I have conferred off-list with Kevin Venzke, and now agree with him that
the "Tied at Top Pairwise Disqualification, Top Ratings" method I
suggested (20 Nov 2011) almost certainly does fail the FBC, so
I withdraw that proposal and instead suggest this simpler method:
*Voters submit 3-slot ratings ballots, default rating is Bottom
signifying least preferred, Top rating signifies most preferred, the
other ratings slot is Middle.
According to the "Tied-at-the-Top" pairwise rule (TTP), candidate X
beats candidate Y if the number of ballots on which X is given a higher
rating than Y *plus the number of ballots on which X and Y are both
rated Top* is greater than the number of ballots on which Y is given a
higher rating than X.
If any candidates (or candidate) TTP beats all other candidates,
elect the one of these with the highest Top-Ratings (TR) score.
Otherwise elect the candidate with the highest TR score.*
I call this "Tied at Top rule Pairwise Beats-All// Top Ratings"
(TTPBA//TR).
It is similar to Kevin Venke's Improved Condorcet//Approval (ICA)
method, the only difference being that it uses Top-Ratings instead of
Approval. It was Kevin who invented the special "tied at the top"
pairwise rule.
http://wiki.electorama.com/wiki/index.php?title=Tied_at_the_top
http://wiki.electorama.com/wiki/Improved_Condorcet_Approval
http://nodesiege.tripod.com/elections/#methica
TTPBA//TR (or TTBA,TR) meets the Plurality and Mono-add-Plump criteria.
Chris Benham
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