Henrik: I figured that after doing all the theoretical calculations some real numbers might be interesting, so for fun I went to the historical records of all US presidential elections from 1856 to 2004 and got the Dem/Rep vote percentages. I normalized those to 100% of the vote to minimize the effect of odd elections (like 1860), then took the ratio of Dem to Rep.

For 38 elections, the mean was 0.994 with S.D. 0.29. On a histogram with bin size 0.2 I got a distribution looking pretty much normal, considering the small population size:

Bin/Frequency
0/0
0.2/0
0.4/0
0.6/2
0.8/7
1/11
1.2/11
1.4/3
1.6/2
1.8/1
2/1

Throw the numbers in a quick Excel plot and it's pretty neat.

This suggests to me that the large majority of US presidential elections are determined by chance.

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