[EM] British Colombia considering change to STV

[Jonathan Lundell]

On Apr 30, 2009, at 8:38 AM, Kristofer Munsterhjelm wrote:

> Kathy Dopp wrote:
>> STV has *all* the same flaws as IRV but is even worse.
>> It is unimaginable how anyone could support any method for counting
>> votes that is so fundamentally unfair in its treatment of ballots and
>> produces such undesirable results.
>
> The reason is very simple: the Droop Proportionality Criterion. The  
> DPC ensures that a group of voters greater than p times (the number  
> of voters)/(the number of seats + 1) can get p representatives on  
> the council.
>
> As the number of seats increases, the actual result within each  
> group becomes less important, whereas that the DPC is held becomes  
> more important. Therefore, STV works well.
>
> Other multiwinner methods fulfill the Droop Proportionality  
> Criterion, as well, but they're not very well known. Schulze's  
> Schulze STV (reduces to Schulze, which is Condorcet, when there's  
> only one winner) as well as QPQ also meet this criterion.
>
> According to my tests, QPQ is better than STV, which in turn is  
> better than Condorcet modifications to STV. I haven't tested Schulze  
> STV, since it requires a lot of space for very large assemblies.
>
> The precise scores are (lower is better):

Remind us, please, what your scores are.

>
> Mean    Median   Method name
> ----------------------------------------------
> 0.1491  0.11647  QPQ(Sainte-Laguë, sequential)
> 0.15509 0.13423  QPQ(Sainte-Laguë, multiround)
> 0.20964 0.20585  STV
> 0.22939 0.21622  STV-ME (Plurality)
>
> My simulation has somewhat of a small state bias, though: it counts  
> accuracy of small groups more than accuracy of large groups.
>
> A smaller simulation (only assemblies of few seats, so that Schulze  
> resolves within reasonable time) gives these results:
>
> Mean    Median   Method name
> ----------------------------------------------
> 0.12374 0.01416  QPQ(Sainte-Laguë, multiround)
> 0.12754 0.02213  QPQ(Sainte-Laguë, sequential)
> 0.14783 0.0316   Schulze STV
> 0.15264 0.04725  STV
> 0.15984 0.05199  STV-ME (Plurality)
>
>> STV is nonmonotonic, counts the 2nd and 3rd choices only of some
>> voters in a timely fashion when it could help those choices win, does
>> not even count any of the 2nd or 3rd choices of a large group of
>> voters whose first choice loses, excludes some voters from the final
>> counting rounds, and is in all ways the worst imaginable voting  
>> system
>> that I've ever heard anyone propose.
>
> I'm not certain if it's possible to make a multiwinner method meet  
> both the Droop proportionality criterion and monotonicity. The party  
> list apportionment criterion most like monotonicity is this (quoting  
> from rangevoting.org):
>
> Population-pair monotonicity: If population of state A increases but  
> state B decreases, then A should not lose seats while B stays the  
> same or gains seats. More generally, if A's percentage population  
> change exceeds B's, then A should not lose seats while B stays the  
> same or gains seats.
>
> (end quote)
>
> In the context of groups with solid support, this should mean "If  
> more people stop supporting group B, or switch their support from  
> group A to group B, then A should not get fewer seats in the  
> assembly".

There's a typo here, right? Should be "switch their support from group  
B from group A".

> The rangevoting page then continues,
>
> "Theorem (Balinski & Young): All 'divisor methods' (and,  
> essentially, only divisor methods) are both House and population- 
> pair monotone; but they all disobey quota.", and "Meanwhile,  
> Hamilton satisfies quota but disobeys both monotonicity properties.  
> That leads to the question of whether an apportionment method exists  
> that satisfies all three properties. The answer is "no" – the last  
> two properties are incompatible ..."
>
> Quota is the same as Droop proportionality in this case.
>
> It might not be applicable to ranked methods, but at least there's  
> the possibility. If the above can be generalized to ranked methods,  
> then the best we can do is to have it monotonic within groups.
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