[EM] Approval-Completed Condorcet Redux

[matt matt]

This is mostly Approval with a little CW as illustrated by defining it thus:

1) If the Approval and Condorcet winners differ then the CW is elected when the votes preferring the CW to the Approval winner exceed the Approval winner's approval count total.
2) Otherwise the Approval winner is elected.

Anyone know the probability that there will be different CW and Approval winners?  Less than 1/4?  With more candidates the probability that there will be a CW winner presumably decreases while the probability that given a CW the CW and Approval winners will be different increases.  So maybe it is better to evaluate this method by comparing it to Approval than comparing it with CW.

So, contrary to what Kevin says, this method does appear to ameliorate the CW turkey problem since Approval avoids that problem and this method is mostly Approval.

From: Kevin Venzke <stepjak at yahoo.fr>
Date:  Sun, 22 Jun 2003 05:05:19 +0200 (CEST)

"I thought briefly about this method, and decided I wasn't clear on what it would be good for."
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"Has anyone come up with a more interesting scenario?"

On Wed, 18 Jun 2003, Alex Small wrote:

"Somebody on another mailing list has put forth an interesting
Approval-Condorcet hybrid.  I throw it out for consideration.  I know some people here have done careful analyses of strategy in standard Approval-Completed Condorcet, I'm curious what people think of this:
1)  Everybody submits a ranked ballot, equal rankings allowed, and also indicates yes/no for each candidate.
2)  If there is no Condorcet Winner then elect the Approval winner.
3)  If there is a CW, and he also has the highest approval, elect him.
4)  If the Approval and Condorcet winners differ, compare the Approval winner's approval rating with the number of people who prefer the CW to the Approval winner."
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