Re: Condorcet Voting and Supermajorities (Re: [CONSTITUTIONAL AMENDMENT] Disambiguation of 4.1.5)
At 01:44 AM 11-29-2000 +1000, you wrote:
Why not simply define the terms as they are used by the people who care
about these things, and then clearly express the procedure by which ties
should be dealt with, rather than defining them out of existance?
A.6(2) An option A is said to Dominate another option B, if
there are more votes which rank option A above option B
than there are votes which rank option B above option A.
Can we include a clause here to handle the case where there are an equal
number of ballots ranking A above B and B above A? My opinion is that for
the purposes of this procedure, then A would Dominate B, and B would
Dominate A, rather than neither dominating each other.
That would have the nice property that for any distinct options A, B, we
have at least one of "A Dominates B" and "B Dominates A".
A.6(2a) The Smith Set of options in a vote is the smallest
non-empty set of options, each of which Dominates every
option not in the Smith Set.
Or equivilantly, with the suggestion above, "The Smith Set of options in a
vote is the smallest non-empty set of options, none of which are dominated
by any option not in the Smith Set."
Or, since "domination" is a hard concept to fathom, how about:
The Smith Set of options is the smallest non-empty set of options, none of
which lose in any pair-wise elections against any option outside the Smith Set.
or
The Smith Set of option is the smallest non-empty set of options which lose
in pair-wise contests only to other members of the Smith Set,
A.6(3) If there is only one option in the Smith Set, it is
the winner.
This still leaves the more important problem of how to handle related
(opposing) options in a single vote unaddressed, however. I'm further
inclined to suspect that using Single Transferable Vote to choose the
winner from the Smith Set isn't ideal, but I don't know enough about
the alternatives to give a basis for that suspicion.
The voting-methods pages have lots of suggestions.
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