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.
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