Dave Ketchum wrote:
On Sat, 08 Nov 2008 18:45:38 +0100 Kristofer Munsterhjelm wrote:
I'll add that this phrasing would give states the same power no matter
the relative turnout. If that's not desired, it could be rephrased
differently, but giving states the same power is closer to the current
state of things. The continuous electoral college variant does not
take into account the 23rd Amendment, either.
Ugh.
All of which is fixable. I was just trying to give a rough idea of how
it may be phrased.
Yes. What I'm saying is that it's theoretically possible to
incorporate any voting method into this; however, the results might be
suboptimal if you try to aggregate, say, IRV results this way, since
you'd get both the disadvantages of IRV and Condorcet (nonmonotonicity
for the former and LNH* failure for the latter, for instance).
IRV is a distraction since such ballots could and should be counted as
Condorcet.
Should be a method that at least tries for a result based on comparative
strength of candidates.
Again, that's true. The point of my generalized transformation scheme is
that any method could, theoretically, be incorporated into this form of
compact. Therefore, complaints that it's biased in favor of explicit
Condorcet methods would be weakened (although not completely eliminated,
because of the intersection of limits I mentioned).
States have differing collections of candidates:
In theory, could demand there be a single national list. More
practical to permit present nomination process, in case states desire
such.
Thus states should be required to prepare their NxN arrays in a
manner that permits exact merging with other NxN arrays, without
having to know what candidates may be in the other arrays.
The easiest way to do this is probably to have the candidates sorted
(by name or some other property, doesn't really matter). When two
matrices with different entries are joined, expand the result matrix
as appropriate. Since the candidate indices are sorted, there'll be no
ambiguity when joining (unless two candidates have the same names, but
that's unlikely).
Two candidates with the same name is a problem to solve regardless of
method.
Sorting could be part of the joining, but I demand the results be
exactly the same as if the ballots had been counted into the final
matrix. Doable, but takes a bit of planning.
A possible tiebreaker for same names would be to prepend (or append) the
state of origin to each candidate name. In case two have the same name
in the same state, the state decides who gets to be "number one" and
"number two". These corner cases would be extremely unlikely, but it
doesn't hurt to specify them.
The results should be the same with a plain merge as with a single
count, since a Condorcet matrix entry cm[a][b] just lists how many
voters ranked A > B. Consider voters that couldn't vote on a given
candidate as if they had no effective preference regarding that
candidate. Then, by including the results of some other Condorcet
matrix, if A and B wasn't on that other matrix, cm[a][b] won't change.
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