Juho wrote:
On Aug 28, 2008, at 13:18 , Kristofer Munsterhjelm wrote:
One more approach to this would be to provide "perfect" continuous
geographical proportionality. One would guarantee political and
geographical proportionality at the same time. One would try to
minimize the distance to the closest representative from each voter
and make the number of represented voters equal to all
representatives. In short, distribution of representatives would be
close to the distribution of the voters (while still maintaining also
political proportionality).
There would, of course, be limits to the guarantee of having both
political and geographical proportionality at the same time. If your
immediate vicinity have candidates whose opinion you completely
disagree with, one of geographical proportionality and political
proportionality will have to sacrifice part of itself for the other.
Yes, smaller political groupings would not get as "near"
representatives. That is also natural since there are so few of them. It
is also possible that close to the voter there are many party A
supporters and therefore they get a seat. In the next neighbourhood
there are lots of B part supporters, and so on. But probably we would
still get a more accurate geographical proportionality than with large
districts.
One seat districts would be geographically very proportional, but your
nearest representative of your own party could be far away. In this new
model one could try to improve also this (=> geographical
proportionality within parties too; or count weights for the distances
based on the preferences of individual voters).
That's right. Patching up one-seat districts by using either FMV or MMP
detrimentally affects the geographical proportionality aspect, since
either some seats no longer go to the "true" winners (FMV) or
geographically unrelated top-up seats (MMP), as you said.
In the long run, the effect might self-stabilize, if for no other
reason that if there are many Y-ists in an area, one of them is going
to notice and want to become a candidate.
I'm not quite sure how to do perfectly continuous geographical
proportionality.
I think perfect geographical proportionality would violate perfect
political proportionality, so we can only provide approximate
geographical proportionality if political proportionality is a must.
Let's take a basic closed list method. First we will count the exact
proportionality split between the parties. Then we will (in theory)
check all possible combinations of candidates that respect the agreed
political proportionality split. Out of these we could elect e.g. the
one where the average distance to the nearest representative is lowest.
Here's one idea, based on the opinion reconstruction ideas I've been
having the last few days. The ballot format is closed party list PR.
First figure out how many seats each party is entitled to, which can be
done using Sainte-Laguë. Call the number of representatives p. Then
construct an estimate of the probability function over all locations in
the country, that a random voter there votes for the party - this can be
done using kernel density estimation if I'm not mistaken. Finally,
choose a set of p from the number of candidates running on the party
list so that the difference between the estimate made using population
data and the estimate made using only the points for those candidates is
minimized. Elect that subset, which, using this method, should be the
candidate subset whose geographical distribution most closely
approximates the geographical distribution of the voters.
There are two problems with this idea (three if you count the
computational intractability of trying all subsets). The first is that
the party always gets the number of seats it "deserves" on a national
basis, meaning that if all the candidates are clustered around the
capital, there's no incentive to spread out because all the subsets will
be equally bad (and thus equally good). That could perhaps be handled by
not listing candidates more than a certain distance (or number of
voters) away from the voter, so that having too distant candidates makes
the party incur an effective vote penalty. If one does so, however, even
a perfectly estimated probability distribution will differ from the real
probability distribution.
The second is the devil in the details of kernel density estimation:
it's not obvious to me how one would pick the bandwidth. Would it have
the same bandwidth for the estimation based on the candidate set as that
based on the population set (because candidates are people as well), or
different bandwidths? And if so, how does one determine the optimal
bandwidth choice for two-dimensional KDE? I know too little about kernel
density estimation to answer this.
For this method, the similarity measure would probably be one of the
good proportionality measures as mentioned in
http://www.votingmatters.org.uk/ISSUE20/I20P4.PDF : root-mean-square,
Sainte-Laguë index, Gini disproportionality measure, Loosemore-Hamby
index, or Monroe index.
It would be very hard to generalize this idea to party-neutral PR, but
if the method works by reconstructing opinion space based on
preferences, then the geographical distribution could be added as yet
another dimension (or rather, two). Political/geographical balancing
would then be done by artificially smoothing the data on the
geographical dimensions, thus dampening both political
disproportionality as well as the incentive towards parochialism.
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