<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">Jameson,<BR><BR>49: C (sincere)<BR>27: A>B (sincere)<BR>24: B (sincere is B>A, but are trying to steal election from A).<BR></div>
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<DIV style="RIGHT: auto">"You mean that sincere is B>A."</DIV>
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<DIV style="RIGHT: auto">Yes, sorry for that blunder (which I've fixed everywhere in this message). Thanks for pointing<BR>it out.<VAR id=yui-ie-cursor></VAR></DIV>
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<DIV style="RIGHT: auto">"Also, it's not really important, but I've repeatedly pointed out that the term "chicken dilemma" </DIV>
<DIV style="RIGHT: auto">is a more descriptive name for this situation, and also (as far as I know) one which has precedence."</DIV>
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<DIV style="RIGHT: auto">I think the term "chicken dilemma" has quite a different connotation. Maybe I would just talk about</DIV>
<DIV style="RIGHT: auto">"defection incentive", but since Mike seems to be the one who is most concerned about it I'm happy </DIV>
<DIV style="RIGHT: auto">for him to call it what he likes.</DIV>
<DIV style="RIGHT: auto"><BR style="RIGHT: auto">Chris Benham</DIV></DIV></SPAN>
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<DIV style="RIGHT: auto" class=yiv1565972029gmail_quote>2011/11/20 C.Benham <SPAN dir=ltr><<A href="mailto:cbenhamau@yahoo.com.au" rel=nofollow target=_blank ymailto="mailto:cbenhamau@yahoo.com.au">cbenhamau@yahoo.com.au</A>></SPAN><BR>
<BLOCKQUOTE style="BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex; PADDING-LEFT: 1ex; RIGHT: auto" class=yiv1565972029gmail_quote><BR style="RIGHT: auto">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>A, but are trying to steal election from A).<BR> </BLOCKQUOTE>
<BLOCKQUOTE style="BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex; PADDING-LEFT: 1ex" class=yiv1565972029gmail_quote><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" rel=nofollow target=_blank>http://wiki.electorama.com/<U></U>wiki/index.php?title=Tied_at_<U></U>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.<BR><BR>In the above example election no candidate is disqualified
and C wins. If the B supporters<BR>vote sincerely then C will be disqualified and A will win.<BR><BR>My suggested name for this method "Tied at Top Pairwise Disqualification, Top Ratings"<BR>(TTPD,TR) is currently tentative and unenthusiastic, so if it is agreed that it meets the FBC<BR>then I'm open to other suggestions.<BR><BR>Chris Benham<BR><BR><BR><BR><BR><BR>----<BR>Election-Methods mailing list - see <A href="http://electorama.com/em" rel=nofollow target=_blank>http://electorama.com/em</A> for list info<BR></BLOCKQUOTE></DIV><BR></DIV><BR><BR></DIV></DIV></div></body></html>