Weighing The Options

George Monbiot's latest attempt to pin down smoke made me remember a half-formed thought experiment I toyed with a couple of months ago but never finished. Partially this was because I had no values to work with, but having swiped some, I thought I'd give it a spin, since maths doesn't really seem to be happening this afternoon.

Suppose you decide to go in for a full body scan. You're not sure if there's anything wrong, but other people have suggesting to you there might be, so you figure it's worth checking things out. At the end of the scan, you go to collect your results, and find to your surprise that there a fully one hundred doctors waiting for you. It's a slow day at the hospital, so they've all looked at your scan data, and they all wanted to pitch in. Providing second through to one-hundredth opinions, if you like.

Ninety-seven of them tell you that you have cancer. The other three say you don't, either claiming that no cancer symptoms are present, or that while the symptoms are cancer are there, it's far more likely that you have a combination of several other diseases that combine to look like cancer, so it isn't worth worrying about.

Let's say you go with the majority, and thank the three dissenting doctors for their time. With them gone, you ask what you should do. Seventy four of those doctors remaining tell you that they have a drug that has been proven to alleviate your condition, and though curing it is close to impossible, the drug will significantly reduce your chance of serious symptoms up to and including death. Ten of them say that their professional opinion is that the drug will alleviate your condition as claimed, but that they are cannot state with certainty that it will. Eight more claim the drug may or may not be useful. Five tell you it's a placebo.

This is the part that always confuses me about a lot of people who argue we shouldn't do anything about global warming. The argument that science hasn't "proven" anything is equivalent to telling the eighty four doctors recommending the drug that until they convince their thirteen colleagues to recommend it as well (with only five of them arguing it isn't useful), you won't be taking the drug, thanks. A lot of crap gets thrown around at this point, comments like "this isn't science, it's an opinion survey" (copyright Sean Hannity), and "statistics isn't science because it cannot predict with 100% accuracy" (copyright at least one poster in any internet discussion about global warming ever), but none of it seems particularly convincing here.

There is an alternative tack taken by those arguing for inaction is more sympathetic, of course. If the drug being discussed is massively expensive, there's a risk assessment calculation to be made between the chance of dying of cancer, and taking a useless drug whilst having no money. Even that doesn't work too well in this context, though, because once you've been diagnosed with a potentially terminal illness, I think the amount of money people would spend on medication is liable to be a fairly high percentage of their income. Perhaps the more of the dozen or so nay-sayers in the group change their mind, the more money you'd be prepared to risk, but refusing to spend anything until you can be persuaded to go all-in seems counter to human nature. Even if you can't be persuaded to buy the whole course of treatment, people are liable to at least get hold of some of it (and there is certainly evidence that this happens).

I'd guess that the main argument against all of this is that medical doctors are seen to be more reliable than climate scientists. One wonders how much of that opinion is based on truly understanding the way climate science works, and how much is down to the fact that we have to trust doctors as an alternative to getting really, really sick, combined with the mercy of never having to watch doctors argue about the best treatment for your condition (certainty is much easier to fake if you're the only one talking). If you saw a choir of doctors each time you were handed test results, things might be very different. Certainly, diagnosing illnesses and recommending treatments is, generally speaking, an exercise in statistics as well [1], and I would suggest that responding to a cancer diagnosis (along with a bill for the necessary treatment) by seeking alternative opinions until you find someone to tell you that you're well is behaviour that seems far more odd in the context of a personal diagnosis than it does for a diagnosis for the planet in general.

[1] Let us not forget the standard probability question: if you take a 95% accurate test for a disease carried by 0.01% of the population (so if you have the disease the test will be positive 95% of the time, and if you don't have, the test will be negative 95% of the time) , what is the chance you have the disease given your test comes back positive? Medicine is not an exact science, but pretty much everyone pretends it is so as not to totally freak out.

(The answer, by the way, is 0.19%. Some people find this hard to believe; one way to think about it is that statistically speaking for every 10 000 who go take the test only one of them will have the disease, and about 500 of the 9 999 healthy people will get false positives.)