I was wrong...

The Securities and Exchange Commission didn't even wait (as I thought they would) for the next disaster to strike before shooting the messenger. The new rules require to pay a premium in order to short-sell any stock that fell in value by 10% or more since the previous day.

Mixing it up

Recently I watched a soccer game in which a goal was scored similarly to the one in the video below:

When an attacker has only the goalkeeper in front of him but is approaching the goal form an angle, he has two choices. He can try and place the ball either between the keeper and the "near post" or between the keeper and the "far post." Shooting towards the near post is the less risky option; the striker is less likely to miss the target altogether than when he aims for the far post. However, a near post shot is easier for the keeper to save (provided that he dives in the right direction). In the game I was watching the striker shot towards the near post and scored, just like in the video. The announcer then said: "In situations like this one, when the striker scores on a near post shot it's always the keeper's fault." I hear that line quite often actually. It's wrong, and a little game theory can show why.

A one-on-one when the striker is charging the goal at an angle is a 2x2 simultaneous move game. The striker has two options: "shoot near" or "shoot far," and the keeper can either "dive near" or "dive far". The important thing here is that the keeper as well as the striker make their decisions simultaneously, i.e. each picks his strategy not knowing what the other will do. (If the keeper waits to see which way the striker shoots before deciding where to dive, it will be too late to stop the shot. If the striker takes too long to shoot, the keeper will simply scoop the ball from under his feet.) Now saying that a near post goal is always the keeper's fault is equivalent to saying that keepers should always dive towards the near post; since near post shots are easy to save if you dive in the same direction, this would ensure that no goals (or almost no goals) would be scored on those kind of shots. But it wouldn't be a reasonable thing for a goalkeeper to do. If the keeper always dives near, then the striker could always shoot far towards the unprotected corner of the goal, and score with a very high rate. What the keeper needs to do instead is to play a mixed strategy: randomize between diving near and diving far. This will force the striker to randomize between shooting near and shooting far, and reduce the rate at which goals are scored in these situation to a minimum. Now since near shots are easier, the keeper should protect the near post more than the far post; i.e., he should dive near with probability higher than diving far. But, in equilibrium, he can't dive near every single time, and thus every once in a while a striker will score shooting towards the near post. And it won't be the keepers fault at all.

From Woodstock to Wall Street

The creed of almost every ideological group contains beliefs that, to non-members, appear bizarre to the point of being funny. When it comes to conservatives, one of such memes is the conviction that all things wrong with our society today are a direct consequence of the destruction of traditional morals by the hippies. The newest incarnation of this belief blames flower children for the financial collapse of 2008. This appears to be one of the claims of a documentary titled "Generation Zero" made by Citizens United.

Now I haven't actually seen this movie, so I cannot say how important this connection is for its overall narrative. All I know about the film comes from what's been written about it, as well as two clips from a Sean Hannity special devoted to it. And from that, it's clear the filmmakers do indeed make this claim. They blame the financial crisis on culture, specifically on erosion of personal responsibility that has its roots in the Summer of Love (as one of the producers colorfully put it, personal responsibility has been "left in the mud of Woodstock"). Some other humorous claims made in the documentary are: the abandonment of ethics of personal responsibility caused the shift from partnerships to publicly trading companies; the dot-com bubble of 1995-2000 was caused not by the market's overconfidence in future profits of IT companies but by the fact that most members of the greatest generation have retired by mid-nineties, leaving the stock market in the hands of their irresponsible children; and, quoting from the above-linked Christian Science Monitor article:

Producer David Bossie (...) says generational narcissism, as represented by the 1969 Woodstock Festival, is responsible for the excessive spending, mortgage crisis, and recklessness on Wall Street. "The people who were at Woodstock turned into the yuppies of the '80s and the junk bond traders of the '90s and the Wall Street executives of the 2000s," he says. "They went from Woodstock to driving a Jaguar."

In addition to the obvious, two things Bossie says are baffling to me: What on Earth is so bad about yuppies or junk bonds?

(HT: Mark Thoma.)

The power of self-deception

Each year in the U.S., around 42,000 people die in car accidents. We could save all those lives. The only thing we'd have to do is enforce a maximum speed limit of 10 miles per hour or thereabouts. So why don't we do it?

Because we don't consider safety to be infinitely valuable. We trade it off for utility. We sacrifice around 40,000 lives a year in exchange for some gains in convenience, efficiency and wealth; or, more precisely, each driver and passenger accepts certain non-zero risk of dying in a car crash in order to enjoy certain benefits in terms of quality of their life.

It sounds extremely cynical, and it is. It often benefits us to behave in a cynical way. However, most of the time it does not benefit us to admit that we're being cynical, because cynics are perceived (correctly) as untrustworthy in repeat interactions. This is why we've evolved such tremendous capacity for self-deception. When we're making a cynical trade-off, we pretend that there actually is no trade-off--not just to others but to ourselves as well.

Megan McArdle provides an absolutely staggering example of such self-deception at work. The setting is the Congressional Toyota hearings going on right now. McArdle describes an exchange between Representative Mark Souder and Secretary of Transportation Ray LaHood. At some point, LaHood says that his agency considers passenger safety to be priceless. To which Souder replies that this isn't actually true and that we're in fact trading off safety for convenience: if we enforced a speed limit of 30 mph we'd be saving a lot of lives but we don't do it because we recognize that it would make us a lot poorer.

Here comes the amazing part: LaHood disagrees with this, saying that lowering the speed limit to 30 mph would not save any lives, and that this fact is the reason we have minimum speed limits. When Souder reminds him that the actual reason we enforce minimum speed limits is to decrease variance in speeds with which drivers travel, LaHood says: "I don't buy your argument, Mr. Souder".

You might say that this isn't self-deception but outright lying; LaHood understands there is a trade-off but, as a politician, doesn't want to admit it in front of the voters. I doubt it. It is perfectly possible for people (even very smart people) to be sincerely convinced they believe X while at the same time behaving as if they believed something completely different. It's actually easier for a politician to deceive his voters if he's not conscious of the fact that he's lying in the first place. The take-home point of all this is: don't waste your time trying to determine if this or that politician sincerely believes what he says is true. It doesn't matter. Sincerity is overrated.

Nature show

Ritualized dominance displays in humans:

If you think this is ridiculous, think again. You do it too.

(HT: Marginal Revolution.)

Something will have to come to a screeching halt

This makes for an interesting read: a report from the National Center for Policy Analysis dealing with "unfunded obligations" of European governments. What exactly are unfunded obligations? They basically are a crude measure of sustainability of a given government's fiscal policies, assuming that current policies as well as trends in output growth and demographic structure will continue unchanged. More specifically, what the author does is the following. He assumes that in all countries of interest, all relevant policies (e.g. retirement and welfare programs, healthcare funding, retirement age, tax rates, etc.) will continue as they are now all the way through 2050. He also assumes that demographic trends (such as fertility, immigration and life expectancy growth rates, etc.), and GDP growth rate, will continue at their current levels until 2050 as well. He then calculates the present value of total public debt that a given country will have accrued in 2050 if all those assumptions hold true. Or, equivalently, the value of capital that each government would have to set aside right now in order that this capital, earning interest equal to that government's current borrowing rate, would allow it to fully pay its liabilities in 2050. The results of those calculations for fourteen European countries are presented below:

The values of unfunded liabilities are huge; on average, an European government would have to set aside capital equal to 4.343 of its current GDP today in order to fund them in the future. The driving force behind this is demography. As of now, in all countries of interest, fertility rates are below generation replacement level, and life expectancy is rising. If this were to continue indefinitely, the ratio of net payers to net payees would get lower and lower. This means that tax revenues would increase only slightly while the number of people entitled to payments from the government would increase immensely.

Of course, this analysis doesn't really mean that in 2050 the public debt of France will be equal to 549% of its GDP. Rather, it means that, in the future, France will have to try to reverse its negative demographic trends, or speed up its GDP growth, or severely cut its social programs--because otherwise it will go bankrupt. Some movement in the demographic trends can actually be seen already; in recent years in France and Scandinavian countries, fertility rates have been increasing and have now reached levels close to generation replacement. It's quite likely that that level will be surpassed soon and this, coupled with encouraging immigration, could get those countries out of trouble without having to cut government services too drastically.

Now take a quick look at the unquestionable leader in unfunded liabilities: Poland. If the assumptions used in the report hold, then in 2050 Polish public debt will be more than fifteen times its current GDP. Poland can't dig itself out of the hole by changing the demographics alone; its current government expenditure structure is completely unsustainable. Or is it? If this estimate of fiscal imbalance is accurate, then why does anyone want to buy long-term Polish government bonds?

What once was cheered is now booed

Here's a small piece of anecdotal evidence of the fact that social norms can change very quickly indeed: a video clip showing a conservative activist named Ryan Sorba condemning CPAC 2010 for inviting GOProud (which is a pro-Republican gay organization). Sorba gets booed.

(HT: Megan McArdle.)

A definition can't be wrong. But it sure can be useless.

A quote from an article in a Polish daily newspaper reads (translation mine):

Sociologists have observed that consumption has become the life goal of most Poles, even though they still think that, ultimately, happiness in life comes through family and pursuing hobbies.

This quote is using a strange definition of the word "consumption," one that I have never seen before. Normally, both in economics and colloquial language (and both in English as well as Polish), consumption simply means doing things for their own sake. Whenever you're using a good or pursuing an activity as a goal in itself, and not as a means to some end, that's consumption. Which means that taking care of one's family or pursuing one's hobbies is consumption too. And, naturally, consumption is the ultimate goal in life (in fact, the only goal in life)--by definition.

Unless of course you're using a different definition, which sociologists (maybe just Polish sociologists) seem to. The quote appears to be making a distinction between using material goods (which is called consumption) and seeking non-material goals (which is presumably called something else, though we don't know exactly what). Now I know that criticizing a definition isn't really a terribly constructive activity. So long as you're coherent, you can define your terms any which way you please. But why would you? The "material vs. non-material" distinction is conceptually completely useless.

Go back to your own Golden Age

People glorify the past, sometimes very distant past. I don't know why, nor do I really care; instead I just wish to point out the obvious: thinking that long time ago life was great reveals deep ignorance of history. Before the Industrial Revolution, life was characterized by poverty that is hard for us now to imagine, constant back-breaking labor, frequent bouts of various diseases, short life-spans, etc. Everyone but the very wealthiest had to work incredibly hard their entire lives, and still lived on the brink of starvation. While now we consider it natural that our society grows wealthier over time and that our children will have better lives than we do, this concept was completely alien to our ancestors. Before the Industrial Revolution there was no GDP growth to speak of anywhere in the world. The contemporaries thought that the happy days of humanity were already gone. Old legends from virtually every culture contain stories of a Golden Age in the past when people had their basic material needs met and were happy, along with some explanation as to why that great period had to end leading to the terrible misery to be experienced forever after.

There is one additional, and often underestimated, fact which makes the good old days seem like a nightmare when compared to the times we live in now. The past was incredibly violent, incomparably more so than the present. Here is a paper (gated) estimating homicide rates in what is now Germany and Switzerland between the years 1300 and 2001. The measuring unit is number of homicides per 100 000 people per year, and homicide is defined very narrowly as civil murder or manslaughter; deaths resulting from wars, ethnic cleansing expeditions or any other form of "organized killing" are excluded from the count. In 2001 the homicide rate hovered around 1 on pretty much the entire studied territory. Between 1300 and mid-1600's, the rate varied from 20 to 100. Murder was commonplace. Remember: this doesn't include war deaths. Also remember: if homicide was so much more common than it is now, so must other violent crimes (assault, robbery, rape) have been. Now tell me again that you wish you'd have been born in the Middle Ages.

Why were medieval people so much more violent than we are? The reason can't be genetic (we don't evolve this fast), so it must be cultural. Which brings me to the second topic of this post: the feedback loop between laws, law enforcement, and social norms.

It's a truism to say that social norms of a given society influence the laws by which that society governs itself. But it's underestimated (mostly by conservatives I think) how often causality runs in the other direction: the laws of a society influence its social norms. In 1350, there was no law enforcement to speak of; you were on your own. Given that, it shouldn't surprise anyone that homicide was perceived by society as a perfectly legitimate way of settling disputes. It's only now, when we have courts and a powerful police force, that murdering someone to resolve an ongoing conflict is seen as morally unacceptable.

This particular change of social norms took entire centuries, but it doesn't always have to be the case. Sometimes a change in law or law enforcement practices can trigger an incredibly rapid change in people's moral convictions. My favorite example of this is what happened in the U.S. after Loving v. Virginia. This case, decided by the U.S. Supreme Court in 1967, amounted to overturning all state-level legal restrictions on interracial marriage that were in effect at the time. A national public opinion poll conducted shortly after the Court's decision showed that over seventy percent of Americans disagreed with it and thought that states should be free to ban interracial marriage if they wanted to. If this poll were replicated now, or even twenty years ago, what do you think that percentage would have been?

Very often we hear that you can't "shove social change down people's throats" because it simply doesn't work. I beg to differ; it definitely can work.

Conflict of interest no one seems to notice

No one except Steven Landsburg, that is:

Am I the only one who finds it a little unseemly that the regulatory response to Toyota's recent problems is being formulated by the owners of General Motors?

The intellectual most frequently forced to turn in his grave is...

Kurt Gödel, by far. His incompleteness theorem is definitely the most abused piece of formal reasoning ever written. (By "most abused" I mean "invoked as implying the most non-mathematical consequences absurdly far-removed from the domain in which it has any applicability.") I've read and/or heard in conversations, arguments which quite seriously purported Gödel's theorem to imply (in no particular order): postmodernism, creationism, existence of God, non-existence of God, "inevitability of human condition" (I'm not joking), computability of human intelligence, non-computability of human intelligence, impossibility of complete knowledge of mathematics, impossibility of complete knowledge of anything, existence of immaterial soul, non-existence of pretty much anything... etc., etc.

I don't know what it is about this particular bit of knowledge that elicits so much crackpottery.

Catholic creed is actually falsifiable

A bit of logical trivia: the creed of the Catholic Church is falsifiable; that is, it's possible (at least in principle) to disprove it. Here's why.

The Catholic creed is a set of dogmas, i.e. propositions that every Catholic is required to believe. This set is unchangeable, and Catholics cannot "pick and choose" which dogmas to believe; if you doubt even one of them, you cannot call yourself a Catholic. Now one of those dogmas states that it is possible to prove the existence of God "by means of unaided reason." What this means is that it's possible to carry out a purely logical proof of the existence of God, one that does not contain any ethical or empirical propositions.

Many such proofs were attempted, by many great philosophers (St. Augustine, Duns Scotus, Thomas Aquinas, Blaise Pascal and Immanuel Kant among them), but without success. That is, all known purely logical proofs of the existence of God are flawed. This does not mean that such proof is impossible, of course. But if anyone showed that the existence of God is impossible to prove by means of unaided reason, it would become logically impossible to be Catholic.

Rationalizing death

Thinking about the cheerful topic of death is unavoidable after watching the "Young at Heart" documentary. The way the choir is marketed and perceived is symptomatic of how we view death (although, to be fair, the movie is less superficial than that). The performers, as well as the whole idea behind the choir, are though of as "cute." But the performers themselves don't think that; to them, participating in the choir seems to be mostly a distraction from the nagging thought that they are going to die soon.

Death is both horrifying and unavoidable. This is why we cannot truly face the reality of it or its implications; if we tried to do that, we'd be too paralyzed by fear to do anything with our lives. We therefore have various defense mechanisms in order to shield ourselves from the truth that is too terrible to grasp. We try to think about death as little as possible. We have in-built coping mechanisms that allow us to keep going after we've been struck by an unspeakably horrible event of losing someone close to us. We have religion that tries to console us by telling us that death isn't the end of our conscious life. We rationalize death by inventing philosophical arguments as to why it isn't really as bad as we think it is (it "gives meaning to our life," "makes us try harder to do something with our time" etc.)

Ultimately, all those defense mechanisms fail, and the knowledge that we are going to die is causing all of us considerable amounts of pain and despair. I suspect that even religious people, in their heart of hearts, do not really believe that their consciousness will survive the death of their bodies. (I only suspect that though; I do not claim to know what other people believe.) In one of Bertrand Russel's essays, there is a great anecdote that neatly illustrates religion's ultimate failure to soothe our fear of death. During a conversation with one of his religious friends, Russell kept asking him the question: "What do you think will happen to you after you die?" The friend kept dodging the question, but when he realized Russell wasn't about to drop it, finally gave his reply. "I suppose I shall inherit eternal bliss," he said, "But why must we talk about such unpleasant matters?" Nor does it give us much consolation to insist that death gives meaning to our lives. Deep down we all know what was so greatly verbalized by Eliezer Yudkowski:

(...) if we were all hit on the head with a baseball bat once a week, philosophers would soon enough discover many amazing benefits of being hit over the head with a baseball bat: It toughens us, renders us less fearful of lesser pains, makes bat-free days all the sweeter. But if people are not currently being hit with baseball bats, they will not volunteer for it.

Here is a song from the movie. The song is mediocre (sorry, not a Coldplay fan), but it doesn't matter. The audience weeps, partly in sympathy with the performer who has just lost his friend and who is hanging on to his own life by a thin thread, but also in self-pity, knowing that the same horrible thing is going to happen to them as well.

Dictatorships wear fake mustaches

One of the questions I've never been able to find a satisfactory answer for is: why did communist regimes bother to organize parliamentary elections?

The first answer that comes to mind is probably something like: in order to pretend to the outside world that they were democracies. But this can't be right. If you're serious about pretending to be something you're not, you need to at least keep up some appearances. So if you're pretending to be a democracy, you need to make your parliamentary elections look at least superficially like free elections that happen in democratic countries. The communists paid absolutely no attention to keeping up such appearances. Sure, there were multiple names on the ballot for voters to choose from, but all all of them were candidates of one party. (There were examples even more extreme than that. In 1952 elections in Poland, the number of names on the ballot was the same as the number of seats in parliament.) No communist government has ever allowed outside observers to participate in the ballot-counting process. In short, there was absolutely no effort on part of the communists to make their elections look anywhere close to legitimate.

Well then, perhaps it was turnout that mattered to those governments. Perhaps communists treated those elections as a job approval measuring device. By looking at true turnout numbers they could infer just how unpopular they were among the people (as most of those opposed to the communist rule made a point of boycotting the elections), and then by officially announcing fraudulent turnout numbers, they got to spread propaganda about how popular they were.

While the first part of this hypothesis might be true (but then the question is, was it really worth the costs?), the second part cannot. When you lie, you need to lie plausibly, and official turnout numbers were anything but. In all communist countries, they hovered around 98% in every single election they had. Everyone and their mother knew those numbers cannot be legitimate. If your life depends on changing your physical identity, you get a plastic surgery; you don't just walk around wearing fake mustache you bought at a Halloween costume store hoping no one will recognize you.

Pretending makes sense only if you think you're fooling someone and, judging by their lack of effort, the communists harbored no such convictions. Plus, those elections were costly; they required spending money that could be used to strengthen the secret police or to buy more luxurious cars and houses for the Politburo members. Thus, it seems to me that the true purpose of parliamentary elections organized by communist regimes had to be something other than "pretending they were democracies." I just don't know what that purpose was.

Innumeracy, sort of

Recently, this NYT article made the rounds. It is about the implications of the fact that in most large American colleges, the ratio of female to male students is approaching 6/4. In the article, we read the following:

Jayne Dallas, a senior studying advertising who was seated across the table, grumbled that the population of male undergraduates when you looked at it as a dating pool. "Out of that 40 percent, there are maybe 20 percent that we would consider, and out of those 20, 10 have girlfriends, so all the girls are fighting over that other 10 percent," she said.

Now it's fairly clear what Jayne Dallas is trying to say. What she actually means is "Out of that 40 percent, there is maybe 50 percent that we would consider, 50 percent of those have girlfriends, so all the girls are fighting over that other 10 percent." But even though we know what she means, the quote still should have been edited, because she uses her terminology incorrectly; 20 percent out of 40 percent is 8 percent, not 20, and 10 percent out of 20 percent is 2 percent, not 10.

Next time they'll shoot the messenger too

In September of 2008, just after the collapse of Lehman Brothers, the U.S. Securities and Exchange Commission (SEC) banned short-selling stocks of financial companies. The objective was to bring up the prices of those stocks which at that time were in a free fall.

The critics were pointing out that prohibiting short sales will decrease the liquidity of the stock market and that, more generally, thinking that outlawing bad news makes them go away is just silly.

Was the ban a success? A recent paper by Alessandro Beber and Marco Pagano claims otherwise; here's the abstract:

Most stock exchange regulators around the world reacted to the 2007-2009 crisis by imposing bans or regulatory constraints on short-selling. Short-selling restrictions were imposed and lifted at different dates in different countries, often applied to different sets of stocks and featured different degrees of stringency. We exploit this considerable variation in short-sales regimes to identify their effects with panel data techniques, and find that bans (i) were detrimental for liquidity (...) (ii) slowed down price discovery, especially in bear market phases and (iii) failed to support stock prices, except possibly for U.S. financial stocks.

Even some regulators agree with these conclusions; former SEC chairman Christopher Cox said

Knowing what we know now, we would not do it again. The costs appear to outweigh the benefits.

But I would bet that the lesson hasn't actually been learned. When the next big crisis hits, short-selling will be banned again. In times of financial emergency, there is enormous pressure on the government to "do something," and shooting the messenger is an easy way to appear to the public as if you were, in fact, doing something.

Nerd test

If you don't think this is funny, you clearly aren't one.

(HT: Alexandre Borovik.)

The price of being a politician

Is having to say things like

We need to stand up to the special interests, bring Republicans and Democrats together, and pass the farm bill immediately.

That's from Barack Obama's statement released back in November 2007. Now Obama is a very intelligent man. There's no way that he didn't fully realize how incredibly inane, ridiculous and perverse this statement was when he was putting his signature underneath it.

Is it at all possible to be a high-ranking politician and still have a soul?

(HT: Megan McArdle.)

Who says we don't understand Bayes' rule?

When dealing with conditional probabilities, people commonly make a mistake called ignoring the prior. Suppose you get tested for a disease that is present in 0.5% of the population. It's a very accurate test: when applied to a healthy person, it comes up negative 99% of the time; when applied to a sick person, it comes up positive 99% of the time as well. Your test comes back positive; what's the probability that you're sick?

Most people (including highly educated ones, e.g. doctors) will say it's 99%. This answer is way, way wrong; the actual probability is slightly over 33%. The mistake comes from ignoring the fact that it is highly unlikely that the test has been administered to a sick person in the first place, because only o.5% of the population carries the disease.

The technique that allows us to solve problems of this sort is called Bayes' Theorem. To calculate the probability that you're sick given that you tested positive--let's denote that by Prob(S|+)--you need three pieces of information:

1) The probability that the test is positive given that you're sick, or Prob(+|S).

2) The "base" (or prior) probability that you're sick, regardless of any additional information, or Prob(S).

3) The probability that the test comes back positive, regardless of any additional information, or Prob(+).

Now all that Bayes' Theorem says is that

Prob(S|+) = [Prob(+|S)Prob(S)]/Prob(+)

Even though the result of the calculation may sound surprising, the formula is simple and makes immediate sense (and, in our particular case, gives the answer of 0.3322).

But why is the result counterintuitive? Why are we so prone to ignoring the prior, if Bayes' formula is so obviously true and, in addition, mathematically simple? I remember having a conversation with an NYU game theorist about this; he was amazed that people systematically make such a simple mathematical error while at the same time being able to routinely solve mathematical problems orders of magnitude more complex than that.

Problems like what?, I asked.

He said: like, for example, walking.

He was right. Being able to walk requires whatever part of the brain that is responsible for walking (I have no idea which part it is, I don't know my anatomy) to be able to solve problems isomorphic to fantastically complex systems of differential equations, and to solve them over and over again at mind-boggling speeds. So if we can do things like that, why do we stumble on something as simple as Bayes' rule?

The answer is that we can actually do Bayes' rule just as well as we can do walking. But, like walking, we can only do it subconsciously. Just because we can walk doesn't mean we can actually consciously perform all the complex mathematics involved in successful walking; and conversely, just because our conscious thought has trouble grasping Bayes' rule does not mean that it isn't subconsciously applied somewhere inside our body.

It is applied. Neurons do it. Suppose there are two connected auditory neurons, A and B. Neuron A receives some stimulus S from the set of many possible stimuli, and then sends a certain response R to neuron B. The receiving neuron is then trying to guess which stimulus was received by neuron A, given the response it's got from it. In other words, it's trying to "estimate" Prob(S|R). How does it do it? By doing chemical things that can be accurately modeled by a very simple equation:

Prob(S|R) = [Prob(R|S)Prob(S)]/Prob(R)

Looks rather familiar.