Re: The envelope problem, and a possible solution
[ QUOTE ]
@econ: Depending on the amount of money in the envelope, someone might indeed use this information for switching which I expect to influence EVj. However, as I understand it, stated in the original problem, it's not a matter of psychology. If you are indeed allowed to estimate EV according to the method of argument 1, switching would always be +EV. And if you believe arguemtn 2 to be true, it wouldn't matter. It's therefore that I simplified the problem to always switching.
[/ QUOTE ]
My argument isn't based on psychology, it's based on Bayesian statistics. According to Bayesian statistics, statisticians can have believes about random variables before they gather any data on them. These beliefs are called "priors."
The only prior that allows arguement 1 to be correct is believing that the value of the smaller envelope is distributed uniformly from 0 to infinity. But this distribution doesn't make sense . . . it means you think $5 Billion is as likely a value as $5.
For any other "prior," argument 1 fails.
|