[EM] Single/Multimember districts (was Re: In defence of IRV)

[Kristofer Munsterhjelm]

On 11/18/21 9:57 PM, robert bristow-johnson wrote:
> 
> 
>> On 11/18/2021 9:12 AM Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
>>
>>   
>> On 16.11.2021 15:52, robert bristow-johnson wrote:
>>> Unfortunately it's top-two vote getters.  Each voter has two votes.
>>
>> That's not a particularly good method, no; but if you succeed getting
>> BTR-IRV enacted, and you decide to advocate for replacing the top-two
>> method with STV, you could use the BTR version.
>>
>> Every STV variant with the same surplus election mechanism passes Droop
>> proportionality, so modifying the elimination mechanism (like BTR-IRV
>> does) won't make it fail Droop. So getting BTR-IRV passed shouldn't
>> hinder future adoption of STV.
>>
> 
> But Kristofer, there is a little bit of a problem using BTR for
> multimember STV.  Consider the 2009 election in Burlington.  Suppose we
> stopped at two candidates (because we have two seats) instead of one.
> Then the Plurality candidate (Kurt Wright) and the Condorcet candidate
> (Andy Montroll) would be elected to the two available seats.  The Hare
> IRV winner (Bob Kiss), who was actually preferred by voters over the
> Plurality candidate (Wright), which is what was demonstrated in the IRV
> final round in 2009, that IRV winner would not have been elected in
> multi-winner BTR-STV.  Some people might say that Kiss should be in the
> top two (and elected in a two-winner contest).

Fortunately, the multiwinner version has an additional election 
component where candidates who exceed a Droop quota of first preferences 
are always elected and the surplus redistributed. This avoids the 
problem you're referring to.

To show in practice: the Burlington election ballots are

  1332: M>K>W
   767: M>W>K
   455: M
  2043: K>M>W
   370: K>W>M
   568: K
  1510: W>M>K
   495: W>K>M
  1289: W

after every candidate but Montroll, Kiss, and Wright have been 
eliminated. The first preference counts are as follows:

Montroll: 2554
Kiss: 2981
Wright: 3294

The Droop quota for two seats is 8829/3 = 2943.

As both Wright and Kiss exceed a Droop quota before any reweighting has 
been done, they both win, and so the two-seat outcome consists of Wright 
and Kiss (not Montroll).

The more I look, the more the Burlington election looks like the Left, 
Center, Right example (https://electowiki.org/wiki/Left,_Center,_Right). 
Not only does IRV get both wrong, but they both show that house 
monotonicity is incompatible with Condorcet and the DPC.

-km