<html><head><style type="text/css"><!-- DIV {margin:0px;} --></style></head><body><div style="font-family:times new roman, new york, times, serif;font-size:12pt"><DIV>Raph,<BR></DIV>
<DIV>*If (assuming there are more than two candidates) the ballot <BR>rules don't constrain voters to expressing fewer than three <BR>preference-levels, and A wins being voted above B on more <BR>than half the ballots, then it must not be possible to make B <BR>the winner by altering any of the ballots on which B is voted <BR>above A.*<BR><BR></DIV>
<DIV>"....is the criterion effectively the following?<BR><BR>If the winner is preferred to another candidate on the majority of the<BR>ballots, it must not be possible to make any such candidate win by<BR>modifying the ballots where that candidate is preferred to the winner."</DIV>
<DIV> </DIV>
<DIV>Yes.</DIV>
<DIV><BR>"By requiring that at least 3 levels are possible, you are effectively<BR>forcing lots of methods to fail."</DIV>
<DIV> </DIV>
<DIV>Such as? It is news to me that there are "lots of methods" with ballot</DIV>
<DIV>rules that restrict the voter to fewer than three preference-levels.</DIV>
<DIV> </DIV>
<DIV>In the past I've encountered arguments along the lines that Approval</DIV>
<DIV>(and/or vote-for-one plurality) meets some criterion (that it obviously</DIV>
<DIV>doesn't) because the ballot rules don't allow me to give an example of</DIV>
<DIV>it failing.<BR></DIV>
<DIV>So I've developed the habit of taking care to side-step such sophistry.</DIV>
<DIV> </DIV>
<DIV>My reference to "more than two candidates" was partly about that I<BR>don't mind if the ballot-rules prevent the voters from expressing more<BR>preference-levels than there are candidates.<BR><BR>Thanks for taking an interest.</DIV>
<DIV> </DIV>
<DIV>Chris Benham<BR><BR></DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>Raph Frank wrote (Fri.Nov.28):</DIV>
<DIV><PRE>I think you have alot of redundant language, is the criterion
effectively the following?
If the winner is preferred to another candidate on the majority of the
ballots, it must not be possible to make any such candidate win by
modifying the ballots where that candidate is preferred to the winner.
By requiring that at least 3 levels are possible, you are effectively
forcing lots of methods to fail. Also, just because most methods
would meet the criterion in the 2 candidate case isn't a reason to
exclude that case.</PRE><PRE><BR> </PRE><!--endarticle--><!--htdig_noindex--></DIV></div><br>
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