even important ones such as brand name reputation.

And this is my last post on accounting. Unless something else interesting occurs to me.

Understanding Accounting: The Short Version

I have been teaching a new course that includes two weeks explaining accounting to law students. To do so, I first had to understand it myself. I think I now do, and in the hope that the information might be useful to others … .

Rule 1: The terms "debit" and "credit" are only there to confuse. Most of the time they mean the opposite of what they should: An increase in assets is a debit, a decrease in assets (or an increase in liabilities) a credit. Equity–the net value of the firm to its stockholders–is an exception to that rule. A credit to equity is an increase, a debit a decrease. For closely related reasons, the income account is another exception: Revenue is a credit, expense a debit.

Rule 2: The essence of double entry bookkeeping is that every item appears twice, once on the left hand side of a T account, once on the right. If you buy some oil, that is a reduction in (credit to!) cash and an increase in (debit to!) inventory; the two amounts are equal because accountants measure the value of something, in this case oil, by what you paid for it. If someone gives you money, that is an increase in (debit to!) cash and a matching increase in (credit to) equity. Similarly, if you sell the oil for more than you paid for it the difference ends up in equity, although only after going through an extra pair of T accounts (income/expenses) intended to make sure that the transaction shows up on the income accounts as well as the firm's balance sheet.

Rule 3: The reason the left hand (debit) side of a T account is good if it shows assets or liabilities but bad if it shows equity or income is that an increase in assets can be balanced either by an increase in liabilities (you took out a loan, giving you cash, an asset; the money you owe is a liability) or by an increase in equity (you bought low and sold high, increasing cash without increasing liabilities, hence increasing equity). An increase in liabilities is bad, an increase in equity is good--but either can balance an increase in assets, so they have to be on the same (credit) side of a T account.

Rule 3': The reason liabilities are like equity is that equity is a "liability" the firm owes to its stockholders. This is shorter than Rule 3 but less enlightening.

Rule 4: When an item doesn't show up where you think it should in the accounts, the reason is that it is being shifted forward or backward in time in order to group expenses with the income they produce.

Read the rules three times, think about them, and with luck you will understand accounting considerably better than I did a week ago.

Unschooling: The Advantage of the Real World

One point raised in comments on my recent unschooling post was that you sometimes have to do things you don't like, a lesson we can teach our children by making them study things they are not currently interested in studying. It is an interesting point, and I think reflects a serious error.

We want our children to learn what the real world is like. One way of doing that is to construct a synthetic world designed to imitate the real one. To teach them that they will sometimes have work to accomplish things, even if they don't want to, we assign them homework they aren't interested in doing and reward them with grades. If grades don't work well enough, we reward the grades with cash, as some parents do.

What this approach leaves out is the causal connection between the work and the accomplishment. Someone else has told you to do unpleasant work, someone else will reward you for doing it, but there is, from your standpoint, no logical connection between the two. Doing homework does not, so far as you can tell, actually produce money.

The alternative to a synthetic world is a real world–the one we and our children are living in. If you don't tune your harp, it won't sound very nice when you play it. If you don't tidy up your room, at least occasionally, you won't be able to find things you want. If you don't sometimes do things your younger brother wants you to do, he won't do things you want him to do. That world also teaches the lesson–getting what you want sometimes requires doing things you would rather not do. And it gets the causal connection right.

Home Schooling: Family as Peer Group

My most recent post summarized The Nurture Assumption by Judith Harris, which argues that the peer group, not the family, is the important environmental influence on the adult personality.

The author partly qualifies that claim by observing that, for some children, the family is the peer group. She gives as an example the case of a black worker with four daughters who decided that they were all going to be doctors–and ended up with one doctor and three other professionals. The way he did it was by making the family the set of people with whom his daughters chiefly interacted, and with whose values they identified. I think that describes my upbringing as well–I was very much an outsider in school, seeing my family as real people and my age peers as at least mildly alien. I gather from correspondence with Judith Harris that it may have been true of her as well.

This suggests an important point about home schooling–it is, among other things, a way of making it more likely that your children's parents, siblings, and a few friends will function as the effective peer group. Seen from one standpoint, that means parents trying to control their children, mold them in their own image. Seen from the other side, the choice is between the parents' values and the values of a random collection of kids–and most parents know which they prefer.

There are some disadvantages to the approach, of course. I was never entirely socialized to the surrounding society; one result is that I regard argument nont as a way of expressing hostility but as an entertaining and educational activity, an attitude that can quite easily get one in trouble. And there are other ways in which most of the people around me still seem slightly alien, more so than they probably would if I had identified with my age peers when growing up. Yet, all things considered, I prefer the attitudes, values and worldview I was brought up with to those more generally prevailing.

Many years ago, my parents expressed concern as to whether they should have made more of an effort to bring their children up in their ancestral religion, celebrated Hannukah instead of Christmas, perhaps sent me to Hebrew School. My reply was that I thought it better to be brought up, as I was, in the religion they actually believed in--18th century rationalism, the world view of Adam Smith and David Hume.

Christmas Books: 1

Finding presents for friends and relatives is often a problem, made harder by the economist's puzzle of why one should give presents instead of giving cash and letting the recipient, better informed about his own preferences, decide how to spend it. A possible answer is that although I know less about the recipient, I know more about the gift. Acting on that principle, I occasionally pick a book that I and my wife particularly liked, buy a bunch of copies, and give them out as Christmas presents.

It occurred to me that some readers of this blog might be interested in hearing about them.

The Nurture Assumption by Judith Harris:

The author argues that while children are shaped by both genetics and environment, the relevant environment for most of them is not the home but the peer group. By her account, none of the popular stories about birth order, child rearing practices, and the like as determinants of adult personality are supported by the evidence. Human beings are good at recognizing that different rules apply in different environments. The typical child can and does show one face to his parents, a different one to his peers–and it is the peer group version that grows into the adult personality.

If she is right–and I think it likely that she is–that raises an interesting question about the history of psychology. How could beliefs about things such as the influence of birth order and childrearing be widely held within a scientific community when there was no evidence they were true?

Part of the answer is the confusion between genetic and environmental causation. Someone confident that personality depends only on environment will interpret similarities between parent and child as due to the affect of the environment provided by the parent. To distinguish between the two alternatives you need to look at children reared by people other than their biological parents. When you do so, it turns out that the observed similarities are in large part due to genetics.

Another part of the answer has to do with the nature of statistical evidence. Suppose you believe that birth order affects personality. You get personality evidence on a bunch of people, test for correlations between personality and birth order, and find one. First born daughters are (say) more self-confident than second and third born. You come up with a plausible explanation–the eldest child has had the experience of bossing her younger siblings around–and publish. The correlation is confirmed at the .05 level, meaning that there is no more than one chance in twenty that it could be due to chance.

Another believer in the importance of birth order does a similar study. He finds no effect for first born daughters, but discovers that last born sons are more optimistic than first born. He too comes up with a plausible explanation and publishes.

The process continues for many years. Occasionally someone is unable to find a correlation–and, since failure is rarely interesting, abandons that project in favor of something more likely to get published. Looking at the literature, it is obvious that birth order affects personality–practically everyone agrees about that–even if the details are a matter of dispute.

Only when it occurs to someone to combine the results from many studies does it become clear what is happening. With considerably more than twenty possible relations between birth order and personality, pure chance will usually result in a significant correlation for one of them–a different one each time. Pool the data and the result vanishes.

The origin of Harris's book makes an interesting story. It started as an article published in The Psychological Review. The article provoked a lot of mail–partly about the controversial argument, partly asking who the author was, since nobody in the field had ever heard of her.

Judith Harris had gotten a masters in psychology from Harvard and been discouraged from going further by a professor who assured her that she did not have the makings of a successful scholar. She left academia, married, and helped support her family by coauthoring child development textbooks. Eventually she concluded that a good deal of what those textbooks said was not supported by the evidence. The result was the article–which received the journal's prize for the year's best.

The prize is named after the Harvard professor who told her that she had no future as an academic. God, Judith Harris concluded, has a sense of humor.

Problems with Blogger

I have this blog set up so that comments both appear on the blog and come to me as email. In recent days, a number of comments have come as email that have not appeared on the blog. I assume this is some sort of bug in blogger, and thought it worth mentioning so that people would know I'm not deliberately blocking them. Such comments include ones from James Klock, Bryan Eastin, Anonymous (on language instruction) and Albatross--and I may have missed some.

If your comment doesn't appear after an hour or so, you might want to try resubmitting it.

The Case for Unschooling

Unschooling is currently in the news, our children (12 and 15) are unschooled, and the best defense is a good offense, so …

One of the assumptions built into the conventional version of K-12 schooling, private and public, is that there is some subset of human knowledge, large enough to occupy most of twelve years of school, that everyone needs to know. That assumption is false. There is a very short list of skills–reading, writing or typing, and simple arithmetic are the only ones that occur to me–that almost everyone will find worth learning. Beyond that, education involves learning things, but not any particular things. The standard curriculum is for the most part an arbitrary list of what happens to be in fashion–the subjects everyone is required to pretend to learn.

Consider, as examples, English composition, American history, algebra, geometry, and trigonometry. Each will prove very useful so some people, occasionally useful to more, and almost entirely useless to quite a lot. And, although practically every high school graduate is supposed to have learned each of those things, many, probably a majority, have not--as anyone who has taught college freshmen can testify.

A second assumption is that the way for children to learn things is to be told "this is what you must learn today," assigned some reading, and sat down to listen to a teacher. One result is that children spend most of their time being told things they have no interest in knowing. Another, given the diversity of interests and abilities, is that a third of the pupils in a classroom are bored because they already know what is being taught, a third are bored because they are completely lost, and only the middle third are, with luck, listening, understanding and learning. A sufficiently good teacher can improve those numbers somewhat–but sufficiently good teachers are scarce.

One observed result is that most children regard education as unpleasant work, to be avoided when possible. Another is that schools spend six years teaching things–arithmetic, say–that the average kid could learn in a year or two. If he wanted to. A third is that we end up with high school graduates many, perhaps a majority, of whom do not actually know many of the things they have spent all those years pretending to learn.

There is at least one more thing wrong with the conventional model. Judging sources of information on internal evidence is a very important intellectual skill. In the classroom, that skill is anti-taught. The pupil is told things by two authorities–the teacher and the textbook–and his job is to believe what they say. Here again, a sufficiently good teacher may be able to overcome the logic of the setting and teach some degree of critical thinking–but here again, sufficiently good teachers are rare.

One of the great advantages of the Internet, considered as an educational tool, is that it is so obviously an unfiltered medium, leaving it up to each reader to figure out for himself how much to trust his sources of information. It isn't perfect, but at least it is teaching the right lesson instead of the wrong one.

The views I have been expressing are not based on any extensive surveys, but they are based on experience. I went to a first rate private school, my wife to a good suburban public school. Both of us had a few good teachers and classes, but what we most remember is being bored most of the time. I learned more about the English language reading Kipling's poetry for fun and going through a book or two a day, largely Agatha Christie and her competitors, during summer vacation, than I did in English class. I learned more about political philosophy arguing politics with my best friend than I did in social science.

There are a number of alternatives to the conventional model. The one we have chosen is unschooling–leaving our children free to control their own time, learn whatever they find of interest. I sometimes describe it as throwing books at them and seeing which ones stick. In our case the sticky ones included The Selfish Gene (my daughter at about 12), How to Lie With Statistics (both kids), How to Take A Chance (a popular book on probability theory, of especial interest to my son, at about ten, because of his interest in role playing games), and lots of fiction, much of it intended for adults.

No doubt they will end up not knowing several of the things on the standard curriculum–as will many of those subject to it. But my son has learned more history and geography from books and computer games than he would have in elementary school history classes–and avoided the fatal lesson that learning things is boring work, to be avoided whenever possible. My daughter has some catching up to do in math before she is ready for college–but both kids regard solving two equations with two unknowns (and integer solutions) as an entertaining puzzle.

In the background, as I write this, my daughter is practicing on her harp. Without anyone telling her to.