Bertrand's Ballot Theorem

Bertrand's Ballot Theorem

Sorry for the vertical video, this was originally posted on Tiktok!

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[JK-fjeh]

"But what about bad paths that never come up to cross the x-axis?" From the setup of the problem this is impossible- we know Alice wins, so at some point it must cross the x-axis and we can do the mirror trick.

[fibbooo]

I love combinatorics! A great proof too- it makes use of the slight subtly that a tie is also a fail (in the visual language of the proof, a bad path is any that touch the axis, not just those that go beneath it) but a second rewatch made that clear. Great job!

[shayneweyker]

Doesn't it matter in what order the votes arrive to be counted? Consider: If the votes from subgroup of voters that as a group favor one candidate Alice are counted before a different subgroup that favor the other candidate Bob there mere fact that the votes are counted in this order will have biasing effect that will make early predictions of the winner flawed.

[qr]

I stumbled upon this problem trying to think about whether Bill and Ted was doomed to hell or purgatory of the grim reaper kept on extending tournament lenghts (best 3 out of 5, best 4 out of 7 ...) In that movie, bill and Ted's bogus journey 😆