Take a chance

I bought a lottery ticket, just to change my luck.
I thought I wouldn't mind alosin', cause it only cost a buck.
I won an electric toaster, and a baritone sax,
But I had to pawn my guitar, just to pay off the tax.
How come I always lose?
You got to suffer if you wanna sing the blues.

Like David Bromberg, people tend to perceive patterns in events. Sometimes they are really there, so it's a useful faculty. The tubers form in this place at this time every year; the lion wakes from mid-morning to mid-afternoon. But if we can't discern a real pattern, our minds will invent one. Does David always lose in order that he can sing the blues? Was Big Mama born under a bad sign?

Superstitions help us make sense of the world, but when scientists don't know how to make exact predictions, they depend on probability and statistics instead. Probability theory is philosophically vexed. The philosophy of science in its simplest expression depends on the principle of verifiability and repeatability, but are probabilistic statements consistent with these principles? If I say the chance of throwing a 6 on one roll of the die is 1 in 6, is that verifiable?

In fact, if I roll the die 6 times, it is unlikely that I will get exactly one 6. And if I repeat the experiment, I will get many different results -- to be precise, there are 6^6 possible results considering the order of the rolls, each of which is equally probable. Results that yield exactly one 6 are more numerous than results yielding other numbers of 6's, but that does not mean they will necessarily be the most numerous in any given set of trials.

Nevertheless, gamblers who know the odds and play by them will almost always come out ahead in the long run if they are playing against others who do not. They will not buy lottery tickets or play slot machines or roulette, because they know the odds are against them. Yet many people do play these games. Why? Often, they believe that there is some influence or determinant of the results, that they can take advantage of to tip the odds, be it prayer, the interpretation of dreams, runs of good or bad luck, or the results of previous trials -- that is, 6 hasn't hit for a while, so it's due.

But there is another feature of risk, or chance, when applied to real world situations, that scientific attempts to make policy have difficulty with, and that is the valuation of outcomes. The high probability of losing a dollar, for David Bromberg, seemed inconsequential compared with the much smaller probability of winning the greater prize of a toaster and a saxophone. Of course, it turned out he was mistaken, but given that he forgot about the taxes, was his initial decision actually "irrational"? That's hard to say. But it also mattered what the toaster and the saxophone were worth to him in the first place. I already happen to own more than one of both items, so I would not be interested in entering a lottery to win them. But there are other prizes that might tempt me to part with a small sum.

So, when it comes to weighing the "appropriateness" of medical interventions, as I touched on yesterday, we have a problem. The question never has a "scientific" answer. Information about probabilities can inform our choices, but it can never determine them. In fact, while on the margin health care payers always restrict choices -- in the United States as much as in the United Kingdom, by the way -- most of the information about costs and risks and potential benefits is treated as support for making personal choices, not as a restriction of choice. Unfortunately, few of us as patients and potential consumers of medical services are well equipped to understand or apply this information.

I suspect that's a major reason why a lot of people don't want to have it -- they're afraid of having knowledge that will only confuse and distress them. Psychologists have found that there is a point beyond which most people want fewer choices, not more.

Anyway, having set up some of the framework for this discussion, I will pursue it further in coming days.