Here’s something I slopped together recently. I’m not really familiar with the literature on any of this, so maybe it’s all pretty well known (or well known to be confused). Anyhow, comments are welcome, and I apologize in advance for my usual pile of typos, grammatical errors, and other miscellaneous blunders.
Johnny Woulda, 45, has had chronic tendonitis in both of his elbows since he was about 30. He’s always been told that there’s no help for it except rest and steroid injections, but the rest hasn’t worked, and he’s afraid the injections will be worse for him than the elbow pain. He takes a bus to work every day and one day he sees a poster that says “Do you have tendonitis? We are testing a new non-steroidal oral drug, and if you are an otherwise healthy male between the ages of 18 and 48 you could earn $100 by taking part in our clinical trial.” The drug company, Montrezl, is interested in testing the effectiveness of their experimental product, Elbowftra©. Based on their tests on chimpanzees, which have no belief one way or the other whether they are being given a real drug, they believe that Elbowftra© drug would have at least a 50% effectiveness rate on humans people—higher if the person is credulous (the sort of person now spending a ton of money on herbal remedies). The FDA has assured Montrezl that if they can confirm that at least 30% more human volunteers are cured by Elbowftra© than are cured by a sugar pill placebo, as determined by blind reviewers, they should have no problem getting their drug approved. On the other hand, if there’s not much difference between Ebowftra’s effectiveness and that of a placebo, there isn’t much hope.
Let us suppose now, that there is something a little unusual about chronic tendinitis sufferers like Johnny Woulda. They happen to not only be extremely desirous of getting relief from their pain, but more credulous than a randomly chosen subject. If you even suggest to one of this group that you’ve got a pill that MAY work, a couple of doses is quite likely (about 70%) to provide them long-term relief from both their inflammation and their pain symptoms. The problem for Montrezl is that for this cohort there is no significant difference between the effects of Elbowftra© and the placebo: they both have around a 70% effectiveness rate. This means that a double-blind experiement will likely result in a determination by the FDA that Elbowftra is garbage and may not be sold.
This produces a paradox which may be put as follows:
Let S= people in the trial; X = any pill; E = Elbowftra©; and P = a sugar pill of no medicinal value. Assume too that the FDA is very careful and strict, only allowing curative drugs to be sold.
1. (X) (if X is safe and helps at least 50% of those taking it in double-blind clinical trials, then X should be allowed to be sold). [premise]
2. E is safe and at cures elbow tendinitis in 70% of those taking it in double-blind clinical trials. [premise]
3. Therefore, E should be allowed to be sold. [2 & 3]
4. (S) (X) (X is allowed to be sold, then it is rational for S to believe that X is curative of something). [FDA accuracy and stringency assumption]
5. It is rational to believe that E is curative of elbow tendinitis. [3 & 4]
6. (P) ~(P has the power to cure any medical ailment). [medical valuelessness of placebos]
7 E is no more effective than P in clinical trials. [premise]
8. (S) (X) (P) (if X is no more effective than P in clinical trials, it is irrational for S to believe in the power of X to cure anything. [What is no better than something useless must itself be useless]
9. It is irrational to believe that E is curative of elbow tendinitis effective on at least 50% more individuals than no drug at all.
We have thus proven that it is both rational and irrational to believe in the effectiveness of Elbowftra©.
It is easy to see the similarities between this paradox and Newcomb’s paradox of the money boxes. It is argued there that since it is irrational to believe that there could ever be less in both boxes than there is in one box, it must always make sense to take both boxes. This is in the face of the obviously rational approach of predicting that the future will be like the past.
The logical, apparently scientific sort—the type that believes that sugar pills cannot cure tendonitis—can always be expected to take both boxes: “How can it ever make sense not to? The money is either in the second box or it isn’t—my choice can’t affect the outcome!” But the credulous pragmatist, like Johnny Woulda, is more interested in the cure than the scientific truisms. He doesn’t care if it is his belief that is causing the success-creating effect or not: he just wants his elbow to stop hurting (or to become a millionaire if he’s playing the Newcomb game). The concern of how these apparently crazy results might happen, being purely academic, holds little or no interest for him.
The thing is, being just a thought experiment, there is no actual empirical basis for the Newcomb results, only a discussion of pragmatic versus academic dispositions. But there is plenty of empirical support for the existence of the placebo effect. One really can improve one’s elbows if one believes. This is not like Pascal’s wager, where there’s no basis for supposing that anybody has ever benefitted from what seems like a completely wacky supposition of the existence of some kind of diety. On the contrary, it’s a well-known fact that the credulous are more likely to do better in clinical trials. We even have a name for it—“the placebo effect.” We may say that the person who takes ginko biloba based on anecdotes of a couple of friends is just deluding herself, but—again assuming it’s completely safe—only good would seem to come from these kinds of “delusions.” And if a belief is really (not just in-pretend) success-producing, why is it more delusional to have it than not to have it?
I think the problem with assessing the Newcomb paradox is that those who insist on taking both boxes don’t REALLY BELIEVE that the past empirical results could have been as they are described by the one who sets up the story for them. As it seems impossible to this type that the single box taker has always (or almost always) gotten away with the big money and the two-box taker gotten screwed, they feel that their choice of both boxes is more rational than that of the (credulous, not to say stupid) pragmatist. But it is the pragmatist who is actually relying on the empirical results rather than the insisted upon theorems (“There just has to be at least as much money there for you if you take both boxes!” “There’s no way glucosamine can help tendons!”). These “musts” and “no ways” are not really science, however; they are simply denials of the accuracy of the actual empirical results based on a supposed knowledge of what must be the case—given the logical principles or scientific laws. So who is really the religious thinker here after all?