[EM] British Colombia considering change to STV

[Kristofer Munsterhjelm]

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):

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". 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.