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

[Kevin Venzke]

Hi Chris,
 

>>De : C.Benham <cbenhamau at yahoo.com.au>
>>À : em <election-methods at electorama.com> 
>>Cc : MIKE OSSIPOFF <nkklrp at hotmail.com>; Kevin Venzke <stepjak at yahoo.fr> 
>>Envoyé le : Dimanche 20 Novembre 2011 23h43
>>Objet : [EM] TTPD,TR (an FBC complying ABE solution?)
>>
>>
>
>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.
The beatpath-like logic regarding candidate Z looks bad. The only things I accomplished with the tied-at-the-top 
rule are a minmax variant and a C//A variant. No known FBC method at all uses any kind of beatpath tracing. So
it would be revolutionary if a method of this complexity satisfied FBC.

I'm having problems easily thinking through how the method works. But this is the question to ask: By lowing your
favorite out of the top position, can you evict some other lower-ranked candidate from the top tier? If you can, that is
surely going to be handy in some situation.

This non-reciprocal TTP beating concept is really odd to me. The TTP votes for X and Y with respect to the other
are exactly the same count. If Y can't beat X even with the TTP votes, then X certainly doesn't need to have those
TTP votes to beat Y. It's a simple X>Y pairwise win.

Kevin
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