On Tue, 11 Nov 2008 20:16:55 +0100 Kristofer Munsterhjelm wrote:
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.
My point was that this is a problem affecting ANY election method,
thus not needing special attention for Condorcet.
Again, the method does not matter. If the name Bush turns up from two
different sources it is essential to determine whether it is:
One candidate, for whom the votes must be summed or
Two candidates, competing separately, that must somehow be identified
as such.
That's true, but for methods that only need an array (like Plurality, or
a weighted positional method where the method was agreed upon in
advance), this happens more or less informally. States don't pass around
explicit arrays with candidates in specific orders when tallying
Presidential votes, they just say "Bush got this many, Gore got that many".
The other side of the coin is that non-summable methods would be in real
trouble. Any compact solution defaulting to a method that isn't summable
would somehow have to set up an infrastructure (either in counting or in
communication), wherein a central unit coordinates.
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.
Not being sure what you mean by "simple merge", I will repeat my demand.
For example, assume A is a write-in which CANNOT be planned on but
must be adjusted for when counting the ballots. The national NxN
array must include A reflecting proper counts for all votes in the
US. True that such an A is unlikely, but to be expected more if you
assume it will never happen.
A simple merge sorts the arrays by name (and tie-breaking info, like
name of state of origin). Then it merges the data, summing cells if the
candidate in question exists in both matrices, otherwise inserting the
relevant rows and colums in the right place so that the result (merged)
matrix is still sorted.
For instance, consider these matrices:
x A B
A -- 30
B 35 --
and
x A C
A -- 100
C 25 --
Assuming that this represents 100 votes for A then 100 A>C is represented.
If B was also in the matrix there would be 100 A>B. This last 100 fails
to show up below:
The result is
x A B C
A -- 30 100
B 35 -- 0
C 25 0 --
and the expanded matrix stays sorted. Individual write-ins can be
handled by considering each voter's ballot as a Condorcet matrix, then
merging that in as above. In extreme case (each voter names a different
write-in), that would make the matrix expand by a lot, but if that's a
concern, sparse representation formats can be used.
--
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Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.
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