[EM] British Colombia considering change to STV

[Kristofer Munsterhjelm]

Jonathan Lundell wrote:
> 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.

Each candidate and voter gets assigned a number of binary opinions or 
issues ("yes" or "no" for each). Each voter ranks the candidates so that 
those that agree with him on more issues get ranked above those that 
agree with him on fewer.

An "opinion profile" with regards to a subset of the electorate is 
simply a vector of k fractions (for k issues): the first is what 
proportion of the set say "yes" for the first issue, the second is the 
same for the second, and so on.

Then a method's raw (un-normalized) score is just the RMSE of the 
opinion profile of the council elected by that method (provided the 
ballots consistent with the ranking mentioned before) and the opinion 
profile of the people. The more like the people the council is, the 
lesser the RMSE, and the better the score.

In order to remove randomization effects (perhaps some opinion 
configurations are harder to fulfill than others), I make a bunch of 
random councils. The best one (most proportional) gets assigned score 
zero, while the worst one (least proportional) gets assigned score one. 
The normalized score is just the unnormalized score normalized between 
those two extreme points.

I do this lots of times (1000 times for the Schulze STV one) with 
different council, voter, and opinion numbers, and then the mean is 
simply the mean of the normalized scores, and the median is similarly 
the median. Most truly proportional rules have mean scores below 0.25. 
0.3 to 0.4 have semiproportional rules (D'Hondt without Lists), 0.5 and 
above is very majoritarian.

I think the small state bias arises from that the various opinions are 
completely uncorrelated. I'm not sure, though. For that matter, I don't 
know if the small state bias is real, but I'm guessing so from that 
IRV-as-multiwinner (n winners, just pick the n last eliminated) and SNTV 
gets quite good scores.

>> 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)

Note that these scores are lower. I think this is because I only checked 
small councils (since otherwise, Schulze STV would take forever, being 
exponential in the number of seats).

>> 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".

Yes. More accurately:

"If A gains more supporters (as a percentage of the population) than 
does B, then A should not lose seats while B gains them or stays the 
same". In the standard monotonicity case, B loses x while A gains that x.