<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>Kevin,</DIV>
<DIV> </DIV>
<DIV>You wrote (9 Jan 2009):<BR></DIV>
<DIV>"Well, with "Mutual Majority," when X may win, it's possible that by<BR>adding bullet votes for X, then every other candidate becomes able to<BR>win."</DIV>
<DIV> </DIV>
<DIV>No it isn't. (Can you give an example?) </DIV>
<DIV> </DIV>
<DIV>"Is there any way to explain, why it isn't completely absurd, that adding<BR>bullet votes for X should cause other candidates to become eligible to <BR>win?"</DIV>
<DIV> </DIV>
<DIV>No.<BR></DIV>
<DIV>"Why is mono-add-plump important?"<BR></DIV>
<DIV>Because as an election method algorithm that fails it simply can't have any</DIV>
<DIV>credibility as a quasi-intelligent device (which is what it is supposed to be)</DIV>
<DIV>and because satisfying it should be (and is) very cheap.</DIV>
<DIV> </DIV>
<DIV>"Since you value Majority as a criterion, it seems to me that you<BR>can't attack the CDTT by attacking the underlying concept."<BR></DIV>
<DIV>Yes I can, because the Majority concept is only vulnerable to Irrelevant</DIV>
<DIV>Ballots which is much less serious than Mono-add-Plump. </DIV>
<DIV><BR>A candidate X can fall out of the set of candidates "not excluded" (that</DIV>
<DIV>Marcus seems to think means something significantly different from "allowed </DIV>
<DIV>to win") by Majority by the removal of some irrelevant ballots (that simply </DIV>
<DIV>ignore all the candidates in that set); whereas X can fall out of the CDTT by </DIV>
<DIV>adding some ballots that purely bullet-vote for X.<BR></DIV>
<DIV>Also I specified that by itself this fact only makes Beatpath GMC (Marcus's</DIV>
<DIV>criterion that says that the winner must come from the CDTT set) appear</DIV>
<DIV>uniquely weird and suspect, not that it was conclusively damning.</DIV>
<DIV> </DIV>
<DIV>"If we view CDTT somehow as an election method, then when it fails<BR>mono-add-plump, the bullet votes for X are not simply "strengthening"<BR>X, they are also *weakening* some pairwise victory of Y over Z, which X<BR>had relied upon in order to have a majority beatpath to Z."</DIV>
<DIV><BR>That just testifies to the absurdity of an algorithm specifically putting some<BR>special significance on "majority beatpaths" versus other beatpaths.</DIV>
<DIV> </DIV>
<DIV>"Of course, you can always use the mechanics of the method to explain why<BR>something has happened. But it seems to me that the bullet voters aren't<BR>purely "strengthening" X, they are also weakening Y and thereby also X".</DIV>
<DIV> </DIV>
<DIV>This contention that "bullet voters for X aren't purely strengthening X" but are<BR>in some way "also weakening X" is completely absurd.</DIV>
<DIV> </DIV>
<DIV>"This is an oddity inherent to beatpaths, really"</DIV>
<DIV> </DIV>
<DIV>I think only to beatpaths that measure "defeat strengths" in a silly way.</DIV>
<DIV> </DIV>
<DIV>><I> But I contend that here in my "situation 2"<BR></I>><I> election Beatpath GMC does exclude<BR></I>><I> the clearly strongest candidate C. </I></DIV>
<DIV><EM></EM> </DIV>
<DIV>"You're attacking a lot more than just beatpath GMC with this scenario.<BR>Excluding C is required by SFC (the 51 B voters are basically assured<BR>LNHarm when voting for C, since B might be the sincere CW) and also<BR>basically any WV method."</DIV>
<DIV> </DIV>
<DIV>Yes, you catch on quick.</DIV>
<DIV> </DIV>
<DIV>><I> In other words the CDTT set can fail to include the<BR></I>><I> candidate that on overwhelming <BR></I>><I> common-sense (mostly positional) grounds is the strongest<BR></I>><I> candidate (e.g. C in "Situation # 2").<BR></I><BR>"Having read that archive post the motivation behind the criteria <BR>(especially the Smith-compatible one) is unclear to me.</DIV>
<DIV>...The only reason you gave for adding a beatpath requirement is that <BR>you're "still interested" in Condorcet methods."<BR></DIV>
<DIV>Sorry, do I need a better reason? One of my standards is that a single-winner<BR>voting method should meet one of Later-no-Harm, FBC and Condorcet.<BR>I value compliance with (voted) Condorcet and (voted) Smith-Schwartz.</DIV>
<DIV> </DIV>
<DIV>> ...<EM>I consider the addition of </EM><I>compliance with "beatpath GMC" a negative if <BR></I>><I> without it the method can meet "Smith- Comprehensive </I><I>3-slot Ratings Winner" <BR>> (which </I><I>should be very very easy).<BR></I><BR>"It should be very easy? What methods are there other than Schwartz//Approval?"</DIV>
<DIV> </DIV>
<DIV>That will do to be going along with.</DIV>
<DIV> </DIV>
<DIV>Chris Benham<BR><BR><BR><BR>Hi Chris,<BR><BR>If we view CDTT somehow as an election method, then when it fails<BR>mono-add-plump, the bullet votes for X are not simply "strengthening"<BR>X, they are also *weakening* some pairwise victory of Y over Z, which X<BR>had relied upon in order to have a majority beatpath to Z.<BR><BR>Of course, you can always use the mechanics of the method to explain why<BR>something has happened. But it seems to me that the bullet voters aren't<BR>purely "strengthening" X, they are also weakening Y and thereby also X.<BR>This is an oddity inherent to beatpaths, really.<BR><BR>As far as I can tell you are calling this failure "absurd" for no reason<BR>except mono-add-plump. Why is mono-add-plump important? If it were more<BR>difficult to satisfy, like Participation, I doubt it would ever come up.<BR>This failure doesn't create a huge strategy problem: If you guess that you<BR>might be better off staying home than bullet
voting, then probably you can<BR>also guess which beatpaths your vote needs to reinforce in order to <BR>protect the candidate you want.<BR><BR>--- En date de : Ven 9.1.09, Chris Benham <<A href="http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com"><FONT color=#810081>cbenhamau at yahoo.com.au</FONT></A>> a écrit :<BR>><I> No, I only wrote that the beatpath GMC *concept* is<BR></I>><I> "vulnerable to <BR></I>><I> Mono-add-Plump."<BR></I><BR>I find it difficult to nail down what this means. It seems clear from<BR>Markus' mails that he isn't going to discuss a criterion as though it<BR>were a method. Woodall also had to define criteria differently in order<BR>to apply them to sets. But to apply criteria to a concept?<BR><BR>><I> I think that all methods that fail Independence from<BR></I>><I> Irrelevant Ballots are silly and<BR></I>><I> that methods should meet the Majority
criterion. The<BR></I>><I> Majority *concept* is <BR></I>><I> "vulnerable to Irrelevant Ballots" because<BR></I>><I> candidate A can be the only candidate<BR></I>><I> allowed to win by the Majority criterion and then we add a<BR></I>><I> handful of ballots that<BR></I>><I> all plump for nobody and candidate A no longer has a<BR></I>><I> majority.<BR></I><BR>This is problematic. The same concept underlies both Majority and the<BR>CDTT. Since you value Majority as a criterion, it seems to me that you<BR>can't attack the CDTT by attacking the underlying concept.<BR><BR>><I> The point of my Dec.29 demonstration was to refute any<BR></I>><I> notion or assumption<BR></I>><I> that all candidates in the CDTT (i.e. those not excluded by<BR></I>><I> Beatpath GMC) must<BR></I>><I> be "stronger" (i.e. more representative of the<BR></I>><I> voters and so more deserving of victory)<BR></I>><I> than any of the
candidates outside the CDTT. <BR></I><BR>Well, you would have to define "representative." In the three-candidate<BR>case, at least, I think it's a problem to elect a candidate who isn't<BR>in the CDTT.<BR><BR>><I> This was only the first part of my argument that Beatpath<BR></I>><I> GMC [compliance] is a<BR></I>><I> "mistaken standard". What other<BR></I>><I> criterion/standard says that the winner must come<BR></I>><I> from set S, with S being a set that a candidate X can be<BR></I>><I> kicked out of by an influx<BR></I>><I> of new ballots that all plump (bullet-vote) for X?<BR></I><BR>Well, with "Mutual Majority," when X may win, it's possible that by<BR>adding bullet votes for X, then every other candidate becomes able to<BR>win.<BR><BR>You're talking specifically about mono-add-plump, but in a real single-<BR>winner election method this would be exactly the same phenomenon:<BR>Additional bullet votes
for X cause X to lose to someone else.<BR><BR>Is there any way to explain, why it isn't completely absurd, that adding<BR>bullet votes for X should cause other candidates to become eligible to <BR>win?<BR><BR>><I> By itself that isn't conclusively<BR></I>><I> damning because it doesn't prove<BR></I>><I> that Beatpath GMC can exclude the strongest candidate. <BR></I>><I> <BR></I>><I> 25: A>B<BR></I>><I> 26: B>C<BR></I>><I> 23: C>A<BR></I>><I> 26: C<BR></I>><I> <BR></I>><I> But I contend that here in my "situation 2"<BR></I>><I> election Beatpath GMC does exclude<BR></I>><I> the clearly strongest candidate C. You ignored the last<BR></I>><I> few paragraphs of my last post:<BR></I><BR>You're attacking a lot more than just beatpath GMC with this scenario.<BR>Excluding C is required by SFC (the 51 B voters are basically assured<BR>LNHarm when voting for C, since B might be the sincere CW) and
also<BR>basically any WV method.<BR><BR>If you want to use approval-based or positional arguments, I guess you<BR>won't find much to support in the Condorcet world.<BR><BR>><I> .. I don't accept your suggestion that compliance with<BR></I>><I> beatpath GMC is acceptably cheap <BR></I>><I> (let alone free), because it isn't compatible with<BR></I>><I> my recently suggested "Smith- Comprehensive <BR></I>><I> 3-slot Ratings Winner" criterion, which I value much<BR></I>><I> more.<BR></I>><I> <BR></I>><I> <A href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html"><FONT color=#0000ff>http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html</FONT></A><BR></I>><I> <BR></I>><I> In other words the CDTT set can fail to include the<BR></I>><I> candidate that on overwhelming <BR></I>><I> common-sense (mostly positional) grounds is the
strongest<BR></I>><I> candidate (e.g. C in "Situation # 2").<BR></I><BR>Having read that archive post the motivation behind the criteria <BR>(especially the Smith-compatible one) is unclear to me. For an example,<BR>why couldn't you propose instead "CDTT-C3RW"? The only reason you gave <BR>for adding a beatpath requirement is that you're "still interested" in<BR>Condorcet methods.<BR><BR>><I> So given a method that meets what I've been recently<BR></I>><I> calling "Strong Minimal Defense" <BR></I>><I> (and so Minimal Defense and Plurality) and Schwartz (and so<BR></I>><I> fails LNHarm and meets Majority <BR></I>><I> for Solid Coalitions), I consider the addition of<BR></I>><I> compliance with "beatpath GMC" a negative if <BR></I>><I> without it the method can meet "Smith- Comprehensive<BR></I>><I> 3-slot Ratings Winner" (which<BR></I>><I> should be very very easy).<BR></I><BR>It should be very easy? What methods
are there other than Schwartz//Approval?<BR><BR>Kevin Venzke<BR><BR><BR></DIV></div><br>
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