Re: The envelope problem, and a possible solution
[ QUOTE ]
it takes only logic ... to see that the bet in (2) can be converted to an obviously poor bet ... That's not a mystery to me or anyone who thinks through it clearly.
The challenge is to come up with a consistent way of computing which bets to take. It's a lot harder than it looks. The envelope paradox is simplified to make the basic contradictions clear, which makes it easy to "resolve" with ad hoc techniques. But those techniques are not much practical help in realistic problems.
[/ QUOTE ]
I am stubbornly sticking to my prior my belief about you, Aaron, which is that you are an educated and intelligent man who can communicate effectively via the written word. That's why I've got to believe that there is some gross misunderstanding going on here.
In both the Paradox and in PTB's Prop Bets, the only techniques we need to use in order to arrive at the "sensible" conclusions are the techniques of elementary probability, such as assumptions [1]-[4] of my previous post. These are consistent, they are certainly not ad hoc, and they are extremely helpful in a wide array of realistic problems. Are you denying this? What am I missing here?
|