Juho wrote:
On Mar 10, 2010, at 7:26 PM, Kristofer Munsterhjelm wrote:
Juho wrote:
I'm not aware of any sequential candidate elimination based method
that I'd be happy to recommend. One can however describe e.g.
minmax(margins) in that way. Eliminate the candidate that is worst in
the sense that it would need most additional votes to win others,
then the next etc. In the elimination process one would consider also
losses to candidates that have already been eliminated (I wonder if
this approach makes it less "natural looking" than the elimination
process of IRV).
To my knowledge, Schulze-elimination is the same as basic Schulze. In
other words, if you run Schulze, eliminate the loser, run it again,
etc, you end up with the original result. That's not very useful, but
still...
It might also be that any "full-blown candidate elimination method"
(you run the election as if the one that was eliminated never stood)
with a weighted positional base method (Borda, Plurality, ...) is
nonmonotonic. I can't prove it though!
One more addition to this elimination discussion. Maybe ability to give
an ordering of the candidates is more important (and more generic) than
using an elimination process. The preference graphs that many Condorcet
methods use may not be as easy to understand to the voters as plain
ordering is.
In principle single winner methods need not be able to produce any
ordering of the candidates. It is enough to pick the single winner. But
in order to make it easy to the voters and candidates to understand the
results (and to explain e.g. how close some candidate was to winning the
election) good and simple graphical and numeric information may be
valuable in practical elections.
Both of the advanced methods give an ordering, as do the obvious ones
(Minmax, least reversal, Copeland, second order 2-1-Copeland...). They
don't provide numerical information ("this close to winning"), but that
is hard: I read a paper about extending Schulze to do so, and it used
some rather complicated use of linear programming. Could you sell that
to the public? Not very likely, unless they happened to be of the same
kind that voted for the use of Meek in local New Zealand elections.
(I have to add that if people want to keep the USA as it mostly is, a
two party based system, then I must recommend FPTP :-). And if not,
then maybe also some additional (maybe proportionality related)
reforms are needed.)
Wouldn't something like Condorcet multiwinner districts be better?
Pick a good Condorcet method and send the 5 first ranked on its social
ordering to the legislature. That would pick a bunch of centrists
(thus have "stability"), but it would pick the centrists people
actually wanted.
Hm, that might not provide a true two-party system, though. One could
also have a "PR" system where the number of votes is weighted so that
parties with broad support gain superproportional power, but then the
question becomes why one should bother with the PR at all.
Maybe Condorcet + single winner districts is a more stable approach.
That combination makes a two-party system just somewhat softer, and
allows the party structure (in individual districts) to evolve in time.
Another approach to systems between proportional representation and the
two-party approach could be to have a proportional method but use
districts with only very few representatives (2, 3,...). That would
provide rough but in principle accurate proportionality and still give
space only to few major parties. (Obviously my definition of full
proportionality must be "with 1/n of the votes you will get one seat
(where n = number of representatives)".)
An interesting hybrid, I think (and I've mentioned it before), would be
to have a bicameral system where senators are elected according to a
statewide Condorcet method (pick a good centrist for each state), and
the House representatives are elected according to PR.
Having just a single from each state may be /too/ centrist, but to pick
two senators from each using a proportional ordering might work - as
long as it doesn't introduce partisan division.
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