More on Education

Before I switch to another topic

Compulsion, Incentives, and Literacy

Reading is a useful skill. If you want children to learn it the obvious starting point is to ask what they would enjoy reading, since it is easier to get someone to do something if he likes doing it. The answer might be comic books, car magazines, science fiction, fantasy, soap opera summaries, D&D rule books, or any of a wide variety of other sorts of written material. 

That is not the approach taken by conventional K-12 schooling. The books students are assigned to read are chosen either because they are viewed as good literature — famous books from the past or current books that English professors approve of — or because they teach lessons that the people selecting the books want taught. That could be religion, patriotism, acceptance of homosexuality, any of a wide range of other lessons, depending on political and educational fashion. While they might be books students enjoyed reading — I am very fond of Kipling, some of whose stories might be assigned reading in an English class — that is not what they would be chosen for, so the odds are not very good.

The ability to read is useful to almost everyone. Appreciation for great literature no doubt can enrich one's life, but on the evidence of what people actually read it does not enrich the lives of a very large fraction of the population. That suggests that learning the former should have higher priority than learning the latter. In an educational environment where teachers can advise and persuade pupils but not compel them it will, because teachers who insist on telling their pupils to read books that the teacher likes and the pupil does not will soon find their advice ignored. In an environment where teachers can tell students what books to read and grade down those who fail to obey there will be a temptation to assign the books the teacher thinks the student ought to read, sacrificing the higher priority of literacy for the lower priority of literature — or, sometimes, propaganda.¹ 

Which may explain why Johnny can't read.

I encountered a different version of the same logic a good many years ago in my own work. My Price Theory textbook was out of print.  I decided to rewrite it into a book targeted at the proverbial intelligent layman, the sort of book that gets read for the fun of it while teaching the reader the basics of an academic subject. My model, insofar as I had one, was The Selfish Gene, a book from which I learned quite a lot about evolutionary biology.

There was an important difference between the book I had written and the book I was writing: Since the latter was not a textbook, nobody would be forced to read it.² If at any point the reader decided that it was not worth continuing, I would lose him. To deal with that problem I followed a deliberate policy of starting each chapter with a hook, a puzzle that would sufficiently engage the reader to persuade him to finish the chapter to find the solution. Economics is full of such puzzles; I do not know how hard it would be to do the same thing in another field.

The result, Hidden Order: The Economics of Everyday Life, has been one of my most successful books. Incentives matter — including mine.

Unschooling for Grownups

The current model of higher education consists, for many young adults, of spending four years partying and socializing while pretending to acquire the liberal education that was a social or professional requirement for a small elite a century or more ago. A substantial fraction graduate knowing almost nothing of large parts of what they are in theory being taught,³ a fact unlikely to surprise any professor who has taught a required course and observed how many of his pupils are trying to memorize enough bits of the textbook to pass the exams. To see which bits they think qualify, look at a used textbook and see what has been highlighted.

That suggests the possibility of a more attractive model, one in which young adults get on with their lives while educating themselves. That could mean working, it could mean getting married and rearing children, for those with a little inherited money and simple tastes it could mean trying to write novels, do volunteer work, engage in some other activity that they find a satisfactory way of spending their time. It could even mean a life centered on parties and socializing, supported by whatever minimal amount of paid labor it requires, just done outside of the expensive framework of college or university.

And meanwhile, if they want an education, they could be getting it by reading books, using educational software, taking webbed courses, interacting with people online, the higher-ed version of unschooling. It is how I got quite a lot of my education. I ended up teaching at the graduate level in two different fields, law and economics, in neither of which I had ever taken a course for credit.

There are, unfortunately, some practical problems with getting your education outside of school:

If you serve in the military, you get great educational benefits, but they can only be used in a conventional school.

You need to attend a conventional school for licensing in a wide variety of fields, from HVAC, plumbing (sometimes),⁴ and electrical work to medicine, law and nursing. if you spend 20 years teaching education classes in college, you will have to go back to school and take those same classes before you are allowed to teach in a public high school.

Companies offer their workers educational benefits, which are tax deductible, but only for conventional education.

Feds offer tax credits for education, but only for conventional schools.

Those examples are mostly borrowed from a commenter on my blog. From another :

Role-playing games have contributed a lot to my education in history. Way back in the 1970s, when I was playing Dungeons and Dragons out of the little tan books, I became curious about what things cost and how prices of equipment were figured, and so I started reading medieval economic history. And from that I began to gain a notion of what real medieval economies were like. And that led me on to history of science, history of technology, economic history generally, legal history, and military history . . . and the sort of general history that tries to take all those into account. I've done even more of it since I started writing books for Steve Jackson Games; my current work on GURPS Low-Tech has had me reading recent historical studies of catapults, warhorses, boats, non-Western firearms, camels, and several other topics. I like to think I've gotten a better sense for how differently historical societies worked. . . .

Which brings me to …

World of Warcraft as Education

You are teaching economics at a large university. A substantial fraction of your students play or have played World of Warcraft, which they probably find more interesting than a textbook. You too play WoW, so know that the game contains a complex economy. You announce a course in WoW economics and get a gratifyingly large enrollment. Now what?

WoW has markets and prices, including an auction house with many buyers, many sellers, and a wide range of products for sale. Starting prices, buyout prices and changes over time are public information. Sale prices are not public but students who buy and sell things in the auction house can keep track of prices paid and received and make the information available to the rest of the class.

Consider one simple question — relative prices of ore. Low level players mine copper, higher level iron, mithril, thorium, … . Higher level ore is refined into higher level metal used to make weapons and armor useful to higher level characters, who typically have more virtual gold to spend, which should lead to a higher demand for higher level ore. A high level player can mine low level ores but not the other way around, which you might expect to lead to a higher supply of low level ore. That suggests that prices should be higher for higher level ore.

Sometimes they are but not always. A lot of ore is produced by players who are wandering around killing monsters and doing quests, happen to see a vein, and mine it. As the population of a server accumulates more and more high level characters, more and more time is being spent wandering in high level areas with high level ore, producing an increase in the supply of thorium, a decrease in the supply of copper. Ore, loot, and experience are joint products, like silver, gold, and copper produced from the same ore in the real world.

What about demand? High level characters need high level gear made from high level metal, so one might expect a higher demand for higher level ores. What complicates that is the process of skilling up, becoming a better and better smith or jeweler able to make better and better stuff. Before you can make swords out of mithril you must first make them out of iron, before that copper (I simplify, as any WoW enthusiast will realize). If your high level character decides to take up smithing he must start at the bottom. Even if he himself is a miner he is not spending his time in the low level areas where copper is mined, so goes to the auction house instead — and bids up the price of copper.

Skilling up complicates the pattern of prices in another way as well. To go from making swords of copper to making them of bronze you have to make a lot of copper swords, or daggers, or armor, or … . You cannot use all of it yourself, so sell most of what you make. That sometimes means turning fifty silver worth of material into something you can only sell for forty, paying ten silver for the additional skill from making it. That works for low and medium level gear, made mostly by people who are still skilling up. But the highest level gear is made by craftsman who are already all the way up in skill, get no additional skill by making it. So low level, but not high level, gear often sells for less than the cost of materials to make it.

As these examples suggest, World of Warcraft provides multiple examples of the economics of joint production. Gems, in the base version of the game, are found when mining ore; each time you mine a lump of mithril ore you have some probability of finding an aquamarine. An increase in the price of mithril due to increased demand would result in more being mined, increasing the supply of aquamarines and driving down their price, so a high price of mithril will be associated with a low price of aquamarines if it is due to an increase in demand, a high price if due to a decrease in supply. One homework assignment might be “find another example of joint production, describe and test its implications.”

Patterns of prices in the game change over time, sometimes in comprehensible ways. At one point a new option opened up in the game, a type of character that got to start not at level 1 but at level 55. Your brand new level 55 Death Knight fights like a level 55 but if he takes up smithing it will be at level 1. The effect on the relative prices of low and high end ore and metal is left as an exercise for the reader.

For another example of WoW economics, consider arbitrage. Any miner can convert a lump of iron ore into a bar of iron, a bar of iron and a lump of coal into a bar of steel. The result should be a predictable relation between the market prices of ore and metal or of iron, coal and steel. Students can look on the auction house and see if the pattern holds, try to find and test explanations if it does not. Similarly, any predictable pattern of price changes over time — some things being more expensive on the weekend, say, when more players are online — should open opportunities for enterprising players to buy low, sell high, and make a profit. The result of players doing so should be to raise low prices, lower high prices, and eliminate the pattern. Does it happen?

There is no antitrust law in WoW, which makes it a good place to observe collusive behavior by sellers. My wife, who has spent much more time in the auction house buying and selling than I ever did, observed both an attempt to corner a market and an attempt, at least partly successful, to form a cartel. Her refusal to join it was met by a threat to drive her out of the market by underselling; the organizer of the cartel had apparently not read McGee’s classic article on the myth of predatory pricing.⁵ It had not occurred to her that if she was selling, at an artificially low price, ten times as many gems as the interloper, she was also losing money ten times as fast. It took only a few days for her to discover the flaw in the strategy and abandon it.

In World of Warcraft as in the outside world, cartelization is easier if there are only a few producers. If making some high end item requires a very rare recipe and only three players have it, it may be practical for them to get together and agree on a common (high) pricing policy. With forty crafters that does not work as well. If only three people are making it but forty can, a successful cartel is likely to attract competition.

Another critical issue is elasticity of supply. If many people can make the item but it requires some rare item as an input, a seller who can corner the market on that input, buy all units as soon as they show up, can have an effective monopoly of supply. That works if the input is a rare drop, something produced occasionally as a side effect of doing something else. It does not work for something  that is deliberately produced, since the high price for the input will give other players an incentive to produce more of it.

It might occur to a sufficiently clever WoW monopolist that if he can monopolize a key input he does not need to monopolize the product it is used to make, since he can collect his monopoly profit in the price of the input, letting other players make the product and sell it at a price reflecting what they have had to pay him. He will then be well on his way to understanding a point that generations of anti-trust scholars got wrong — why using vertical integration to extend a monopoly is, while possible, generally pointless.⁶

The formation of teams — two players working together, five doing an instance, ten or more a raid — provides examples of division of labor. Two paladins or two mages make a weaker team than a paladin plus a mage, since mages are good at dealing damage, poor at taking it, useless at healing, making a paladin, tough and a healer, an ideal partner for a mage. The usual five man group consists of a player optimized for getting the enemies to beat on him and surviving the process, a healer, and three damage dealers. Larger groups benefit by additional specialization.

These are a few examples I have come across of economics in World of Warcraft. It should not be hard to come up with enough more to fill a quarter.

Statistics

World of Warcraft provides many opportunities to collect data and try to infer patterns from it, so could be used to explain and apply statistical inference. Consider the question of whether a process is random. There is a tradeoff, as any statistician knows, between type 1 and type 2 errors, between seeing something that isn't there and failing to see something that is. In the environment humans evolved in there were good reasons to prefer the first sort of error to the second: Mistaking a tree branch for a lurking predator is a less costly mistake than mistaking a lurking predator for a tree branch. Evolution has, as a result, given us pattern recognition software that can detect patterns that are not there: hot dice, a loose slot machine, a run of luck.

Players in World of Warcraft see such patterns too. In their case, however, the events might not be random, might be the deliberate result of programming. In the real world it is usually safe to assume that the dice which you have used in the past will continue to produce about a 1/6 chance of each of the numbers 1-6 in the future. In a computer game it is possible that the odds have changed, that the latest update increased the drop rate for the items you are questing from one in four to one in two, even one in one. It is even possible that some mischievous programmer has introduced serial correlation into otherwise random events, that the dice really are sometimes hot and sometimes cold.

At one point I was on a quest which required me to acquire five copies of an item dropped by a particular sort of creature. Past experience suggested a drop rate of about one in four. I killed four creatures, got four drops, and began to wonder if something had changed. The question was one to which statistics, specifically Bayesian statistics, was applicable, and provided an opportunity to contrast that approach with the more familiar approach of classical statistics.

Consider first the latter. The null hypothesis is that the drop rate has not changed, that each creature I kill has one chance in four of dropping what I want. The alternative hypothesis is that the latest update has raised the rate to one in one. A confidence result tells us how likely it is that, if the null hypothesis is true, the evidence for the alternative hypothesis will be at least as good as it is. Elementary probability theory tells us that, if the null hypothesis is correct, the chance of getting four drops out of four is only one in 256. Hence my experiment confirms the alternative hypothesis at better than the .01 level.

Does that mean that the odds that the drop rate has been raised to one in one are better than 99 to 1? That is how, in my experience, people often interpret such results.

1/256 is not the probability that the drop rate has not changed, it is the probability that if it had not changed I would get four drops out of four. To get from there to the probability that it had changed, the probability that would be relevant if, for example, I wanted know at what odds I should be willing to bet someone that the fifth kill would give me my final drop, I need additional information: how likely it is that, just prior to my doing the experiment, the drop rate has been changed. That prior probability, plus the result of my experiment, plus Bayes Theorem, gives me the posterior probability that I want.

Suppose my four drops out of four occurred the first time I played after a patch was installed. By reading the notes on past patches or getting a Blizzard programmer drunk and interrogating him I learn that, in each patch, any particular drop rate has a one in ten thousand chance of being changed. The probability of getting my result via a change in the drop rate is then .0001 (the probability of the change) times 1 (the probability of the result if the changed occurred — for simplicity I am assuming that if there was a change it raised the drop rate to 1). The probability of getting it without a change by random chance is .9999 (the probability that there was no change) x 1/256 (the probability of the result if there was no change). The second number is about forty times as large as the first, so the odds that the drop rate is still the same are about forty to one. And the odds that a student who played World of Warcraft would find that explanation interesting and manage to follow it would be higher than if I were making the same argument in the context of an imaginary series of coin tosses, as I usually do.

World of Warcraft not only provides opportunities to explain statistics, it also provides opportunities to apply it. Auction house data can be used to test the implications of economic theory. If the results don’t fit, the next step might be to apply more sophisticated economics, to introduce transaction costs, risk aversion, market imperfections, features of a thin market. If you are very clever, theory plus statistics might reveal patterns that other players have not yet noticed.

Profitable patterns.

1. An account of someone doing education right, a mathematician showing a group of high school age kids what math was good for and why it was fun.

2. In the interest of honesty I should add that some people are forced to read Hidden Order since it is occasionally used as a textbook.

3. For evidence, see Bryan Caplan, The Case Against Education: Why the Education System Is a Waste of Time and Money.

4. A plumber I know tells me that the requirements for union apprenticeship, which vary from place to place, do not routinely require a college degree nor always a high school degree.

5. John S. McGee, "Predatory Price Cutting: The Standard Oil (NJ) Case," Journal of Law and Economics, vol. 2 (October 1958), p. 137. McGee tested Aaron Director’s argument that the predatory pricing Rockefeller was accused of would not have worked and concluded that it was correct.

6. For details of the argument, see my Law’s Order, Chapter 16, p. 253.