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I think there are misplaced parentheses in your equations. In section 3, they should be:
and so on in future equations. Essentially the parentheses should encompass the +10 term as well in all your equations. It seems your personal calculations were correct because the actual probability bounds that you gave match up with this version of the equation.
Thanks for an in-depth writeup!
Sorry, I shouldn't have assumed that hedonic treadmill is a well-defined/known term. When I say "hedonic treadmill w/ respect to education" I mean a scenario where I worked hard to go to a "top" undergraduate institution and thought I'd feel satisfied but don't end up feeling so. Then, I think that pursuing a "top" MBA will make me satisfied and I work hard towards that and the cycle repeats. Similarly for my career w/ respect to getting that next promotion, etc. The maximiser vs satsificer dichotomy does help as a mental model of how I might alter my mental calculus but unfortunately I think the hedonic treadmill applies quite broadly to my life and not just to a specific issue. Thus, it's a bit difficult for me to divert my attention elsewhere.
Like this idea. This approach can be seen in hedge funds as well. An analyst makes a bet on how/why a stock will perform a certain way and places a corresponding monetary position. The best analysts will take the extra step and conduct a postmortem if they lose money OR if they make money but not for the reasons that they had previously outlined.