Forest,
You recently wrote on the new Yahoo Condorcet list, beginning by
referring to Beatpath, Ranked Pairs, River and MinMax:
However, recently Jobst showed that if one measures defeat strength by
total
approval (of the victor in the pairwise defeat) then all four of these
competing
methods coalesce into one method.
This fact would seem to resolve the controversy unless it turned out
that total
approval was not a good way to measure defeat strength.
However, it seems to be better than winning votes or margins. The
defensive
properties of winning votes that are normally obtained by "defensive
truncation"
can usually (if not always) be obtained by raising the approval cutoff
instead
of truncating the rankings.
Therefore, I suggest that we adopt MinMax(Total Approval) as the Condorcet
proposal.
Is your first sentence above also true of MinMax (Approval Margins)
and the MinMax (Winner's Exclusive Approval)?
By the latter I mean measuring the defeat strength by the number of
ballots that approve the pairwise winner and not the pairwise loser,
as advocated by James Green Armytage.
Chris Benham
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