Crimes Against Logic Read online

  The paternalist who thinks cocaine use is a net cost tacitly assumes that the pleasure is insufficient to compensate for the costs. Since what he assumes here is precisely what is at issue in the debate, he begs the question. Worse. His assumption is sure to be wrong. Those who prefer to snort cocaine after considering p. 113 all the costs must value the pleasure more. Otherwise they wouldn’t prefer to snort. According to their values, snorting cocaine is a net benefit.

  Begging Political Questions

  Many politicians like to present themselves as pragmatists. Theory and ideology are not for them. They are in the business of making practical changes that improve people’s lives. When it comes to making a policy decision, they are guided by common sense and a thorough command of the nuts and bolts.

  Alas, it is harder to avoid ideology than these pragmatists would have us believe. What, for example, does it mean to improve someone’s life? That they are richer? That they have more free time? That they are more likely to go to heaven when they die? If you can’t answer this question, how can you know whether any policy represents a practical measure to improve people’s lives?

  Nor is it just the ends of policy that require ideology or theory. So does knowing the means to those ends. Will free trade enrich the people of America or will protectionism? To answer this question, you need to engage in economic theory. For some, it is just obvious that free trade will make Americans poorer by exporting jobs to low-wage economies. But this isn’t obvious. In fact, it is false. (Any introductory economics textbook will explain why.)

  Whether you like it or not, politics is thoroughly ideological. At the heart of most debates about a specific policy lies a more general ideological disagreement. Yet our pragmatic politicians p. 114 will not engage with the general question. When arguing for or against a policy, they simply take their ideology for granted, perhaps unaware that they are doing so. And so they beg the question. They take for granted precisely what is at issue in the debate.

  Take a topical example. Was the United Kingdom government right to increase income tax to spend more on the National Health Service (NHS), as they recently did? Their justification is that it will lead to more patients being treated in NHS hospitals. This outcome justifies the policy, however, only if the NHS is the most efficient way of delivering health care. Yet that is precisely what opponents of the policy dispute. The debate is really about the relative efficiency of state and private-sector healthcare provision. The government’s defense of their policy begs the question because it simply assumes that the NHS is more efficient.

  The desire to avoid ideological debate can lead to even worse crimes than begging the question. Often the result is total incoherence. Consider, for example, the current debate with Islamic fundamentalism. Most Western politicians reject Islamic theocracy and sharia law. They have their various grounds for disapproval: it is insufficiently democratic, sharia law fails to protect women’s rights, and so on. These may be good objections, but they suffice for the rejection of Islamic theocracy only if the basic religious beliefs of Islamic fundamentalists are wrong. If Allah really does demand sharia law, as the fundamentalists claim, then we should all adopt it as soon as possible. Despotism and sexism are well worth it if they will save us from the everlasting flames of hell.

  p. 115 Of course, most Western politicians do reject this Islamic idea about Allah’s will. But they won’t say so in public. When arguing against sharia law they never point out that Allah does not really exist and so can’t really have insisted on any form of law, sharia included. On the contrary, most who engage in the debate will spend quite some time professing to have enormous respect for Islam. But if they do respect Islam why will they not adhere to its political prescriptions?

  Perhaps I misunderstand what politicians mean by “respect.” Perhaps you can respect a religion whose basic tenets you think false and whose political ideology you believe to be despotic and sexist. Even so, you must admit that it is a little confusing, when rejecting Islamic theocracy, to focus on your respect for Islam rather than your belief that its basic ideas are false.

  A politician cannot tackle directly every theoretical challenge to his position. He hasn’t the time, and many of them are too silly to warrant the effort. He must pick his fights, normally, against his main political rivals. But, once he picks his fight he must fight properly, trying to land blows above his opponent’s belt rather than just dancing evasively around the ring waving triumphantly to his fans in the crowd.

  Disguised Assumptions

  Apparently plain statements can embody contentious assumptions. For example, describing an income tax cut as a “giveaway” assumes that a citizen’s gross income is not her own but is, rather, the property of the government. Describing the government’s spending plans as generous embodies the same assumpp. 116tion. The virtue of generosity does not consist in giving away others’ money: it requires you to give away your own.

  It might be true that everyone’s gross income is the government’s property, but if you simply assume it in a debate with someone who disagrees, you beg the question. Which means that you also beg the question by using language that implicitly assumes it, like describing government spending as generous.

  It isn’t only statements that can in this disguised way beg the question. Questions can too. “Have you stopped beating your wife?” is the famous example. Answer yes or answer no and you seem to confirm your status as a wife-beater. But if your wife-beating status is in dispute, the question begs the question.

  Even a name can beg the question. The Peace Movement of Cold War days provides a nice example. The Peace Movement consisted of those in favor of nuclear disarmament, even unilateral disarmament on the part of the West. They thought this would promote peace and save the world from nuclear Armageddon. Their opponents believed in nuclear deterrence. They thought this would promote peace and save the world from nuclear Armageddon. It is presumptuous, you will admit, for one side in this dispute to label itself the Peace Movement.

  It takes a terrible pedant to worry about such contentious built-in assumptions, and pedantry has got itself a bad name. But don’t let that put you off. As Bertrand Russell said, a pedant is just someone who prefers his opinions to be true.

  10 – Coincidence

  p. 117 My day job brings me into frequent contact with the financial controllers of banks. Quite dull, you probably think. Usually. But occasionally, they say remarkable things. Only last month I made the mistake of suggesting to one that perhaps the events we were discussing had been merely coincidental. He regarded me with an expression between pity and contempt and declared, “I don’t believe in coincidences.”

  Which is interesting. Here is a controller, his job to manage the financial security of a bank, and he declares that he doesn’t believe in coincidences. It’s like the chief of police saying he doesn’t believe in burglary, or a firefighter expressing her doubts about the reality of smoke.

  Any bank faces risks to its financial security. Those to whom it has lent money might fail to repay it, the value of bonds and shares it owns might collapse, or an employee might lose it a fortune through “rogue trading,” as Nick Leeson did Barings Bank. p. 118 And any combination of such events might, purely by coincidence, come at the same time, compounding the loss. Since a financial controller’s job includes calculating how much capital his bank must hold as insurance against such coincidences, it is best if he believes in them.

  Not believing in coincidences is part of a manly pose adopted by many who fancy themselves savvy. They don’t trust strangers, they don’t count their money while sitting at the table, and they don’t believe in coincidences. It’s a shame, because coincidences happen all the time; they are statistically guaranteed to. And failing to believe in them makes you believe in things that really don’t exist, those forces imagined to explain away the appearance of coincidence.

  This chapter concerns the mistakes people make when they fail to recognize simple coincidence at wo
rk, from paying their staff more than they should to believing in God.

  What You’d Expect

  In cricket, batsmen most frequently get out on the score zero, though it is quite possible for them to score more than a hundred runs in an inning. I once heard a panel of professional cricketers attempting to explain this fact. Two explanations were popular. One was that when a batsman has just begun his innings, and so has a score of zero, he hasn’t had time to “get his eye in.” The other was that batsmen are nervous until they have scored some runs. Both explanations attempt to show why a delivery (the equivalent of a pitch in baseball) is more likely to get a batsman out when he is on zero than when he is on a greater score.

  p. 119 But this is not required to explain why zero is the score on which batsmen most often get out. The way cricket is scored means that, even if each delivery a batsman faces is equally likely to get him out, regardless of his score, zero would still be the score on which he would most often get out. A batsman always begins on zero and each time he faces a delivery he can either get out or score anything between zero and six runs. This means that zero is the score on which batsmen face the most deliveries. So you should expect zero also to be the score on which they will most often get out. No need to postulate any further explanation in terms of acclimatization, nervousness, or anything else.

  Something beyond the way the game is scored would be required to explain this statistic only if the frequency of batsmen getting out on zero were greater than would be expected from the game’s scoring system alone.

  Lessons from cricket are generally applicable to life. What, if anything, is required to explain some statistical fact depends on what you’d expect in the first place—what you’d expect if everything were playing out according to the odds. This is so not only when we consider a typical or average outcome, such as the score on which batsmen are most often out, but also when we consider extraordinary events. Extraordinary events are just what you should expect to happen, at least occasionally.

  Consider the bond traders who work for investment banks. Some of them simply execute orders to buy and sell bonds on behalf of their clients, but others trade on behalf of the bank’s own account, proprietary traders, as they are known. Some of these proprietary traders make vast sums of money for the banks that employ them. These are the “star traders” whom banks comp. 120pete fiercely to employ, tempting them with massive salaries and bonuses. Yet there is no reason to believe that these people possess any skill worth paying for. Their extraordinarily profitable trading, on which they are judged stars, may be nothing but luck.

  Before going into this matter further, it will be useful to consider the card game Chancy. The rules of Chancy are simple. Spread before you is a well-shuffled deck of cards, face down. You play by drawing a card from anywhere in the deck. If it is a seven you earn no points. If it is above seven, then you earn the value of the card less seven (e.g., a Queen earns you five). If the card is below seven then you lose seven less the value of the drawn card (e.g., draw five and you lose two). After each turn, the card drawn is returned to the deck, which is then reshuffled. The winner is the player with the highest score after an agreed number of draws by each player.

  Over the long run, you should expect your average score to tend toward zero, since the likelihood and size of earnings and losses on each draw is equal. But there is no impossibility in having a run of luck and accumulating a large positive score. On the contrary, the probability of any such run of luck can be calculated.

  For example, the probability of five consecutive draws being earners (i.e., above seven) is 2 percent, and the chance of five consecutive draws being big earners (Jack or better) is 0.065 percent. This means that if a large number of people sat down to play a five-draw game of Chancy, you would expect 2 percent of them to draw only earners and 0.065 percent of them (1 in 1,500) to draw only big earners. These winners possess no skill lacked by the other players; the game provides no way for skill to affect the outcome. The winners have just been lucky, as we knew in p. 121 advance some would be. Just as the rules of Chancy guarantee that, in a large enough sample, the average score will be zero, so they also guarantee that some players will be big winners.

  Now, let’s return to bond trading. How much it resembles Chancy is hotly debated. Those traders with “high scores” will assure you it is a game of skill, not luck. But that is irrelevant for the point I wish to make. Even if bond trading is a game of skill, you can still win by luck. The prices of bonds go up and down, by lesser and greater amounts. Even if a trader made her buy and sell decisions by tossing a coin, given enough luck she could still be a big winner.

  Suppose, then, that you own or manage an investment bank. One of your proprietary traders has five consecutive big wins and earns your bank a fortune. Deutsche Bank hears of this incredible feat and attempts to poach him from you, offering a salary of $750,000 and guaranteed minimum bonus of $2,000,000. Should you top this offer to keep your star trader or cheerfully say goodbye to someone who has just had a run of luck that there is therefore no reason to believe will be repeated?

  There are two ways to answer this skill or luck question. One was suggested already. If it is skill rather than luck, then this successful trading should persist. Observe your trader at work. If his success continues over very many trades and through different market conditions (trending, volatile, and so forth), then the probability that it is just luck will approach zero: he is clearly a wizard of finance.

  The second is to think about what information is available to your trader and how he makes his decisions. Could he possibly predict bond price changes or follow a trading strategy that beats the odds?

  p. 122 Answering the skill or luck question is not easy. The expected random distribution of performance in bond trading is harder to calculate than the distribution of Chancy scores; the bond markets are more complex than this simple card game. So it will be correspondingly harder to tell whether or not a trader’s performance can reasonably be attributed to luck. And this complexity also makes it difficult to know whether or not a trader’s decision-making processes could possibly give him any advantage. Yet, if you manage an investment bank, you should try to answer these difficult questions. Otherwise, for all you know, you are paying people enormous salaries merely for having been lucky.

  Remarkably, investment banks make no serious attempt to answer the skill or luck question. They simply assume that a run of success is evidence of financial wizardry, even when the success would require only moderate luck. When the sums involved are large enough, even one or two wins will do. “Look, she has just made us $500 million. That can’t be luck!” This is precisely what was said about several traders of emerging markets government bonds in the late 1990s—only days before they lost their banks millions of dollars when the Russian government defaulted.

  The strongest evidence that investment banks just assume success is due to skill is their habit of offering successful traders from competitor banks vast sums of money to switch employer. The tactics of these traders are a mystery to the banks that court them. Perhaps they bought when the coin landed heads and sold when tails. Their new employer neither knows nor, apparently, cares.

  p. 123 Investment bankers seem to agree with those primitive tribespeople who assume that any good or ill fortune that befalls someone must be due to some quality of the person—that there is really no such thing as luck at all. In this spirit, I suggest a new line of business for them. Investment banks should employ former winners of Lotto jackpots to buy Lotto tickets for them. No salary could be too high for these wizards of ticket selection.

  Coincidental Healing

  I have a friend who believes in homeopathy. He once tried to convince me that its effects are not due to the placebo effect by telling me about a sick dog that responded positively to homeopathic potions. It’s not a bad argument regarding the placebo effects of homeopathy. Since dogs don’t know they’ve been given medicine, improvements in their health can
’t be due to the psychosomatic effects of such knowledge. But my friend had mistaken my concern. I don’t think homeopathy works via the placebo effect; I don’t think it works at all.

  How can I maintain this skepticism in the face of the cured dog? And in the face of my friend, who has had the same ailment cured several times by homeopathy? Quite easily. This dog and my friend would have got better anyway. Consumption of homeopathic medicine preceded their recoveries but that doesn’t mean it caused them. It’s just a coincidence.

  To think that what follows something must be caused by it is to commit a fallacy so famous that it has a Latin name: the post hoc ergo propter hoc fallacy (the after this therefore because of this fallacy). Events may happen in sequence, and even in close p. 124 proximity to each other, without being cause and effect. Just as I sit down, the lightbulb blows. It doesn’t mean that sitting down caused the lightbulb to blow.

  Event A caused event B only if B’s occurrence depended on A’s: only, that is, if B wouldn’t have occurred if A hadn’t. This condition isn’t met in the case of the lightbulb. The lightbulb’s blowing didn’t depend on my sitting; it would have blown even if I hadn’t sat down. B can follow A without depending on A.

  No one would think that sitting caused the bulb to blow because everyone knows that isn’t how the world works; sitting isn’t the kind of thing that causes lightbulbs to blow. Knowing how the world works—knowing what sorts of things cause what—depends on what we observe following what, but not on a mere handful of observations. One dog getting better after taking a homeopathic medicine cannot alone show that homeopathy has its alleged curative effects.