8 Aug
2013
8 Aug
'13
12:07 p.m.
THEOREM by W.A.Whitworth 1878 then J.L.F.Bertrand 1887: If candidate P gets p votes and rival candidate Q gets q votes, p>=q, then the probability that throughout the count P is always ahead, is (p-q)/(p+q).
--More generally, the probability that P always has more than k times Q's vote-count, equals (p-k*q)/(p+q) exactly, if k>0 is an integer and p>=k*q. This more general theorem was shown by A.Aeppli in 1923 using a "reflection and rotation" geometric idea, not just reflection. Marc Renault: Four proofs of the ballot theorem, Maths Magazine 80,5 (Dec 2007) 345-352.