On Mar 11, 2010, at 11:41 PM, Kristofer Munsterhjelm wrote:
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")
At least minmax(margins) does. It gives each candidate the number of
additional votes that would guarantee victory to them. That is quite
simple and could be used to e.g. provide information to the voters
while the counting is in progress ("1000 votes still not counted, 100
first preference votes would be enough to win"). Also a simple
histogram would tell how each candidate is doing at the moment.
, 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.
Yes, having also representatives that are non-partisan by nature could
add something interesting and useful to an otherwise very party
oriented and divided community.
(One could btw call this kind of representatives "widists" instead of
"centrists" since Condorcet would pick a candidate with wide support
instead of a candidate that is supported specifically by the centrist
parties. Or maybe also term "centrist" has some similar meaning in
addition to referring to the parties in the centre.)
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.
This sounds a bit risky. An alternative approach would be to elect the
single candidates from smaller areas and thereby increase their number
and their locality. Local representatives would also be more tied to
all the people that they are supposed to represent. If we go down to
village level then all voters may know the representative personally
and that candidate is also personally responsible to each one of them.
Juho
----
Election-Methods mailing list - see http://electorama.com/em for list info
