by Jamie Whyte
How then do we confirm such causal claims?
First, let’s take a probabilistic view of causation. That is, let’s say not that if A hadn’t happened B wouldn’t have, but only that if A hadn’t happened the chance of B happening would have been lower. In other words, causes make their effects more likely. This is the sense in which smoking causes cancer and regularly playing Lotto causes penury.[10.1]
Now, suppose our causal hypothesis is that taking homeopathic medicine cures influenza. The chance of recovery in any period of time is higher if you take a homeopathic medicine than p. 125 if you do not. We test this hypothesis by taking two sufficiently large groups of influenza sufferers who are in all identifiable respects the same: each group has the same distribution of ages, sexes, races, general health, and so forth. To one group, we give the homeopathic medicine (the test group), to the other, we do not (the control group). We then check the recovery times of the people in each group.
In the group who have taken no medicine, recovery times will vary. Some will get better remarkably quickly, most in about a week (let’s say) and some will take several weeks to recover.
This immediately shows why individual cases of fast recovery prove nothing about the efficacy of homeopathic medicines: some people will recover quickly with no medicine at all. To establish p. 126 homeopathy’s efficacy the distribution of recovery times in the group given the medicine must be significantly better than that in the control group, as illustrated in the following chart.
I do not believe the claims for homeopathy because such test results have not been produced.[10.2] There is nothing special about homeopathy here. All medicines must pass such tests to estabp. 127lish their efficacy. Indeed, there is nothing special about medicine. Any true claim about what causes what should be able to pass such tests.
Believers in dubious medical treatments have a ready answer for negative test results. “Of course,” they will tell you, “it doesn’t work for everyone.” This response can be legitimate, provided the type of person for whom it supposedly works is specified. We can then test this hypothesis by repeating our experiment, except this time with our two groups populated only by the type for whom the treatment allegedly works. If the hypothesis is true, we should see a better distribution of recovery in the test group than in the control group.
Normally, however, the only criterion suggested for someone being of the right sort is that she does, in fact, get better. But then we are back where we started. People take the medicine, some get better quickly while others do not, and we have no reason to believe that everyone would not have done equally well without the medicine.
This simplified account of how alleged medical effects are tested is not controversial. Yet many refuse to take it seriously where their own health is concerned. Documentaries about alleged medical scandals are never short of people who claim to know that their cancer was caused by the power pylons in the backyard or that their daughter’s suicide was caused by the anti-depression drug she was taking, even when experiments of the kind I have described show no connection between power pylons and cancer or antidepressants and suicide.
The journalist nods encouragement as the cancer victim assures us that he knows the cause of his disease. But how he p. 128 acquired this knowledge, contrary to the results of scientific experiments, is never explained. How does having cancer bestow a magical power to discern its cause? All he knows is that there is a power pylon in the backyard and that he has cancer. Which isn’t enough to know that the pylon caused the cancer.
Thank You Lord for Making Me Likely
The existence of each of us is extraordinarily improbable. Had things been even slightly different—had that shrapnel entered your grandfather’s chest two inches to the right, had that train not been delayed so that your parents did not meet at the platform, had the drugstore not sold out of condoms that night—then you would not have existed. How easily all this might never have been. Sets you to thinking, doesn’t it?
Indeed it does. And what many conclude is that it could not have been a coincidence after all. Surely nothing that important—my existence—can have been a matter of chance. No, it was fated that my parents should meet at the station, that the drugstore should have a run on Trojans, and that sperm number 203,114 out of the millions issued by my father that fateful night should be the one to win the race and fertilize my mother’s egg.
The conceit of this thinking is breathtaking. Had things gone differently—had your mother not met your father at the platform, for example—then although you would not have existed, someone else would have. Your mother would have met someone else and reproduced with him instead. And had things gone differently in other ways, then yet other people who do not now exist would have: even a different sperm from your father would have meant a different person. To say that your existence is fated is to say p. 129 that fate or God or whoever is supposed to arrange these things prefers you to all the many possible people whom your existence has ruled out. You must really be special.
Most theologians are humble to the point of ostentation and so wouldn’t dream of adopting such an egocentric view of how they came to be. But many do attempt to use the improbability of human existence, if not their own personal human existence, to show that God exists. The argument follows just the line above. They begin by noting how improbable the existence of human beings would be if God did not exist. And from this fact alone they conclude that God exists.
George Schlesinger makes the argument as follows:
In the last few decades a tantalizingly great number of exceedingly rare coincidences, vital for the existence of a minimally stable universe and without which no form of life could exist anywhere, have been discovered . . . The hypothesis that [the requirements for life were] produced by a Being interested in sentient organic systems adequately explains this otherwise inexplicably astonishing fact.[10.3]
The existence of humans is indeed improbable. The laws of nature that govern our universe are but one set out of infinitely many possible sets of laws of nature. And had they differed only slightly the universe would be a mere swirl of subatomic particles, free from medium-sized objects like rocks, trees, and p. 130 humans. And even given the actual laws of nature, evolutionary history could have taken different twists and turns and failed to deliver human beings.
So the premise of this theological argument, that human existence is unlikely, is true. But it provides no ground for believing in God. Showing why not is useful because it illuminates a common fallacy in probabilistic reasoning. Before identifying this fallacy, however, it is easy to see that the argument is invalid. If it were valid we could conclude, without the aid of any evidence, that all lotteries are rigged. Which, I hope you will agree, we cannot.
Suppose Jill has won Lotto. This was very improbable, about a one in fifteen million chance. Unless, of course, the lottery was rigged in her favor. Therefore, the lottery was rigged in her favor. Or, as George Schlesinger would put it, the hypothesis that the lottery was rigged in her favor adequately explains the otherwise inexplicably astonishing fact that Jill won.
There is nothing special about Jill. Suppose Jack had won the Lotto instead. This, too, would have been very improbable had the lottery not been rigged in his favor. So, if Jack wins, we may also conclude that the lottery was rigged. Indeed, whoever wins, we may conclude that the lottery was rigged in his favor, because his winning would otherwise be very improbable.
The original theological version of the argument has precisely the same absurd consequence. Suppose the laws of nature had indeed been slightly different so that humans did not exist. Then other things would have existed instead. And their existence would have been no less improbable than ours, since if the laws of nature had been slightly different, these things would not have existed. Unless, of course, God wanted them to. So, no matter p. 131 what the laws of nature and hence what kinds of things in the universe, their improbability would always lead to the conclusion that God exists.
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br /> The basic error in the argument is a confusion about probabilities. “Which hypothesis is more probable?,” we are asked, “that humans exist by chance or that God made it so?” As a general principle, we ought to believe the more probable hypothesis. And which hypothesis makes our existence more probable? Obviously, that God brought us about on purpose.
If you haven’t already noticed the slip, consider another case. Jack has just won a game of poker. Which hand makes this outcome most probable? A royal flush. If Jack had a royal flush, then he was certain to win. So, should we conclude from the fact that he won that Jack had a royal flush?
Obviously not. The probability of getting a royal flush is very low, and winning with a lesser hand is quite likely. The hand Jack most probably won with is not a royal flush, despite the fact that it is the hand that, if he had it, would give his winning the highest probability.
The fallacy in our theological argument should now be clear. The statement,
1. Given God’s existence, the existence of humans is probable,
does not entail,
2. Given the existence of humans, God’s existence is probable.
p. 132 To infer 2. from 1. is to make the same mistake as inferring from the fact that a royal flush makes winning most likely, that Jack’s winning makes it most likely that he had a royal flush. So this theological argument is structurally defective.
Nor would it work even if we were ready to commit the required statistical fallacy. What makes theologians think that God’s existence would make human existence probable, in the way that a royal flush makes victory in poker probable? There’s God, sitting wherever He sits, contemplating all the universes He might create, with their various laws of nature, planets, creatures, and all manner of things that we cannot imagine . . . and He chooses this one! I do not mean to indulge in the kind of self-flagellation that Christians enjoy when not trying on this theological argument, but I mean to say can this really be God’s best option?
Even given the existence of God, it is entirely a matter of luck that we should exist, because it is entirely a matter of luck that He should prefer this kind of universe. How do theologians explain this extraordinary coincidence? Perhaps God was created by an über-god who prefers gods who prefer this kind of universe. But that would be a matter of luck too. And so we will soon have an infinity of gods, each explaining the next god’s extraordinarily unlikely preferences.
I have met several people who, when explaining the extreme youth or old age of their parents, have told me, “Of course, I was an accident.” Well, if they can admit it, why can’t we all? Our existence is not due to the preferences of some fabulous Being: it’s just dumb luck. Why people should feel bothered by this I don’t know. They have won the lottery of life!
11 – Shocking Statistics
p. 133 Statistics are the chemical weapons of persuasion. All good politicians and businesspeople know this. Release a few statistics into the discussion and the effects will be visible within moments: eyes glaze over, jaws slacken, and soon everyone will be nodding in agreement. You can’t argue with the numbers.
Yes you can. Even when the numbers are right, they often don’t show what they are alleged to. For example, newspaper editorialists are always leaping from statistics about changing behavior to conclusions about changing, and usually worsening, values. Behavior can change, however, not because values do but because the circumstances do. Teenagers commit more street crime now than in 1980. Is that because teenagers have less respect for private property or because there is now so much more to steal from people on the street—most notably, their mobile phones? People eat more now than they did in 1950. Is that because we have become gluttonous or because food is cheaper?
p. 134 Drawing the wrong conclusion from statistics is an interesting mistake, however, only if the statistics are right in the first place. And often they are not. Consider the following statistics:
35 percent of British children live in poverty.
50 percent of small-business owners would switch banks to receive a discount of 0.25 percent interest on their overdrafts.
25 percent of young drug users have smoked cannabis with a parent.
2 percent of young women suffer from anorexia nervosa, and 20 percent of sufferers die from it.
Each is from a reputable source. Each is also the result of a simple error of statistical method. (Sources don’t seem to become reputable by being good at statistics.)
Understanding these errors is not difficult, as I hope this chapter will show, but it is important. Widespread statistical naïveté allows nonsense statistics like these to become the “hard facts” that inform decision-making.
British Poverty
Soon after coming to power in 1997, the New Labour government drew our attention to a shocking fact: 35 percent of children in the United Kingdom live in poverty. Not absolute poverty, of course; even the poorest are at no serious risk of going without food, housing, schooling, or medical care. Rather, 35 percent of p. 135 children live in relative poverty: by the standards of modern Britain, they are relatively poor.
On pages 99-102, I complained that the Labour government played fast and loose with this ambiguity in the word poverty. “We need to fight poverty,” they claimed. Why? Because poverty is dreadful and there is so much of it. But this is merely a play on words. Absolute poverty is dreadful (but rare); relative poverty is common (but not so dreadful).
In this chapter, however, I want to set that issue aside and examine only the claim that 35 percent of British children live in relative poverty. This claim illustrates a common way in which statistics can mislead: by being based on an improper measure of the phenomenon in question.
The government measures the number of people who live in relative poverty as the number living in households with incomes less than 60 percent of the national median income. We must accept that 35 percent of children live in such households. Still, why should we conclude that 35 percent live in relative poverty? Why, in other words, is household income less than 60 percent of the national median a good measure of relative poverty?
The short answer is that it isn’t. In a country like the United Kingdom, disposable income inequality is a hopeless way of measuring relative poverty.
To see this, consider two twelve-year-old boys who live next door to each other. They live in the same quality of house, attend the same school, go to the same doctor when they are sick, wear the same brand of athletic shoes, and so on. Indeed, their material well-being differs in only one respect: p. 136 Jimmy’s parents give him £10 a week in pocket money, Timmy gets only £5 pounds from his. Should we conclude that, since his disposable income is only half of Jimmy’s, Timmy is a pauper relative to Jimmy?
Obviously not. Jimmy and Timmy’s consumption is almost identical. Let’s suppose that the housing, clothes, schooling, medical care, and so on that they both receive are worth £100 per week, and that both spend all of their pocket money. Then Jimmy consumes £110 per week and Timmy consumes £105 per week. Though Jimmy’s disposable income is double Timmy’s, he is only 5 percent better off.
When a large percentage of consumption is not paid for out of disposable income, differences in disposable income will always exaggerate differences in the ability to consume. And it is the ability to consume that is important with regard to poverty, including relative poverty.
So the government’s measure of relative household poverty is wrong. Like Jimmy and Timmy, British households need not pay for much of what they consume out of their disposable incomes. Most importantly, medical care and education are delivered by the state, funded out of tax revenues. And, so far as the government’s measure of poverty is concerned, housing is free too, since it uses disposable income after housing costs.
In a paternalistic society like Britain differences in disposable income will overstate differences in consumption capacity and hence in the number suffering relative poverty. This point has nothing to do with redistribution of wealth. If
taxes were high but all benefits were paid in cash rather than state services, then disposable income would accurately reflect consumption capacp. 137ity, and relative income would be a reasonable basis for evaluating relative poverty. The further a society moves from the “all cash” model toward an “all state services” model, the worse is the disposable income measure of poverty. And Britain is very far from the “all cash” model.
When presented with a statistic involving something hard to measure, such as poverty, happiness, or beauty, you should always check the measure used. Often it will be a crude approximation, acceptable for some purposes but not others. Sometimes it will be plain wrong.
Having alerted you to the danger, however, I can offer no general guidance on how to tell good measures from bad. Each measure must be examined as it is encountered. This will often be difficult, since alleged statistical facts are usually served up plain by newspapers, politicians, and businesspeople, with little information about the precise measure used. Then the proper attitude is open-minded skepticism.
Switching Banks and Other Lies
The higher you price the products you sell, the greater the profit you make on each sale (unit profit). So why not just set outrageously high prices? Because you would have no sales. Unlike unit profit, sales volumes decrease as prices rise. If you want to maximize your aggregate profit, as most business owners do, the best price is the one that finds the right trade-off between unit profits and sales volume.
To work out this best price, you need to know the unit profit at any given price and the volume at that price. The former is p. 138 simple when you know your costs.[11.1] But knowing how price affects volume requires you to understand the price sensitivity of customers. And that is more difficult.