Economists v philosophers Round V
John is at the casino and he puts $100 on the number 12 spot at the roulette table. While the wheel is spinning, John dies suddenly. The body is removed and the casino manager finds John’s wife and sole heir Jane. The manager now needs to give Jane the money she’s inherited from John. Instead of just giving Jane the $100, however, he decides to cover the wheel and offer Jane the following choice. She can either choose to just take John’s $100 or else she can leave the $100 on the table and the manager will uncover the wheel. If it turns out that the ball has landed in the 12 slot Jane will get the $3,200 payoff, if not she will get nothing. Jane chooses to take the $100 so the manager gives it to her, then uncovers the wheel revealing that the ball had, in fact, landed on the 12.
Yglesias agrees that Jane adopted the correct decision procedure (since the odds were unfavorable), but nonetheless goes on to say
The purpose of the procedure, after all, is to get you the most money possible, and given these circumstances, Jane could have made more money by taking the bet. Thus, there is a sense in which Jane did the wrong thing
This example seems to me to suffer from exactly the same problems as the stock market example put up in the Stanford Encyclopedia of Philosophy which, the post informs me, is by Walter Sinnott-Armstrong .
First, the claim that the choice of accepting the manager’s offer would have yielded a higher outcome is unjustified. The casino might, for example, have welched on the bet. Since this is a low-probability event, it’s true that, conditional on the knowledge that the ball landed on the 12, accepting the offer would be the better option in the ex ante sense I’ve proposed. But on the ‘actual outcome’ criterion Yglesias and Sinnott-Armstrong are defending, there’s no way of telling for sure whether it was better or not.
Second, while betting on 12 and being paid the $3200 is ex post a better option than not betting and being paid the $100, it’s not the best option. It would be better still, for example, to leave the $3200 on the table and bet it on the winning number for the next roll (assuming of course, that the casino paid up).
As in the stockmarket example, if we have perfect knowledge, no best option exists. On the other hand, if we don’t have perfect knowledge, we can’t identify the best option, even ex post.
Does it do any harm to say to say that “The purpose of the procedure, after all, is to get you the most money possible”? I think it does. A characteristic feature of the optimal procedure in most choice problems of this kind is that it gives you a zero probability of getting the best possible outcome. By contrast, as in the Reagan example I posted recently, there are lots of problems where one option may give you the best outcome with high probability, but a very bad outcome with low probability. It’s easy to slide from “The purpose of the procedure, after all, is to get you the most money possible” to a decision rule that says something like “maximize the chance of getting the best outcome” and the latter is clearly wrong.
To sum up, the criterion that the best action is the one with the best actual consequences is at best useless and at worst dangerously misleading as a guide to decisions, and non-operational as a rule for evaluation. At least for an economist, that’s enough reason to say that it’s not a sensible criterion.
A final point. It seems to me that philosophical examples have a lot of gratuitous violence. Why is this? Did we really need to kill John in the first act?