[EM] British Colombia considering change to STV
Kristofer Munsterhjelm
km-elmet at broadpark.no
Thu Apr 30 08:38:59 PDT 2009
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.
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