[EM] CC incompatible with Participation & Consistency
nkklrp at hotmail.com
Sat Jan 19 16:13:48 PST 2002
Say that before you vote, there's no BeatsAll winner, and the
circular tiebreaker picks X as the winner.
Then you & a few others add your ballots, and you all vote X over Y,
and Y over Z.
But it happens that, before you voted, Y's only defeat was by Z,
and Y lost to Z by a 1-vote margin.
So now you've made Y beat Z and become the BeatsAll winner.
That shows CC's incompatibility with Participation.
Say we specify that all of the new voters voted X in 1st place.
Now the original voters elected X, and the new voters would elect X,
but, when combined, they elect Y.
So CC is also incompatible with Consistency.
I should add that no other pair-comparison is close enough for
the new voters to affect it.
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