"Toxin X is a substance that will make you violently ill for a few hours. However, it has no long term effects of any kind. As an experiment in psychology, I'm offering you a million dollars if tonight at midnight you fully intend to drink toxin X by tomorrow at noon. You don't actually have to drink the toxin; all you have to do is to intend to drink it. Your intention will be tested by a device similar to a polygraph which my people have developed and which has been shown to be 100% accurate. If at midnight you have the intention, a million will be wired to your bank account. The only other conditions are that you are to make no bets, do anything that will cause you to become irrational, or arrange for any way to avoid the effects of the toxin."

Suppose you decide that being ill for one day is a reasonable price to pay for a million dollars. Your first thought is to therefore agree to the proposal. It then occurs to you that you won't even have to become sick in order to win the money. All you have to do is to intend to drink the toxin. You don't actually have to carry out your intention.

But now if you know ahead of time that you don't actually have to drink the toxin, then you can't really intend to drink it. So you tell yourself you really do have to drink it. But then if at midnight you really did intend to drink the toxin, and you got the million, then come the next day you would no longer have any reason to drink it: you've already been paid and drinking the toxin would make you unnecessarily sick.

Is there any way for you to win the money?

>>> Decide to drink the poison regardless of the polygraph results.  Honor that decision by taking the toxin at noon the next day despite having the million dollars in your bank account.  Problem solved, abeit some sickness must be endured.

Hmmm... This reminds me of the old Predictor paradox. The predictor is some kind of supernatural entity who puts a certain amount of money in two boxes if he predicts that you'll open both of them, and a different amount if he predicts you'll only open one of them. Once he's put the money in, though, it is there and nothing can be done to change that. So it doesn't really matter what you do. Or does it?

In this puzzle, let's say I do what Benjamin suggests. I am a good and honest person. I plan to drink the toxin before noon whatever happens. I always keep my promises. But..... After the money is given to me, what difference does it make if I drink the toxin? Nothing at all can change the fact that I've been given the money. There is no possible benefit to drinking the toxin later on.

I think that this idea (of promising to drink the potion regardless) doesn't work from the perspective of pure rationality. After the money has been given to you, there is no rational reason for drinking the toxin. There are no benefits at all, and you will end up worse than you were. Knowing that you are rational, you know that you will not drink the toxin. Therefore you will fail the test.

The only way that you can succeed is if you bring in the ideas of morals and ethics and other philosophical concepts. To keep your promise after the fact you have to keep promises for the sake of keeping promises. This requires either religious beliefs or an abstract idea of right and wrong. You have to keep your promise because you believe that it would be wrong not to.

This implies that this is an extremely rare breed of dilemma. Using only the logical rules of the puzzle, without resorting to higher powers, the rational action will always end up worse than the irrational action (using rational and irrational in the purely logical sense of picking the option that will be most favorable. It's not a moral judgment on the value of keeping promises!). This is paradoxical, because in this case the rational action does not end up maximizing profits. It's no good trying to say that the rational action would be to drink the toxin, as this would maximize profits, because there is no doubt that drinking the toxin after the fact is an irrational thing to do. A rational person will never do an irrational action by definition.

This is better than the Prisoner's Dilemma in this regard, because in the PD you can show by pure reason that in the long run altruism is the most rational action. The pure rationalist can play the PD and maximize his outcomes. In this situation (without bringing in external help), the pure rationalist will always lose to the irrational action, which is paradoxical.

Very interesting... Any thoughts?

Edited on April 20, 2004, 11:49 pm

Posted by Sam on 2004-04-20 23:42:19