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

[Stéphane Rouillon]

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 <km-elmet at broadpark.no>
>To: Warren Smith <warren.wds at gmail.com>
>CC: election-methods at electorama.com
>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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