In article <email@example.com>, Robert Israel <firstname.lastname@example.org> wrote: [...] >So the probability that the winning candidate loses in the popular vote >is approximately F(-m s/sqrt(SN-(ms)^2)), where F is the standard normal >cdf. > >For example, with S=51 and N=10^6 we would have s = 5.726033806 >and m = 797.8847608, and F(-m s/sqrt(SN-(ms)^2)) = F(-.8323716341) >= .2025996041. > >Asymptotically, m = sqrt(2 N/Pi) and s = sqrt(2 S/Pi), so >-m s/sqrt(SN - (ms)^2) -> -2/sqrt(Pi^2-4) = -.8255161606.
Very slick, I like it. Just as a reference point for some of us who may be slightly inclined towards the concrete, here is a simulation of 20 elections with N=101, S=11, with the state by state and national totals, and electoral result, each marked + or - accordingly as the given candidate won or lost:
Three runs of 10000 elections gave anomalous results 1981, 1940, and 1928 times. Your formula predicts 10000*F(-0.86185771) = 1943.83 . Almost too good! ... but it was fair and square. ( Although, one might fairly argue that if they hadn't looked good, I would have tried some more. )