David D. Friedman's Blog, page 9
November 9, 2012
Wanted: Maps + a Time Machine
My wife and I left San Jose a little after 7 this evening, heading for Sacramento, where we are teaching at an SCA event tomorrow. In planning the trip—including stops going, coming, or both to visit my grandchildren in Berkeley and my sister's in Davis—one important question was when traffic would be heavy, what time rush hour starts and ends on the relevant highway on a Friday in November.
My Android phone shows me current traffic conditions, but the designers carelessly neglected to attach a time machine, so I did not have the option of seeing today's information yesterday or the day before. Someone should correct that omission. There is no way of knowing for certain what traffic will be like this Friday, but what traffic was like last Friday, and the Friday before, and the same time of year last year and the year before, are all public information. By combining information of that sort with sophisticated statistical analysis, it should be possible to make a pretty good prediction of future traffic a day, a week, even a year in advance.
What I am imagining is a web page that looks very much like the Google Maps picture on my phone, with the traffic layer selected. The only addition would be the ability to set date and time.
Does it already exist somewhere?
My Android phone shows me current traffic conditions, but the designers carelessly neglected to attach a time machine, so I did not have the option of seeing today's information yesterday or the day before. Someone should correct that omission. There is no way of knowing for certain what traffic will be like this Friday, but what traffic was like last Friday, and the Friday before, and the same time of year last year and the year before, are all public information. By combining information of that sort with sophisticated statistical analysis, it should be possible to make a pretty good prediction of future traffic a day, a week, even a year in advance.
What I am imagining is a web page that looks very much like the Google Maps picture on my phone, with the traffic layer selected. The only addition would be the ability to set date and time.
Does it already exist somewhere?
November 8, 2012
How not to Teach Math—or Economics
A recent conversation with my younger son, frustrated over his undergraduate math course, reminded me of my long standing objection to how math, and for that matter economics, are often taught. Theorems are proved with a rigor that is more than the students really need—especially in economics, where rigorous proofs can be applied to the real world only by combining them with non-rigorous models. The rigor is not only more than the student needs, it is more than any save the ablest students can understand. It is one thing to follow a proof step by step. It is a different and much more difficult thing to hold the proof in your head and understand why it is right.
My usual example of the problem is the failure to teach students of calculus why the fundamental theorem, that integrating and taking a derivative are inverse operations, is true. It is possible to give a non-rigorous but intuitively persuasive proof of the theorem in about five minutes, one that any student who understands what the two operations are can follow and has a good chance of remembering. If any reader is sufficiently skeptical to warrant the effort, I can do it here.
In my experience, very few of the students who take calculus, even at a good school, are ever shown the proof; I would be surprised if more than one in fifty, a year after taking the course, could reproduce the more rigorous proof that they were, presumably, taught. To check the former impression, I asked my wife for her experience. Her response was that she was taught calculus twice, the first time at a good suburban school (but by an incompetent teacher), the second time at a top liberal arts college. To the best of her memory, she was never shown the proof.
I take as a further piece of evidence the math problems that my son was asking my help with—having assured me that the rules did allow him to discuss homework problems with people. One of them was a problem so trivial that a bright ten year old could probably have solved it without having taken the course, provided only that the problem itself was clearly explained to him. I take the fact that such a problem was assigned as evidence that the instructor believes a substantial fraction of the students do not understand what they are being asked to do, quite aside from knowing how to do it.
It is common, at good schools, to complain against "cookbook mathematics," the sort of course that consists of memorizing the sequence of steps to solve a problem without ever understanding why it works. But it is, I think, an equally serious mistake to present a branch of mathematics in the form in which professional mathematicians structure it after all of the original work in that particular field is done. Not only is it a form in which almost no student not qualified to become a professional mathematician can understand it, it is a form that gives a highly misleading picture of how mathematics, or other forms of theory, are actually done.
I am not a mathematician but I am an economist and know by direct observation how the original parts of my work were done. The process did not start with a step by step proof but with an intuition of how some set of ideas fit together, what characteristics the solution to a problem ought to have. Only after I had groped my way to what was (hopefully) the right answer did I, or someone else, go back and make the argument rigorous.
I am currently working on the third edition of my first book, published about forty years ago. One of the things I am doing is filling in the blanks, working out in more depth and more detail ideas whose essence I understood then and still believe, in most cases, were correct.
Alfred Marshall, arguably the figure most responsible for the creation of neo-classical economics, commented in a letter on the relation between mathematical and verbal arguments in his field. He explained that he worked his arguments out mathematically to make sure they were right. Having done so, he translated them into English. If he could not translate them into English, he burned the mathematics.
There is much to be said for that policy. Mathematics is a more precise language than English for the sort of work Marshall was doing. But it is also a language farther from the intuition of almost all of us. If you have the math and cannot translate it, it is quite likely, although not certain, that the reason is you do not understand it. I sometimes referee journal articles. Occasionally I get one where, if you translate the math into words, it makes no sense—is arguably insane. The author or authors presumably had doctorates in the field. But they were manipulating symbols, not ideas.
My daughter is at the same college as her brother. When she transferred there after two years elsewhere, she was seriously considering majoring in economics. After taking an economics course, she decided on her other alternative major. The reason was not that she does not like economics, or cannot do it—she audited several of my courses while a home schooled student of high school age, and one of my articles contains an idea that I credit in a footnote to her, since it was hers.
The reason was that the course was mostly about the math not the economics. I discussed her experience with a professor at that university of whom I have a high opinion—someone on the short list of people who, when they disagree with me, cause me to seriously consider that I may be making a mistake. He also had a daughter taking economics at the same school. He agreed with my daughter's judgement—that the courses were teaching mathematical rigor instead of economic intuition.
I have let this essay wander from my son's experience to my daughter's by way of mine. But I think the fundamental thread is the same in all. What matters is not remembering but understanding. If you have learned a proof but cannot explain why the result is true, you have been wasting your time.
My usual example of the problem is the failure to teach students of calculus why the fundamental theorem, that integrating and taking a derivative are inverse operations, is true. It is possible to give a non-rigorous but intuitively persuasive proof of the theorem in about five minutes, one that any student who understands what the two operations are can follow and has a good chance of remembering. If any reader is sufficiently skeptical to warrant the effort, I can do it here.
In my experience, very few of the students who take calculus, even at a good school, are ever shown the proof; I would be surprised if more than one in fifty, a year after taking the course, could reproduce the more rigorous proof that they were, presumably, taught. To check the former impression, I asked my wife for her experience. Her response was that she was taught calculus twice, the first time at a good suburban school (but by an incompetent teacher), the second time at a top liberal arts college. To the best of her memory, she was never shown the proof.
I take as a further piece of evidence the math problems that my son was asking my help with—having assured me that the rules did allow him to discuss homework problems with people. One of them was a problem so trivial that a bright ten year old could probably have solved it without having taken the course, provided only that the problem itself was clearly explained to him. I take the fact that such a problem was assigned as evidence that the instructor believes a substantial fraction of the students do not understand what they are being asked to do, quite aside from knowing how to do it.
It is common, at good schools, to complain against "cookbook mathematics," the sort of course that consists of memorizing the sequence of steps to solve a problem without ever understanding why it works. But it is, I think, an equally serious mistake to present a branch of mathematics in the form in which professional mathematicians structure it after all of the original work in that particular field is done. Not only is it a form in which almost no student not qualified to become a professional mathematician can understand it, it is a form that gives a highly misleading picture of how mathematics, or other forms of theory, are actually done.
I am not a mathematician but I am an economist and know by direct observation how the original parts of my work were done. The process did not start with a step by step proof but with an intuition of how some set of ideas fit together, what characteristics the solution to a problem ought to have. Only after I had groped my way to what was (hopefully) the right answer did I, or someone else, go back and make the argument rigorous.
I am currently working on the third edition of my first book, published about forty years ago. One of the things I am doing is filling in the blanks, working out in more depth and more detail ideas whose essence I understood then and still believe, in most cases, were correct.
Alfred Marshall, arguably the figure most responsible for the creation of neo-classical economics, commented in a letter on the relation between mathematical and verbal arguments in his field. He explained that he worked his arguments out mathematically to make sure they were right. Having done so, he translated them into English. If he could not translate them into English, he burned the mathematics.
There is much to be said for that policy. Mathematics is a more precise language than English for the sort of work Marshall was doing. But it is also a language farther from the intuition of almost all of us. If you have the math and cannot translate it, it is quite likely, although not certain, that the reason is you do not understand it. I sometimes referee journal articles. Occasionally I get one where, if you translate the math into words, it makes no sense—is arguably insane. The author or authors presumably had doctorates in the field. But they were manipulating symbols, not ideas.
My daughter is at the same college as her brother. When she transferred there after two years elsewhere, she was seriously considering majoring in economics. After taking an economics course, she decided on her other alternative major. The reason was not that she does not like economics, or cannot do it—she audited several of my courses while a home schooled student of high school age, and one of my articles contains an idea that I credit in a footnote to her, since it was hers.
The reason was that the course was mostly about the math not the economics. I discussed her experience with a professor at that university of whom I have a high opinion—someone on the short list of people who, when they disagree with me, cause me to seriously consider that I may be making a mistake. He also had a daughter taking economics at the same school. He agreed with my daughter's judgement—that the courses were teaching mathematical rigor instead of economic intuition.
I have let this essay wander from my son's experience to my daughter's by way of mine. But I think the fundamental thread is the same in all. What matters is not remembering but understanding. If you have learned a proof but cannot explain why the result is true, you have been wasting your time.
Global Warming as a Casus Belli: An SF Idea
As I mentioned in an earlier post, I have spent a good deal of time recently arguing issues connected with global warming on the Usenet newsgroup alt.global-warming, an experience interesting less for what it taught me about global warming than what it taught me about people arguing for and against it. It occured to me that expanding that online war of words to a literal war in realspace might provide material for an interesting science fiction novel. I don't plan to write it, since I don't think it is the sort of story I would be good at telling. This post is an invitation for someone else to.
The setting is sometime in the fairly near future. Two dissimilar states are adjacent. The larger, richer, and more technologically advanced is dominated by environmentalists concerned with the dangers of global warming. It has replaced virtually all of its fossil fuel energy with energy produced, at a higher cost, in ways that do not produce CO2—solar, wind, perhaps nuclear. Many of its inhabitants, most of its leaders, believe that everyone else should do the same. The neighboring state which is poorer and much less concerned with environmentalism, however, has a lot of coal, which it uses as its chief source of power.
The richer state attempts to pressure its neighbor into following its example, without success. Eventually it takes the latter's refusal to behave in what it considers a globally responsible manner as a casus belli and invades.
To make it a good story the invasion cannot lead to an easy conquest, despite the advantages of the richer state. Perhaps the terrain does not favor high-tech/low manpower warfare. The inhabitants of the poorer state, used to a less comfortable style of life, are more willing to accept the sacrifices that warfare requires. Faced with the threat of foreign conquest, they are willing to pay a higher price to defend themselves than the invaders are to conquer them. What was supposed to be a quick victory turns, as in the case of the U.S. Civil War, into a long and bloody grind.
The military element of the plot is necessary but ought not to be central. What the story is really about is the moral ambiguity of the war on both sides, especially that of the attackers. Seen from one angle, it is the old story of the strong beating up on the weak, with a new excuse. Seen from another, the attackers are risking their lives to protect the world they live in from those who selfishly and irresponsibly threaten it.
The closest actual novel I can think of to this, although without the war, is Fallen Angels by Niven and Pournelle. It is an entertaining story, especially for science fiction fans, since fandom plays a central role in the plot. But it is also an entirely one sided story—there is no question which side is right and which is wrong, who are the good guys and who the bad.
I want my author to play fair, to show good guys and bad guys, good motives and bad, on both sides. A hard core of support for the initial invasion comes from environmentalist fanatics whose real if unstated motive is not to prevent global warming but to punish the evil people who are, as they see it, raping the earth—ideally, after the war is won, trying the leadership of the losing side for global treason. On the other side, an important faction opposing any compromise is made up of people who really are as biased, arrogant, and scientifically ignorant as many of the people on the warming side of the online controversy believe their opponents to be.
Somewhere in the middle are people on both sides who want the rich state to subsidize the poor, either paying the costs of converting its power and transport industry to non-polluting sources or providing it with heavily subsidized energy from their own output. They are opposed, on one side, by those who believe that sinners should be punished, not paid, and on the other by those who see such a proposal as a step towards an energy neo-colonialism that will leave them at the mercy of the providers.
Ideally, it should never become entirely clear which side is right on the scientific issues. The scientific case against the environmentalist program should turn out to be stronger than it at first looks but not clearly correct, leaving the question of whether holding down CO2 output is necessary or even desirable at least somewhat open—so that honest and reasonable people can be found on both sides.
My model for how the conflict should be presented is "No Truce With Kings," an old Poul Anderson novelette set in a post-catastrophe west coast. What I liked about it was that Anderson played fair—fair enough so that the reader was well into the story before he could tell which side the author was on. It helped that the side the author was on was what many readers would consider the wrong one. I won't ruin the story for you by saying which side that was.
Any would-be novelists up for the challenge? They can get lots of free ideas by simply watching the online arguments.
The setting is sometime in the fairly near future. Two dissimilar states are adjacent. The larger, richer, and more technologically advanced is dominated by environmentalists concerned with the dangers of global warming. It has replaced virtually all of its fossil fuel energy with energy produced, at a higher cost, in ways that do not produce CO2—solar, wind, perhaps nuclear. Many of its inhabitants, most of its leaders, believe that everyone else should do the same. The neighboring state which is poorer and much less concerned with environmentalism, however, has a lot of coal, which it uses as its chief source of power.
The richer state attempts to pressure its neighbor into following its example, without success. Eventually it takes the latter's refusal to behave in what it considers a globally responsible manner as a casus belli and invades.
To make it a good story the invasion cannot lead to an easy conquest, despite the advantages of the richer state. Perhaps the terrain does not favor high-tech/low manpower warfare. The inhabitants of the poorer state, used to a less comfortable style of life, are more willing to accept the sacrifices that warfare requires. Faced with the threat of foreign conquest, they are willing to pay a higher price to defend themselves than the invaders are to conquer them. What was supposed to be a quick victory turns, as in the case of the U.S. Civil War, into a long and bloody grind.
The military element of the plot is necessary but ought not to be central. What the story is really about is the moral ambiguity of the war on both sides, especially that of the attackers. Seen from one angle, it is the old story of the strong beating up on the weak, with a new excuse. Seen from another, the attackers are risking their lives to protect the world they live in from those who selfishly and irresponsibly threaten it.
The closest actual novel I can think of to this, although without the war, is Fallen Angels by Niven and Pournelle. It is an entertaining story, especially for science fiction fans, since fandom plays a central role in the plot. But it is also an entirely one sided story—there is no question which side is right and which is wrong, who are the good guys and who the bad.
I want my author to play fair, to show good guys and bad guys, good motives and bad, on both sides. A hard core of support for the initial invasion comes from environmentalist fanatics whose real if unstated motive is not to prevent global warming but to punish the evil people who are, as they see it, raping the earth—ideally, after the war is won, trying the leadership of the losing side for global treason. On the other side, an important faction opposing any compromise is made up of people who really are as biased, arrogant, and scientifically ignorant as many of the people on the warming side of the online controversy believe their opponents to be.
Somewhere in the middle are people on both sides who want the rich state to subsidize the poor, either paying the costs of converting its power and transport industry to non-polluting sources or providing it with heavily subsidized energy from their own output. They are opposed, on one side, by those who believe that sinners should be punished, not paid, and on the other by those who see such a proposal as a step towards an energy neo-colonialism that will leave them at the mercy of the providers.
Ideally, it should never become entirely clear which side is right on the scientific issues. The scientific case against the environmentalist program should turn out to be stronger than it at first looks but not clearly correct, leaving the question of whether holding down CO2 output is necessary or even desirable at least somewhat open—so that honest and reasonable people can be found on both sides.
My model for how the conflict should be presented is "No Truce With Kings," an old Poul Anderson novelette set in a post-catastrophe west coast. What I liked about it was that Anderson played fair—fair enough so that the reader was well into the story before he could tell which side the author was on. It helped that the side the author was on was what many readers would consider the wrong one. I won't ruin the story for you by saying which side that was.
Any would-be novelists up for the challenge? They can get lots of free ideas by simply watching the online arguments.
November 6, 2012
Election Outcomes: My Thoughts
I have already described the reasons why I should not be disappointed at Obama's reelection and why I am. There is a third question I should have asked and didn't, also relevant to my feelings—not the consequences of Obama winning but the implications of the fact that he won. His campaign made heavy use of soak the rich rhetoric, much of it, I think, deliberately dishonest; if he ever mentioned that higher income people pay, on average, a larger fraction of their income as federal income tax than lower income people, or that the bottom half of the income distribution pays essentially no federal income tax, I managed to miss it. (For my view of complications that those facts obscure, see an earlier post). The fact that that rhetoric worked at least well enough to get him elected—despite a collection of negatives that one might have expected to defeat him—is disturbing for what it might imply about the future. It is made only a little less disturbing by the fact that the popular vote looks to be split very nearly evenly—Romney may even win it.
But there is good news as well. It looks as though two of the three attempts to legalize marijuana—Colorado and Washington but not Oregon—are succeeding; they are ahead by sizable margins with about half the districts reporting. That will be the biggest defeat the War on Drugs has suffered in my lifetime. If, optimistically, it is the beginning of the end, that could be more important than which of the candidates I wanted to lose did.
It also looks as though Jerry Brown's attempt to raise my taxes may fail, although that is less clear; the vote is currently 51.8 against, 48.2 for, with only 16.8% reporting. The revision of the three strikes law, which I am in favor of, is winning by a sizable margin, although again that is with most of the vote not yet reported. The results on other ballot measures are mixed.
It looks, from a quick scan of the politico.com map of election results, as though Gary Johnson is going to end up with a little over 1% of the vote. That is nowhere close to the 5% he was shooting for, but I never expected him to get it; it is a pretty respectable showing for a third party candidate in a tight election. Perhaps equally important, in Ohio, the state that got Obama's electoral vote total past the magic 270 point, the margin of victory was only .2% and Gary Johnson got .9%. It is not clear whether Johnson was responsible for Obama's win—polling evidence suggested that he was going to pull votes from both sides. But it is clear that if those votes had gone to Romney he would have won Ohio. Whether that would have given him the election we do not yet know.
And, on an almost but not entirely different topic ... . Obama's win means that he is probably going to be able to appoint one or more Supreme Court justices, one of the arguments some libertarians offered for supporting Romney. It occurs to me that one possible candidate is my ex-colleague Cass Sunstein, a distinguished law professor with an important position in the current administration.
It would be a very interesting appointment. On the one hand, he is smart and charming, which would make him influential on the court, which could be a bad thing if he supports the sort of positions Obama would want him to support. On the other hand, he would be a wild card—an independent thinker who might easily come down on what I would consider the right side of some of the issues the court will face.
But my guess is that Obama won't appoint him—for just that reason.
But there is good news as well. It looks as though two of the three attempts to legalize marijuana—Colorado and Washington but not Oregon—are succeeding; they are ahead by sizable margins with about half the districts reporting. That will be the biggest defeat the War on Drugs has suffered in my lifetime. If, optimistically, it is the beginning of the end, that could be more important than which of the candidates I wanted to lose did.
It also looks as though Jerry Brown's attempt to raise my taxes may fail, although that is less clear; the vote is currently 51.8 against, 48.2 for, with only 16.8% reporting. The revision of the three strikes law, which I am in favor of, is winning by a sizable margin, although again that is with most of the vote not yet reported. The results on other ballot measures are mixed.
It looks, from a quick scan of the politico.com map of election results, as though Gary Johnson is going to end up with a little over 1% of the vote. That is nowhere close to the 5% he was shooting for, but I never expected him to get it; it is a pretty respectable showing for a third party candidate in a tight election. Perhaps equally important, in Ohio, the state that got Obama's electoral vote total past the magic 270 point, the margin of victory was only .2% and Gary Johnson got .9%. It is not clear whether Johnson was responsible for Obama's win—polling evidence suggested that he was going to pull votes from both sides. But it is clear that if those votes had gone to Romney he would have won Ohio. Whether that would have given him the election we do not yet know.
And, on an almost but not entirely different topic ... . Obama's win means that he is probably going to be able to appoint one or more Supreme Court justices, one of the arguments some libertarians offered for supporting Romney. It occurs to me that one possible candidate is my ex-colleague Cass Sunstein, a distinguished law professor with an important position in the current administration.
It would be a very interesting appointment. On the one hand, he is smart and charming, which would make him influential on the court, which could be a bad thing if he supports the sort of positions Obama would want him to support. On the other hand, he would be a wild card—an independent thinker who might easily come down on what I would consider the right side of some of the issues the court will face.
But my guess is that Obama won't appoint him—for just that reason.
Third Party Strategies
Gary Johnson, the presidential candidate of the Libertarian Party for whom I had the pleasure of voting this morning, has been pushing the idea that one should vote for him in order to get the party's total to 5%. Doing so would result in both increased visibility for his party and some legal advantages in the next election.
If that is his objective, where should he be campaigning? The chief argument used to persuade libertarians not to vote for him is that a vote for him is a vote for Obama (according to Romney supporters) or Romney (according to Obama supporters). That makes some sense for a voter in a swing state such as Ohio, although even there the chance that one vote will determine who wins the election is probably under one in a million. But it makes no sense in California, where I live. The only way Romney is going to carry California is in a Republican landslide—in which case he won't need it.
It should therefor be easier for Gary Johnson to persuade people to vote for him in California than in Ohio, especially libertarians but also non-libertarians critical of the War on Drugs, aggressive foreign policy, continued deficit spending, or other policies supported by both of the major party candidates. If his objective is getting as many votes as possible, he should focus his campaign on one party states—one party Republican states might be an even better bet than California, since they are likely to contain more potential supporters.
My impression from news stories is that that is not what he is doing. He is campaigning in both Colorado and Ohio, currently regarded as battleground states, and apparently polling well in both. Campaigning in Colorado might be justified by the tie-in with a ballot issue on legalized marijuana, but it is hard to see how he has any obvious advantages in Ohio.
Which suggests that, despite talk of aiming for 5%, he is really following a different approach. His chance of actually getting 5% of the popular vote is low. His odds of getting enough votes in one or more states to convince the losing party that they would have won if only those voters had voted for him are much higher—which is a reason for them to look for libertarian issues that they could support in the future. The way to maximize the chance of that happening is by focusing his efforts on states where the vote is expected to be close, such as Ohio. I suspect that is what he is doing.
After the election I may ask him.
If that is his objective, where should he be campaigning? The chief argument used to persuade libertarians not to vote for him is that a vote for him is a vote for Obama (according to Romney supporters) or Romney (according to Obama supporters). That makes some sense for a voter in a swing state such as Ohio, although even there the chance that one vote will determine who wins the election is probably under one in a million. But it makes no sense in California, where I live. The only way Romney is going to carry California is in a Republican landslide—in which case he won't need it.
It should therefor be easier for Gary Johnson to persuade people to vote for him in California than in Ohio, especially libertarians but also non-libertarians critical of the War on Drugs, aggressive foreign policy, continued deficit spending, or other policies supported by both of the major party candidates. If his objective is getting as many votes as possible, he should focus his campaign on one party states—one party Republican states might be an even better bet than California, since they are likely to contain more potential supporters.
My impression from news stories is that that is not what he is doing. He is campaigning in both Colorado and Ohio, currently regarded as battleground states, and apparently polling well in both. Campaigning in Colorado might be justified by the tie-in with a ballot issue on legalized marijuana, but it is hard to see how he has any obvious advantages in Ohio.
Which suggests that, despite talk of aiming for 5%, he is really following a different approach. His chance of actually getting 5% of the popular vote is low. His odds of getting enough votes in one or more states to convince the losing party that they would have won if only those voters had voted for him are much higher—which is a reason for them to look for libertarian issues that they could support in the future. The way to maximize the chance of that happening is by focusing his efforts on states where the vote is expected to be close, such as Ohio. I suspect that is what he is doing.
After the election I may ask him.
Redistricting: A Geek Proposal
One of the peculiarities of the U.S. political system is that it is possible in principle for one party to win a majority of both houses of Congress and the presidential election with slightly over 25% of the votes—properly distributed. 50% +1 of the votes in 50%+1 of the congressional districts elect a majority of the house, 50%+1 in the twenty-six smallest population states elect a majority of the senate, although it may take multiple elections, and similarly, with more states, for winning the electoral college.
That uneven a distribution is unlikely to happen by chance—but it is not always necessary to leave it to chance. Back in 1812 Elbridge Gerry, governor of Massachusetts, signed a bill redrawing state senatorial districts in a way that favored his (Democratic-Republican) party. One of the districts looked rather like a dragon, leading critics to dub it a "gerrymander." The term survives, mostly as a verb describing the practice of redrawing electoral districts to favor those who redraw them. It can be used by one party to try to increase the number of its candidates who are elected by concentrating as many as possible of the opposition voters in as few districts as possible and (a somewhat riskier strategy) creating as many districts as possible where their voters are a majority, but not a large majority. It can be done on a bipartisan basis to guarantee incumbents of both parties safe seats by concentrating voters of one party in some districts, of the other in others. California recently redrew districts, using an at least nominally non-partisan group to do it; when I voted this morning, there was a proposition on the ballot to cancel the result. Which reminded me of an old idea of mine for solving the problem.
A state gives some body—the legislature, the Supreme Court, a non-partisan group—the authority to decide among redistricting proposals. There is, however, one restriction. Every proposal must take the form not of a map but of a computer program. Inputs include potentially relevant criteria such as town and county boundaries, but may not include any information on past voting or proxies for voting such racial, educational, or professional characteristics of the population. There is an upper limit to how big the program may be.
That restriction will not prevent people from trying to create programs whose output favors their side, or the body choosing from favoring ones that they think favor theirs. It will, however, sharply restrict their ability to do so, since the information needed to do it well will not be available to the program. They can try various versions, look at the results, and choose the one they like best, but that is all they can do.
That uneven a distribution is unlikely to happen by chance—but it is not always necessary to leave it to chance. Back in 1812 Elbridge Gerry, governor of Massachusetts, signed a bill redrawing state senatorial districts in a way that favored his (Democratic-Republican) party. One of the districts looked rather like a dragon, leading critics to dub it a "gerrymander." The term survives, mostly as a verb describing the practice of redrawing electoral districts to favor those who redraw them. It can be used by one party to try to increase the number of its candidates who are elected by concentrating as many as possible of the opposition voters in as few districts as possible and (a somewhat riskier strategy) creating as many districts as possible where their voters are a majority, but not a large majority. It can be done on a bipartisan basis to guarantee incumbents of both parties safe seats by concentrating voters of one party in some districts, of the other in others. California recently redrew districts, using an at least nominally non-partisan group to do it; when I voted this morning, there was a proposition on the ballot to cancel the result. Which reminded me of an old idea of mine for solving the problem.
A state gives some body—the legislature, the Supreme Court, a non-partisan group—the authority to decide among redistricting proposals. There is, however, one restriction. Every proposal must take the form not of a map but of a computer program. Inputs include potentially relevant criteria such as town and county boundaries, but may not include any information on past voting or proxies for voting such racial, educational, or professional characteristics of the population. There is an upper limit to how big the program may be.
That restriction will not prevent people from trying to create programs whose output favors their side, or the body choosing from favoring ones that they think favor theirs. It will, however, sharply restrict their ability to do so, since the information needed to do it well will not be available to the program. They can try various versions, look at the results, and choose the one they like best, but that is all they can do.
November 4, 2012
Sandy and Global Warming
Quite a lot of people have been offering the destruction due to Sandy as evidence of the evil consequences of global warming. As best I can tell, this claim is supported by three arguments, two of which are wrong and one at least disputable.
The first argument is that Sandy was the worst storm to ever hit New York, as measured by the storm surge:
The second argument is that Sandy was so severe because global warming had raised sea levels. It is true that higher sea levels, all else being equal, result in more damage from flooding. But, checking Wikipedia, which shows sea level back to 1870, the increase since then has been only about eight inches, so it is hard to see how the effect could be very large.
The third argument, which might be right, is the claim that increased global temperatures result in more frequent or more violent storms. I looked into the question a few years ago, when the IPCC's Atlantic hurricane expert resigned in protest against the assertion, made by the person who was going to be coordinating that part of the next IPCC report, that hurricanes had become worse due to warming; the question was discussed at some length in a comment thread here. My conclusion was that the linkage was, at that point, speculative—it might be true, but the evidence was not sufficient to tell. I have not followed the argument since, beyond noting that some supporters of the claim seem to think it has been confirmed and some critics that it has not.
The first argument is that Sandy was the worst storm to ever hit New York, as measured by the storm surge:
"On Monday, sea levels in New York City reached about 14 feet above the average low-tide mark; more than 9 feet above the average high; almost 3 feet above the last record, set in 1821."(Craig Childs, N.Y. Times Op-Ed)That sounds impressive—if you ignore the fact that Sandy happened to hit at high tide. According to one discussion of the question I have seen—readers are welcome to correct it if mistaken—the 1821 hurricane hit at low tide. If we measure the strength of the storm by how much higher the sea level was than it would have been without it, we have to compare the earlier storm to the low tide level, Sandy to the high. By that measure, the 1821 storm was three feet worse than Sandy, not three feet better. So far as I know, nobody has yet tried to argue that global warming increases the probability that a storm will come to shore at high tide instead of low.
The second argument is that Sandy was so severe because global warming had raised sea levels. It is true that higher sea levels, all else being equal, result in more damage from flooding. But, checking Wikipedia, which shows sea level back to 1870, the increase since then has been only about eight inches, so it is hard to see how the effect could be very large.
The third argument, which might be right, is the claim that increased global temperatures result in more frequent or more violent storms. I looked into the question a few years ago, when the IPCC's Atlantic hurricane expert resigned in protest against the assertion, made by the person who was going to be coordinating that part of the next IPCC report, that hurricanes had become worse due to warming; the question was discussed at some length in a comment thread here. My conclusion was that the linkage was, at that point, speculative—it might be true, but the evidence was not sufficient to tell. I have not followed the argument since, beyond noting that some supporters of the claim seem to think it has been confirmed and some critics that it has not.
Who do I Want to Win or Us vs Them
Gary Johnson, of course. But he isn't going to.
The more interesting question is which of the two major party candidates I want to win. What I find interesting, looking at my own feelings, is that there are two different answers.
The rational answer is that the worst outcome might be Obama in control of both houses of Congress, but that that is very unlikely to happen. The second worst is probably Romney in control of both houses, a little more likely. Beyond those two, the order is unclear. On the one hand, my guess is that Obama would want to do more things I disapprove of than Romney. On the other, Romney, if elected, will almost certainly control the House and might control the Senate, or get control of it two years from now. What matters is not what people want to do but what they can do, and Romney might well be able to do more things I disapprove of than Obama.
A further argument is that when Romney talks a free market line but fails to act it, those of us who actually believe in free markets will get blamed for the resulting failures. That, after all, is what happened with the Bush administration. I do not expect either Obama's policies or Romney's to succeed, and if policies are going to visibly fail, I would prefer that they be blamed on someone else. That is an argument in favor of Obama.
My conclusion is that I have little reason to want Romney to win, some reason to want him to lose. I am not confident of that conclusion—one can argue that Romney would be likely to appoint better Supreme Court justices, a point some libertarians have been making in his favor. One can speculate that the influence of the tea party Republicans might push Romney into being a better president than he wants to be. But the spectacle of the Bush administration is a strong argument on the other side.
If I switch the question from what I ought to want to what I do want, from reason to emotion, the result changes. I will be happy if Obama loses, unhappy if he wins.
Human beings have a tendency, perhaps unfortunate, to view the world as us vs them. Obama's supporters are, on the whole, people whose political views are more sharply opposed to mine than those of Romney's supporters. Insofar as my hardwired instincts are trying to sort political struggles into the categories of friend and foe, it is clear which side they put me on. If I think of the election as a football match, I may not be cheering one side, but I am definitely booing the other. Obama's defeat will be a crushing blow for a lot of people who I am inclined to disagree with and disapprove of—and a good thing too. That's my gut level response.
This is not the only time I have observed myself reacting in this fashion. I have spent a good deal of time over the past few months arguing with people in a usenet group devoted to issues of global warming. One of the things that struck me early on was that, although participants represented a range of views on the subject, almost all of them could be grouped, by behavior if not by views, into one side or other. That was how they thought of themselves.
I was not an exception. My actual view was and is intermediate between the two ends of the dispute. I think it is reasonably clear that global temperatures have been trending up unusually fast for the past century or so, and the most plausible explanation I have seen is the effect of human production of carbon dioxide. On the other hand, I do not think there are good reasons to predict that warming on the scale suggested by the IPCC reports for the next century or so will have large net negative effects, a point I have discussed here in the past.
Although my views put me somewhere in the middle, disagreeing with one side on some questions and with the other on others, that is not how I felt or how I was viewed. I spent enough time criticizing arguments made by the believers in global warming to get classified by them with the skeptics (who they labeled "deniers"). That produced enough attacks from the believers to trigger my built in friend/foe detector. I posted criticisms of arguments on the other side when I thought the argument was wrong and I had something to contribute. But, on the whole, I was happy to see believers post bad arguments, since they could be refuted, unhappy to see critics do so; emotionally speaking I was a partisan.
The latest episode in this particular drama involved a point of very little importance for the question of global warming but considerable importance for the egos of the participants in the debate. Various people described Michael Mann, a climatologist associated with the IPCC, as a Nobel Prize winning scientist. Other people, myself among them, pointed out that it was not true. Mann's claim, made by him as well as his supporters, was based on the fact that the IPCC won a Nobel peace prize and had sent a letter with a copy of the prize certificate to various of the people who had contributed to its work, thanking them for their contribution to its winning the prize. Mann exhibited his copy online.
The IPCC, however, does not have the power to give out Nobel prizes, and the certificate quite clearly stated that the recipients were the IPCC and Al Gore. A heated argument followed.
Eventually it became impossible for Mann's supporters to maintain their position, when first a representative of the Nobel Committee and later the IPCC provided unambiguous statements that contradicted it. At that point, most of those who had argued the position dropped it, in at least one case trying to pretend to never have made the argument. One, but only one, tried to insist that the statement from the Nobel Committee, reported from at least two independent sources, must be a fake.
The part of the story relevant to this post was my reaction. The fact that a prominent supporter of global warming had been inflating his credentials implies very little about whether global warming is real, anthropogenic, and dangerous. It was, however, a humiliating defeat for "them," hence a victory for "us," hence a development I enjoyed.
Which is one reason I decided to drop out of that news group and that conversation, at least for a while.
The more interesting question is which of the two major party candidates I want to win. What I find interesting, looking at my own feelings, is that there are two different answers.
The rational answer is that the worst outcome might be Obama in control of both houses of Congress, but that that is very unlikely to happen. The second worst is probably Romney in control of both houses, a little more likely. Beyond those two, the order is unclear. On the one hand, my guess is that Obama would want to do more things I disapprove of than Romney. On the other, Romney, if elected, will almost certainly control the House and might control the Senate, or get control of it two years from now. What matters is not what people want to do but what they can do, and Romney might well be able to do more things I disapprove of than Obama.
A further argument is that when Romney talks a free market line but fails to act it, those of us who actually believe in free markets will get blamed for the resulting failures. That, after all, is what happened with the Bush administration. I do not expect either Obama's policies or Romney's to succeed, and if policies are going to visibly fail, I would prefer that they be blamed on someone else. That is an argument in favor of Obama.
My conclusion is that I have little reason to want Romney to win, some reason to want him to lose. I am not confident of that conclusion—one can argue that Romney would be likely to appoint better Supreme Court justices, a point some libertarians have been making in his favor. One can speculate that the influence of the tea party Republicans might push Romney into being a better president than he wants to be. But the spectacle of the Bush administration is a strong argument on the other side.
If I switch the question from what I ought to want to what I do want, from reason to emotion, the result changes. I will be happy if Obama loses, unhappy if he wins.
Human beings have a tendency, perhaps unfortunate, to view the world as us vs them. Obama's supporters are, on the whole, people whose political views are more sharply opposed to mine than those of Romney's supporters. Insofar as my hardwired instincts are trying to sort political struggles into the categories of friend and foe, it is clear which side they put me on. If I think of the election as a football match, I may not be cheering one side, but I am definitely booing the other. Obama's defeat will be a crushing blow for a lot of people who I am inclined to disagree with and disapprove of—and a good thing too. That's my gut level response.
This is not the only time I have observed myself reacting in this fashion. I have spent a good deal of time over the past few months arguing with people in a usenet group devoted to issues of global warming. One of the things that struck me early on was that, although participants represented a range of views on the subject, almost all of them could be grouped, by behavior if not by views, into one side or other. That was how they thought of themselves.
I was not an exception. My actual view was and is intermediate between the two ends of the dispute. I think it is reasonably clear that global temperatures have been trending up unusually fast for the past century or so, and the most plausible explanation I have seen is the effect of human production of carbon dioxide. On the other hand, I do not think there are good reasons to predict that warming on the scale suggested by the IPCC reports for the next century or so will have large net negative effects, a point I have discussed here in the past.
Although my views put me somewhere in the middle, disagreeing with one side on some questions and with the other on others, that is not how I felt or how I was viewed. I spent enough time criticizing arguments made by the believers in global warming to get classified by them with the skeptics (who they labeled "deniers"). That produced enough attacks from the believers to trigger my built in friend/foe detector. I posted criticisms of arguments on the other side when I thought the argument was wrong and I had something to contribute. But, on the whole, I was happy to see believers post bad arguments, since they could be refuted, unhappy to see critics do so; emotionally speaking I was a partisan.
The latest episode in this particular drama involved a point of very little importance for the question of global warming but considerable importance for the egos of the participants in the debate. Various people described Michael Mann, a climatologist associated with the IPCC, as a Nobel Prize winning scientist. Other people, myself among them, pointed out that it was not true. Mann's claim, made by him as well as his supporters, was based on the fact that the IPCC won a Nobel peace prize and had sent a letter with a copy of the prize certificate to various of the people who had contributed to its work, thanking them for their contribution to its winning the prize. Mann exhibited his copy online.
The IPCC, however, does not have the power to give out Nobel prizes, and the certificate quite clearly stated that the recipients were the IPCC and Al Gore. A heated argument followed.
Eventually it became impossible for Mann's supporters to maintain their position, when first a representative of the Nobel Committee and later the IPCC provided unambiguous statements that contradicted it. At that point, most of those who had argued the position dropped it, in at least one case trying to pretend to never have made the argument. One, but only one, tried to insist that the statement from the Nobel Committee, reported from at least two independent sources, must be a fake.
The part of the story relevant to this post was my reaction. The fact that a prominent supporter of global warming had been inflating his credentials implies very little about whether global warming is real, anthropogenic, and dangerous. It was, however, a humiliating defeat for "them," hence a victory for "us," hence a development I enjoyed.
Which is one reason I decided to drop out of that news group and that conversation, at least for a while.
Market Failure and the Definition of Terms
In discussing the idea of market failure, in class and in public talks, I usually start by pointing out that technical terms often sound self-explanatory and aren't; the theory of relativity, for instance, is not the theory that everything is relative. I go on to explain that "market failure" is an example of that problem. It does not describe all ways in which markets can fail and it is not limited to markets.
As I define it, market failure describes a situation where individual rationality does not lead to group rationality. Non-market examples include the game of prisoner's dilemma, where each defendant makes the correct decision for himself (confess and betray his co-defendant) even though both would be better off if both made the alternative decision, situations where an army runs away and is slaughtered because each soldier is better off running although all are better off if they all stand, and traffic congestion at an intersection that keeps jamming because drivers, trying to cross before the light changes and failing to make it, block the intersection. In each of these cases, each actor is making the correct decision for himself but every actor would be better off, at least on average, if they all made a different decision.
I have just been redoing the argument as a chapter for the third edition of my first book, The Machinery of Freedom. In doing so, it occurred to me to wonder in what sense what I have been saying is true. I am describing how I use a technical term in my field. Can I legitimately claim that others, including other economists, who use it differently are wrong?
There is no central authority to determine how technical terms are defined, and if there was I would not be it. I made no attempt, before pontificating on the subject, to research the usage of other economists; a recent google suggested that what I regard as the incorrect usage is quite common. I should not have been surprised, given that, a year or so back, I emailed the author of a very successful textbook to try to persuade him to change the way in which he used the term. I got back a courteous reply, saying that he would consider the matter.
I concluded that, in writing the chapter, I should be a little more careful in what I claimed. My definition is not what the term means—meaning is defined by use, and lots of people use it differently. My definition is what the term ought to mean.
Technical terms are tools for thinking and communicating. My definition of market failure makes it a better tool for those purposes than an alternative such as "a situation where the market does not allocate resources efficiently." The latter lumps together similar effects from unrelated causes—the market might produce the wrong allocation because the information to deduce the right allocation did not exist when the relevant decisions were made. It fails to identify situations where the same logic is functioning in the same way in different contexts—rational ignorance in voting as an example of the public good problem, prisoners betraying each other as an example of an inefficiently large output (of confessions) due to a negative externality.
I will continue to argue that my definition is the correct one. I will merely be a little more careful to explain what that means.
As I define it, market failure describes a situation where individual rationality does not lead to group rationality. Non-market examples include the game of prisoner's dilemma, where each defendant makes the correct decision for himself (confess and betray his co-defendant) even though both would be better off if both made the alternative decision, situations where an army runs away and is slaughtered because each soldier is better off running although all are better off if they all stand, and traffic congestion at an intersection that keeps jamming because drivers, trying to cross before the light changes and failing to make it, block the intersection. In each of these cases, each actor is making the correct decision for himself but every actor would be better off, at least on average, if they all made a different decision.
I have just been redoing the argument as a chapter for the third edition of my first book, The Machinery of Freedom. In doing so, it occurred to me to wonder in what sense what I have been saying is true. I am describing how I use a technical term in my field. Can I legitimately claim that others, including other economists, who use it differently are wrong?
There is no central authority to determine how technical terms are defined, and if there was I would not be it. I made no attempt, before pontificating on the subject, to research the usage of other economists; a recent google suggested that what I regard as the incorrect usage is quite common. I should not have been surprised, given that, a year or so back, I emailed the author of a very successful textbook to try to persuade him to change the way in which he used the term. I got back a courteous reply, saying that he would consider the matter.
I concluded that, in writing the chapter, I should be a little more careful in what I claimed. My definition is not what the term means—meaning is defined by use, and lots of people use it differently. My definition is what the term ought to mean.
Technical terms are tools for thinking and communicating. My definition of market failure makes it a better tool for those purposes than an alternative such as "a situation where the market does not allocate resources efficiently." The latter lumps together similar effects from unrelated causes—the market might produce the wrong allocation because the information to deduce the right allocation did not exist when the relevant decisions were made. It fails to identify situations where the same logic is functioning in the same way in different contexts—rational ignorance in voting as an example of the public good problem, prisoners betraying each other as an example of an inefficiently large output (of confessions) due to a negative externality.
I will continue to argue that my definition is the correct one. I will merely be a little more careful to explain what that means.
November 1, 2012
California Fraud?
I recently received a bill from the California Board of Equalization (BOE) demanding that I pay them about three hundred dollars in use tax. That puzzled me, since I had already paid the use tax with my California state income tax return—my reporting it on that return is the only reason the BOE knew that I owed it. Just to be sure, I went online and checked my account with the Franchise Tax Board, the body that collects California income tax—it showed me owing nothing.
So I called the number for the BOE. The woman I spoke with told me that they had not received the money from the FTB and that if I did not want them to bill me for it I should call the FTB and have them take care of the matter. I called the number she gave me, got an FTB phone tree with no option of talking to a human being and no reference to use tax.
I checked my California form 540. Line 95 is use tax. Line 111, "Amount you owe," is the sum of line 94, line 95, and line 110. That is what I paid. The sum on line 95 is the same sum as on my "billing and refund notice" from the BOE—to which they added an additional penalty and interest.
I made another phone call to the BOE. This time, after being bounced through several different people, I reached someone who said that she would get in touch with the FTB to find out why they had not forwarded my use tax money and get back to me.
My best guess is that what I am observing is deliberate fraud. California's state finances are a mess. Presumably the FTB failed to pass on to the BOE some or all of the use tax money that the FTB collects for them. Instead of (or in addition to) trying to get their money from the FTB, the BOE decided to double bill taxpayers—send them bills for the money they had already paid. Many taxpayers would simply assume they had made a mistake and pay a second time.
What happens with taxpayers who notice that they are being charged for taxes they have already paid I do not know—presumably I will discover that when (and if) the person from the Board calls me back.
It is possible, of course, that I am misinterpreting incompetence as dishonesty—that at some stage in the process someone made a mistake, which will now be corrected. One reason I doubt that is that what the letter I received said was:
They do not say that I did not pay the money to the FTB, merely that the FTB did not pay it to them. And the final bit, which I missed in the initial draft of this post and have just added, makes it clear that if I paid the money but the FTB didn't pass it on, they want me to pay it again.
I am reasonably sure that if a private firm engaged in that sort of deliberate double billing it would be illegal, and I suspect there would be at least potential criminal liability.
So I called the number for the BOE. The woman I spoke with told me that they had not received the money from the FTB and that if I did not want them to bill me for it I should call the FTB and have them take care of the matter. I called the number she gave me, got an FTB phone tree with no option of talking to a human being and no reference to use tax.
I checked my California form 540. Line 95 is use tax. Line 111, "Amount you owe," is the sum of line 94, line 95, and line 110. That is what I paid. The sum on line 95 is the same sum as on my "billing and refund notice" from the BOE—to which they added an additional penalty and interest.
I made another phone call to the BOE. This time, after being bounced through several different people, I reached someone who said that she would get in touch with the FTB to find out why they had not forwarded my use tax money and get back to me.
My best guess is that what I am observing is deliberate fraud. California's state finances are a mess. Presumably the FTB failed to pass on to the BOE some or all of the use tax money that the FTB collects for them. Instead of (or in addition to) trying to get their money from the FTB, the BOE decided to double bill taxpayers—send them bills for the money they had already paid. Many taxpayers would simply assume they had made a mistake and pay a second time.
What happens with taxpayers who notice that they are being charged for taxes they have already paid I do not know—presumably I will discover that when (and if) the person from the Board calls me back.
It is possible, of course, that I am misinterpreting incompetence as dishonesty—that at some stage in the process someone made a mistake, which will now be corrected. One reason I doubt that is that what the letter I received said was:
"According to information provided to us by the Franchise Tax Board (FTB), you reported a use tax liability on your state income tax return. However, FTB advised the funds were not available to be transferred to the State Board of Equalization (BOE), which is ultimately responsible for the collection of use tax."
"If the use tax was remitted with your FTB return, the use tax was either redirected to a FTB liability or refunded by FTB. Accordingly, the BOE is sending this letter to inform you that the use tax remains due (see enclosed billing notice)"
They do not say that I did not pay the money to the FTB, merely that the FTB did not pay it to them. And the final bit, which I missed in the initial draft of this post and have just added, makes it clear that if I paid the money but the FTB didn't pass it on, they want me to pay it again.
I am reasonably sure that if a private firm engaged in that sort of deliberate double billing it would be illegal, and I suspect there would be at least potential criminal liability.
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