<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt"><div style="RIGHT: auto"><SPAN style="RIGHT: auto">Hi Chris,</SPAN></div>
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<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif"><B><SPAN style="FONT-WEIGHT: bold">De :</SPAN></B> C.Benham <cbenhamau@yahoo.com.au><BR><B><SPAN style="FONT-WEIGHT: bold">À :</SPAN></B> em <election-methods@electorama.com> <BR><B><SPAN style="FONT-WEIGHT: bold">Cc :</SPAN></B> MIKE OSSIPOFF <nkklrp@hotmail.com>; Kevin Venzke <stepjak@yahoo.fr> <BR><B><SPAN style="FONT-WEIGHT: bold">Envoyé le :</SPAN></B> Dimanche 20 Novembre 2011 23h43<BR><B><SPAN style="FONT-WEIGHT: bold">Objet :</SPAN></B> [EM] TTPD,TR (an FBC complying ABE solution?)<BR></FONT><BR><BR>Mike Ossipoff has been understandably concerned about what he calls the "Approval<BR>Bad Example" (ABE), as exemplified by<BR><BR>49: C (sincere)<BR>27: A>B (sincere)<BR>24: B (sincere is B>C, but are trying to steal election from A).<BR><BR>He considers that a voting method must meet the
Favorite Betrayal Criterion (FBC) and<BR>also he objects to the B voters in the above scenario being rewarded for their "defection"<BR>from the sincere {A,B} coalition (as they are with any method that meets both the Plurality<BR>and Minimal Defense criteria).<BR><BR>I suggest this method to fill the bill. It uses Kevin Venzke's special "Tied-at-the-Top"<BR>pairwise rule.<BR><BR><A href="http://wiki.electorama.com/wiki/index.php?title=Tied_at_the_top" target=_blank>http://wiki.electorama.com/wiki/index.php?title=Tied_at_the_top</A><BR><BR>*Voters submit 3-slot ratings ballots, default rating is Bottom signifying least preferred,<BR>Top rating signifies most preferred, the other ratings slot is Middle.<BR><BR>According to the "Tied-at-the-Top" pairwise rule (TTP), candidate X beats candidate Y<BR>if the number of ballots on which X is given a higher rating than Y *plus the number of<BR>ballots on which X and Y are both rated Top* is greater than
the number of ballots on<BR>which Y is given a higher rating than X.<BR><BR>(And of course vice versa, so it is possible for any pair of candidates X and Y that some<BR>ballots show Top rating for both to TTP beat each other).<BR><BR>If any candidate X TTP beats any candidate Y, is not in turn TTP beaten by Y and is<BR>not TTP beaten by any candidate Z that doesn't also TTP beat Y, then Y is disqualified.<BR><BR>Elect the undisqualified candidate that is rated Top on the highest number of ballots.*<BR><BR>I think and hope this meets the FBC. If it can be shown not to then I will withdraw my<BR>support for it. It meets the Mono-add-Plump and the Plurality criteria.</DIV>
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<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">The beatpath-like logic regarding candidate Z looks bad. The only things I accomplished with the tied-at-the-top </DIV>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">rule are a minmax variant and a C//A variant. No known FBC method at all uses any kind of beatpath tracing. So</DIV>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">it would be revolutionary if a method of this complexity satisfied FBC.</DIV>
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<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">I'm having problems easily thinking through how the method works. But this is the question to ask: By lowing your</DIV>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">favorite out of the top position, can you evict some other lower-ranked candidate from the top tier? If you can, that is</DIV>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">surely going to be handy in some situation.</DIV>
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<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">This non-reciprocal TTP beating concept is really odd to me. The TTP votes for X and Y with respect to the other</DIV>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">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</DIV>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">TTP votes to beat Y. It's a simple X>Y pairwise win.</DIV>
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<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">Kevin<VAR id=yui-ie-cursor></VAR></DIV></div></body></html>