[EM] NPV vs Condorcet

[Kristofer Munsterhjelm]

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.