If you look at the slightly more complicated version of 6 voters, with equal chance to vote a, vote b and abstain, you get 36 possible outcomes with lots of combinations possible.
Looking only at the ties
a b # of ways
0 0 1 (ways to pick 0 out of 6 * ways to pick 0 out of 6=1*1)
1 1 30 (ways to pick 1 out of 6 * ways to pick 1 out of 5=6*5)
2 2 90 (ways to pick 2 out of 6 * ways to pick 2 out of 4=15*6)
3 3 20 (ways to pick 3 out of 6 * ways to pick 3 out of 3=20*1)
or 141/729 ~= 19% for a tie.
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‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’ Trying to make sense of computers, The Error Log.
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