[EM] [Election-Methods] about IRV & median voting (answers to Dopp, Roullon)

[Kristofer Munsterhjelm]

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.