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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