Warren Smith wrote:
1. Dopp wanted simple nonmonotone IRV elections examples.
See
http://rangevoting.org/Monotone.html
and here is another:
#voters Their Vote
8 B>A>C
5 C>B>A
4 A>C>B
If two of the B>A>C voters change their vote to A>B>C, that causes
their true-favorite B to win under IRV.
(If they vote honestly ranking B top as is, then their most-hated
candidate, C, wins.)
Those are simple enough, but do you have any that satisfy Dopp's
particular specifications? That is, A wins, but if k (for small k,
preferrably 2) voters join and vote A top, then someone else
(preferrably, the ones they ranked last) wins.
I think that that'll require more than three candidates. My reasoning is
that, in order for an A-first vote to change the winner away from A, it
must have a chaotic influence on the next round. But in three-candidate
IRV, there are only two rounds, and since A is put first, the first
round can't change from A to non-A. Then the second round must be A and
someone else - call that someone else B. But if it's the case that, in
aggregate, B > A and A > C (which is what you'd use to cause
nonmonotonicity), then the addition of the two votes couldn't have
changed the other candidate from C (originally) to B (now), since the
first round only looked at the first preference votes, and the
newcomers' ballots ranked A first.
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