BLP vote shares
Every election result is a point whose shares add to 100%, so the joint distribution sits on a simplex: a line for two shares, a triangle for three, a tetrahedron for four. Look at one setup at a time, or put A, B and C next to A and B only to watch a dimension disappear. Hover any result to find it in every view.
Each share on its own is binomial: nj ~ Binomial(N, πj), with SD √(πj(1 − πj)/N). The dashed line is the mean πj.
Correlation between shares
Cov(ŝj, ŝk) = −πjπk/N
Corr(ŝj, ŝk) = −√(πjπk / ((1 − πj)(1 − πk)))
What removing C does