On Fri, 06 Feb 2009 23:14:27 +0100 Kristofer Munsterhjelm wrote:
This is a simple question: say that you have a multiwinner method that
reduces to Condorcet in the single-winner case, and that this single
winner case uses a Condorcet matrix, so that it's properly summable in
this case. Then say that the method can be counted in the districts
using an (n+1) dimension matrix for the multiwinner election where the
council is of size n.
Each candidate voted for requires a row and column in the N*N matrix.
A possible optimization is to note that all candidates not yet voted for
have identical content for their entries, and thus let them share a common
row and column - expanding total rows and columns used as needed as votes
get counted.
However, it is number of candidates voted for that controls needed size of
matrix - it is only after counting all the votes that deciding which
candidates got enough votes to be interesting is possible.
Write-ins are a special case. If few are expected, they might be treated
as a single candidate. Then count can decide:
Few, as expected - ignore.
Too many to ignore - recount the votes, as needed.
Votes originally counted in multiple precincts or districts? The various
N*N matrices need not have identical sets of candidates - what I write
above should be enough clues as to needed work in merging counts.
Is this (hypothetical) method summable? The size of the matrix depends
(superpolynomially) upon the number of winners to elect, but not on the
number of voters or candidates.
See above.
(Whether or not it's summable, it probably wouldn't be practical in the
real world; with a parliament or council of 100 candidates, the matrix
would be 101-dimensional and thus far too unwieldy.)
While such a matrix may be a bit unwieldy, expecting voters to usefully
analyze 100 candidates should result in punishing those who claim such is
tolerable for presenting to voters.
Asking voters to choose among five seems doable; choosing among ten seems
like about the limit for being useful.
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Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
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If you want peace, work for justice.
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