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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