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<DIV>Kristofer,<BR></DIV>
<DIV>"In 2003, you referred to a method called "Descending Half-Solid<BR>Coalitions", which, despite failing both LNHarm and LNHelp, "might be<BR>preferrable to them". What is DHSC, and does it salvage DAC/DSC?"</DIV>
<DIV> </DIV><FONT face=CMR12~1e>
<P align=left>Quoting Woodall:<BR></FONT><FONT face=CMR12~1e></P></FONT><FONT face=CMR12~1e>
<P align=left>Here are three ways of assigning scores to sets of candidates. Recall that a voter</P>
<P align=left>is </FONT><FONT face=CMTI12>solidly committed </FONT><FONT face=CMR12~1e>to a set </FONT><FONT face=CMMI12>X </FONT><FONT face=CMR12~1e>of candidates if the voter puts the candidates</P>
<P align=left>in </FONT><FONT face=CMMI12>X </FONT><FONT face=CMR12~1e>as the top </FONT><FONT face=CMSY10>j</FONT><FONT face=CMMI12>X</FONT><FONT face=CMSY10>j </FONT><FONT face=CMR12~1e>candidates on their ballot. A voter </FONT><FONT face=CMTI12>acquiesces </FONT><FONT face=CMR12~1e>to a set </FONT><FONT face=CMMI12>X</P></FONT><FONT face=CMR12~1e>
<P align=left>of candidates if they do not indicate a preference for any candidate outside </FONT><FONT face=CMMI12>X</P></FONT><FONT face=CMR12~1e>
<P align=left>over any candidate in </FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>; i.e., either they are solidly committed to </FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>, or else</P>
<P align=left>they vote just for a proper subset of the candidates in </FONT><FONT face=CMMI12>X </FONT><FONT face=CMR12~1e>(and for no candidate</P>
<P align=left>outside </FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>). The </FONT><FONT face=CMTI12>solid coalition </FONT><FONT face=CMMI12>S</FONT><FONT face=CMR12~1e>(</FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>) in support of </FONT><FONT face=CMMI12>X </FONT><FONT face=CMR12~1e>consists of all voters who</P>
<P align=left>are solidly committed to </FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>. The </FONT><FONT face=CMTI12>acquiescing coalition </FONT><FONT face=CMMI12>A</FONT><FONT face=CMR12~1e>(</FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>) in support of </FONT><FONT face=CMMI12>X</P></FONT><FONT face=CMR12~1e>
<P align=left>consists of all voters who acquiesce to </FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>. The </FONT><FONT face=CMTI12>half-solid coalition </FONT><FONT face=CMMI12>H</FONT><FONT face=CMR12~1e>(</FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>) in</P></FONT><FONT face=CMR12~1e>
<P align=left>support of </FONT><FONT face=CMMI12>X </FONT><FONT face=CMR12~1e>consists of all voters in the solid coalition for </FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>, each counted</P>
<P align=left>with weight 1, together with all voters in the acquiescing coalition but not</P>
<P align=left>in the solid coalition, each counted with weight </FONT><FONT face=CMR8 size=1>1</P>
<P align=left>2 </FONT><FONT face=CMR12~1e>; so </FONT><FONT face=CMSY10>j</FONT><FONT face=CMMI12>H</FONT><FONT face=CMR12~1e>(</FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>)</FONT><FONT face=CMSY10>j </FONT><FONT face=CMR12~1e>= </FONT><FONT face=CMR8 size=1>1</P>
<P align=left>2 </FONT><FONT face=CMR12~1e>(</FONT><FONT face=CMSY10>j</FONT><FONT face=CMMI12>S</FONT><FONT face=CMR12~1e>(</FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>)</FONT><FONT face=CMSY10>j </FONT><FONT face=CMR12~1e>+</P></FONT><FONT face=CMSY10>
<P align=left>j</FONT><FONT face=CMMI12>A</FONT><FONT face=CMR12~1e>(</FONT><FONT face=CMMI12>X</FONT><FONT face=CMR12~1e>)</FONT><FONT face=CMSY10>j</FONT><FONT face=CMR12~1e>).</P></FONT>
<DIV><BR><end quote></DIV>
<DIV> </DIV>
<DIV>That means "each counted with weight of half". The 3 rules/methods are<BR>equivilalent if no voters truncate. Above-bottom equal-ranking is assumed<BR>to be not allowed.</DIV>
<DIV> </DIV>
<DIV>I consider it desirable that LNHarm and LNHelp should be in at least </DIV>
<DIV>probabilistic balance, so that 0-info. voters don't have strong incentive</DIV>
<DIV>to either truncate or random-fill.</DIV>
<DIV> </DIV>
<DIV>But DHSC still fails MDT, giving the same result as DSC in the <BR>49A, 48B, 3C>B example. And it should be DACish enough to still</DIV>
<DIV>fail Independence from Irrelelevant Ballots (IIB), so the short answer<BR>to your question is no.</DIV>
<DIV> </DIV>
<DIV>"You said that Schwartz,IRV protects MDT candidates from being buried.<BR>Does that hold for all Schwartz,X if X passes MDT?"</DIV>
<DIV> </DIV>
<DIV>Yes.<BR></DIV>
<DIV>"If QLTD isn't cloneproof (and it isn't), then the result won't be<BR>either, hence we could just as well go with first preference Copeland <BR>(unless that has a flaw I'm not seeing)."</DIV>
<DIV><BR>What is supposed to be the attraction of "first preference Copeland"?</DIV>
<DIV>And how do you define it exactly? </DIV>
<DIV> </DIV>
<DIV>Chris Benham</DIV>
<DIV> </DIV><BR><BR><BR>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">
<DIV style="FONT-SIZE: 13px; FONT-FAMILY: arial, helvetica, sans-serif">Kristofer Munsterhjelm wrote (Friday, 18 July, 2008 ):<BR><BR>Chris Benham wrote:<BR><BR>> At one stage Woodall was looking for the method/s that meet as many of<BR>> his "monotonicty properties" as possible while keeping "Majority" <BR>> (equivalent to Majority for Solid Coalitions). That is what led him to <BR>> Quota-Limited Trickle Down (QLTD) and then Descending Acquiescing Coalitions (DAC).<BR>> <BR>> But I wouldn't conclude from this that for public political elections he <BR>> currently prefers those methods (or DSC) to IRV.<BR><BR>I was going by his statement of DAC being "the first system I'm really<BR>happy with" or something to that effect. It's true that he could have<BR>changed his mind, and given your example below, he probably did.<BR><BR>> They don't meet Mutual Dominant Third.<BR>> <BR>> 49:
A<BR>> 48: B<BR>> 03: C>B<BR>> <BR>> The MDT winner is B, but DSC elects A.<BR>> <BR>> 03: D<BR>> 14: A<BR>> 34: A>B<BR>> 36: C>B<BR>> 13: C<BR>> The MDT winner is C, but DAC elects B.<BR>> <BR>> This latter example (from Michael Harman, aka Auros) I think put<BR>> Woodall off DAC. B is an absurd winner. Without the 3 ballots<BR>> that ignore all the competitive candidates the majority favourite is C.<BR><BR>I agree that it is quite absurd.<BR>In 2003, you referred to a method called "Descending Half-Solid<BR>Coalitions", which, despite failing both LNHarm and LNHelp, "might be<BR>preferrable to them". What is DHSC, and does it salvage DAC/DSC?<BR><BR>> But of course Smith implies MDT.<BR><BR>You said that Schwartz,IRV protects MDT candidates from being buried.<BR>Does that hold for all Schwartz,X if X passes MDT? It would seem to do<BR>so, since burial most often
involves a cycle, and without a cycle the<BR>Schwartz (and Smith) set is just a single candidate.<BR><BR>In that respect, Smith, or Schwartz,[something that passes MDT] is not<BR>redundant, even if Smith itself implies MDT.<BR><BR>> DSC and DAC aren't just "monotonic" (meet mono-raise), they meet<BR>> Participation (which of course is lost when combined with Smith/Schwartz<BR>> because Participation and Condorcet are incompatible).<BR>> <BR>> I think all methods that meet Condorcet are vulnerable to Burial. By <BR>> themselves<BR>> DSC is certainly vulnerable to burial (and has a 0-info. random-fill <BR>> incentive) and<BR>> DAC has strong truncation incentive.<BR>> Your question about QLTD has been asked before:<BR>> <A href="http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015367.html" target=_blank rel=nofollow><FONT
color=#810081>http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015367.html</FONT></A><BR>> <BR>> <A href="http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015369.html" target=_blank rel=nofollow><FONT color=#810081>http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015369.html</FONT></A><BR><BR>I see. If QLTD isn't cloneproof (and it isn't), then the result won't be<BR>either, hence we could just as well go with first preference Copeland <BR>(unless that has a flaw I'm not seeing).<BR></DIV></DIV></DIV></div><br>
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