Please provide a simple example of a Condorcet matrix synthesized out of
an FPTP ranking. Apparently I'm not understanding this at all -- maybe
there *is* a way to look at this that doesn't involve truncation. But
I'm very sceptical of any proposal that involves aggregating different
voting methods in various subjurisdictions into a single result.
Thanks in advance.
--Bob
Kristofer Munsterhjelm wrote:
Dave Ketchum wrote:
On Mon, 20 Oct 2008 19:51:55 -0700 Bob Richard wrote:
> Some states may not be up to Condorcet instantly. Let them
stay with FPTP
> until they are ready to move up. Just as a Condorcet voter
can choose to rank
> only a single candidate, for a state full of such the
counters can translate FPTP
> results into an N*N array.
What would enforcing the truncation of rankings (to a single
ranking) for part of the electorate -- but not the rest -- do to the
formal (social choice theoretic) properties of any given Condorcet
method? Would the effect be the same for all Condorcet-compliant
voting methods?
It is not a truncation. It is interpreting FPTP ballots as if used
by Condorcet voters. Should result in pressure on all states to
conform ASAP.
I am ONLY considering FPTP and Condorcet The exact Condorcet method
cold be stated in the amendment. Note that this is only a single
national election, though there would be extreme pressure on other
government uses of Condorcet to conform.
If you're considering only FPTP and Condorcet, synthesize a Condorcet
matrix out of the FPTP ranking. That'll fix the consistency problems
with Condorcet, since if the other state's already Condorcet, you'll
be adding a real Condorcet matrix and not just a ranking.
On the other hand, perhaps the state will use arguments similar to
those in favor of winner-takes-all and say "if our method says A > B >
C, then we have to maximize the chances of A winning, and failing
that, that B wins". I'm not sure whether the (hypothetical so far)
agreement should then demand Condorcet matrices, or if it should let
the states choose whether to use rankings instead.
Range might be more difficult, since one can transform a rating into a
ranking (and a ranking into a Condorcet matrix), but not easily a
Condorcet result to a rating, or a ranking to a rating. Some Condorcet
methods exist that return aggregate rated ballot outputs (a rated
"scoring" instead of a social rank ordering), but they're very
complex; in an earlier post, I mentioned a continuous variant of
Schulze that uses quadratic programming.
One solution to this might be to have states submit either a Condorcet
matrix or a range vector (n entries if it's plain Range, 2n if it's
with Warren's no-opinion option). Then, at the end, all the Range
vectors are added and the Range result is computed for this. That
becomes one ordering, and a Condorcet matrix can be synthesized from
it. That artificial Condorcet matrix is scaled by the voting power of
the Range states and then added to the real Condorcet matrix, and the
result is given based on that.
--
Bob Richard
Marin Ranked Voting
P.O. Box 235
Kentfield, CA 94914-0235
415-256-9393
http://www.marinrankedvoting.org
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