There are many definitions of monotonicity.
IRV ensures that by adding ballots having the current winner as first
choice, that winner will remain.
IRV cannot ensure that by replacing ballots that do not have the current
winner as first choice by the same number of ballots with this winner in
first place, we would still have the same winner.
Thanks to Warren for the reference, I will comment soon on median voting
limitations...
Stéphane
PS: My name is pronounced ruyon (maybe it can help for the spelling: Rou ill
on ;)
From: Kristofer Munsterhjelm <[EMAIL PROTECTED]>
To: Warren Smith <[EMAIL PROTECTED]>
CC: [EMAIL PROTECTED]
Subject: Re: [EM] [Election-Methods] about IRV & median voting (answers to
Dopp, Roullon)
Date: Thu, 07 Aug 2008 10:32:26 +0200
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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