Why to mix methods...

[Adam Tarr]

Gervase,

This is, more or less, just another way of looking at approval-completed 
Condorcet.  Sure, you consider the approval counts on the front end rather 
than the back end, but the only effect that has it to restrict the winner 
to the Smith set.  You could call this "Smith ACC" if you liked.

That said, this shares the weaknesses of ACC in the sense that the approval 
ballots are irrelevant when they support the Condorcet winner, and they 
create all sorts of strategic problems when they do not.

-Adam

At 12:06 AM 9/27/2002 +0100, you wrote:
>Why not go a lot further with mixing Approval with Ranked Pairs and use
>Approval//Disapproval to sort the pairwise contests.  It's probably easier
>to explain by adapting an example from the list archives:
>
>7:A>B>>C>D
>5:B>>D>C>A
>4:D>C>>A>B
>4:C>D>>A>B
>1:D>>B>C>A
>
>(>> represents the Approval cut-off point).
>
>The pairwise results are as follows:
>
>A>B 15:6
>C>A 14:7
>D>A 14:7
>B>C 13:8
>B>D 12:9
>C>D 11:10
>
>Approval results are: A=7, B=12, C=8, D=9
>
>The pairwise wins for each Candidate are sorted in Candidate Approval
>order.  The pairwise wins for each candidate is then sorted in Disapproval
>order.
>
>The pairwise wins are sorted in Approval order of the pairwise winner.
>The pairwise wins for each candidate is then sorted in Disapproval order
>for each pairwise loser.
>
>B: B>C
>    B>D
>D: D>A => B>D>A
>C: C>A
>    C>D => B>C>D>A
>A: A>B (Ignore)
>
>FINAL RESULT: B>C>D>A
>
>Well, at least it makes the Margins v. Winning Votes debate pointless.  As
>no pairwise votes or margins are counted, I think it is reasonably
>truncation resistant.
>
>I initially thought that this method may not select the Condorcet Winner.
>However, I think it will always select the Condorcet Winner as there is no
>pairwise result that can be added to the Beat Path that would make [This
>Ranked Pair Method Winner and Non-Condorcet Winner] > [Condorcet Winner].
>This is becuase, by definition, for each pairwise contest, [Condorcet
>Winner] > [Each of the other candidates].
>
>I was just wondering if there is a reasonable Condorcet Method that does
>not always select the Condorcet winner.  To a certain extent, I think this
>woudl be a good thing as the method would more likely not fall into the
>Condorcet Criterion Incompatibility with the Participation, Consistency
>and Monotonicity Criteria.
>
>CC incompatible with Participation & Consistency
><http://groups.yahoo.com/group/election-methods-list/message/8506>
>
>CC incompatible with Monotonicity
><http://groups.yahoo.com/group/election-methods-list/message/8452>
>
>Thanks,
>Gervase.
>
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