The question was recently posed: how to choose between Ph.D. programs? The answer can be reduced to a trivial mathematical assessment, whose solution lies in the determination of both (a) the function form and (b) the value of an unknown function, V.
Whatever the form of V, you want to maximize its specific form V(h,m), where h is a test statistic that evaluates the probability of being professionally and personally happy and m is a test statistic that evaluates the probability of your program being well funded and monetarily well supported. Please note that in principle, the function is an approximation – it can have a correlation on m’, the amount of money you will be paid to be part of the program (note! m’ can go negative in certain Ph.D. programs, so don’t choose based on unsigned quantity|m’| but on the actual value m’). However, in principle h and m’ are correlated and that correlation can be factored into h during the maximization process.
I should say that the form of the function V(h,m) is not analytically known, but it has certain boundary conditions. I repeat them here for completeness:
- V(h,m) -> :-( as h->0 and/or m->0
- V(h,m) -> :-) as h->infinity and m->infinity
The form of the function in the intermediate condition that h is finite and m->infinity, or m is finite and h->infinity, is not well described.