Early Election Results

Let Jones and Smith be the only two contestants in an election that will end in a deadlock when all votes for Jones (J) and Smith (S) are counted. What is the expectation value of X_k=|S-J| after k of a total of N votes are counted? The solution is

<X_k>=(2N(N-1; |_k/2_|)(N-1; |_k/2_|-1))/((2N; k))
={(k(2N-k))/(2N)(N; k/2)^2(2N; k)^(-1) for k even; (k(2N-k+1))/(2N)(N; (k-1)/2)^2(2N; k-1)^(-1) for k odd.

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Handelsman, M. B. Solution to Problem 10248. "Early Returns in a Tied Election." Amer. Math. Monthly 102, 554-556, 1995.

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Early Election Results

Cite this as:

Weisstein, Eric W. "Early Election Results." From MathWorld--A Wolfram Web Resource.

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