Wednesday, February 24, 2010

Difficult, difficult, lemon, difficult

Trying to come up with a case to cause trouble for Zimmerman's prospective possibilism. Why? Because I have to, it's my job.

Case 1. (Slightly modified from last time.)

If you go to WR and do everything you should (stay away from drinks), you'll bring about +10. If you go to DG, you'll bring about DG. The problem is that most people like you go to WR and they take to drinking. Then, you'll likely bring about something horrible.

My take on it: you have nothing to lose by going to DG and nothing to gain by going to WR instead. You ought to go to DG, not WR. The problem is that the prospective possibilist doesn't put into the calculation the negative values that arise because of a moral failing that you could avoid simply by not failing in that way.

Case 2. (Not sure this case makes sense, but ...)
You could end up in three places and end up there in four different ways. If you end up in A, that's +36. If you end up in B, that's -90. If you end up heading straight to C via the south road, that's +9. If you head there via the north road, that's +8.

Seems easy, right? Head north to A and collect your +36 whatever that is. Here's the complication. You've been assured that once you head north, you'll forget whether it's A that is +36 or B that is +36. You'll forget whether it is B that is -90 or A that is -90. You'll still remember that if you head to C from the north it's +8. It's not known whether you'll forget because of some failing you are responsible for or not. To the extent that this makes sense, you think it's just as likely that you'll forget for reasons you are responsible for as that you'll forget for reasons that you are not responsible for. You know that when you get to the fork up north where you have to choose whether to go for A, B, or head to C you'll choose to go for C because the expected value of going for C is greater than trying your luck and flipping a coin to decide between A and B. So, why not head for C straight away and take +9 rather than +8?

Why can't the prospective possibilist say this? Because the prospective possibilist sees the value of heading north as something like this:

.5(+36) + .5(+8)

That's greater than +9.

[Why does the prospective possibilist think of the prospective value of heading North this way? Because there's a 50% chance that the failure to know at the fork how to get the +36 is your fault and we fail to reflect that if we say what the prospective actualist says, which is that the prospective value of heading north is +8.]

If the thought that it's a sure thing that you'll forget what the values are that attach to getting A and B, just make it a case where you have exceptionally strong inductive evidence that you'll not remember and divide the expert explanations evenly so that half say that the reason that people who take the path north forget is that they suffer some moral failing that causes the loss of information (e.g., they start to eat the poppies) and half say that they forget and the cause isn't due to some moral failing of the agent (e.g., high altitude). I think we can get the numbers to work if there's some non-zero probability that you'll remember that A will net you +36 such that it seems the expected value of heading to C via the south exceeds the value of heading north but only because there's evidence that you'll forget because of a moral failure on your part.

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