[VanillaCafe]

Maybe I don't quite appreciate the significance. The Informal Proof section seems to boil down to: If the vote is tied and there is one vote left, then that last vote determines the outcome. The existence of a swing vote in this circumstance doesn't seem very surprising.

[verteu]

"Part One" of the informal proof is trivial, for the reason you've described. But "Part Two" is not: It shows that if the "pivotal voter" from Part One votes B>C, then B will beat C in the election, even if everyone else votes C>B.