[EM] Approval variants of MinMax

Chris Benham chrisbenham at bigpond.com
Sat Sep 3 09:56:03 PDT 2005

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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