[EM] TTPD,TR (an FBC complying ABE solution?)

[C.Benham]

Mike Ossipoff has been understandably concerned about what he calls the 
"Approval
Bad Example" (ABE), as exemplified by

49: C     (sincere)
27: A>B (sincere)
24: B     (sincere is B>C, but are trying to steal election from A).

He considers that a voting method must meet the Favorite Betrayal 
Criterion (FBC) and
also he objects to the B voters in the above scenario being rewarded for 
their "defection"
from the sincere {A,B} coalition (as they are with any method that meets 
both the Plurality
and Minimal Defense criteria).

I suggest this method to fill the bill. It uses Kevin Venzke's special 
"Tied-at-the-Top"
pairwise rule.

http://wiki.electorama.com/wiki/index.php?title=Tied_at_the_top

*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.

(And of course vice versa, so it is possible for any pair of candidates 
X and Y that some
ballots show Top rating for both to TTP beat each other).

If any candidate X  TTP beats any candidate Y, is not in turn TTP beaten 
by Y and is
not TTP beaten by any candidate Z that doesn't also TTP beat Y, then Y 
is disqualified.

Elect the undisqualified candidate  that is rated Top on the highest 
number of ballots.*

I think and hope this meets the FBC. If  it can be shown not to then I 
will withdraw my
support for it.  It meets the Mono-add-Plump and the Plurality criteria.

In the above example election no candidate is disqualified and C wins. 
If the B supporters
vote sincerely then C will be disqualified and A will win.

My suggested name for this method  "Tied at Top Pairwise 
Disqualification, Top Ratings"
(TTPD,TR) is currently tentative and unenthusiastic, so if  it is agreed 
that it meets the FBC
then I'm open to other suggestions.

Chris Benham