[math-fun] Re: Death Valley marathon

Thanks to everyone who took the time to explain in more detail why the 7:1 split is right for both the Death Valley marathon version and the office building version. I wrote:

(I have a feeling that there's an Arrow-like theorem lurking here that says that certain seemingly compelling characteristics that fairness should have are actually incompatible.)

I totally retract that. There is in fact a complete first-order theory of this kind of fairness; it's called basic accounting, and the corresponding algorithm is called double- (or multiple-) entry bookkeeping. :-) Jim