<div dir="ltr"><div><div><div>I forgot to add Mono-Add-Plump to the advantages of Buclin over MDDTR. So it should say:<br><br></div>Bucklin:<br><br></div>* Mono-Add-Plump<br><br></div><div>* Use-Precedence<br><br></div><div>* Easier protection of the CWs<br><br></div><div>MDDTR:<br><br></div><div>*CD<br><br></div><div>*LNHa<br><br></div><div>* Precinct-Summabilty<br><br>-----------------------------------------<br><br></div><div>If Bucklin's easier protection is in question, then the comparison is especially more favorable to MDDTR.<br><br></div><div>Michael Ossipoff<br></div><div><br></div><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Sat, Nov 12, 2016 at 4:32 PM, Michael Ossipoff <span dir="ltr"><<a href="mailto:email9648742@gmail.com" target="_blank">email9648742@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div><div><div><div><div><div>Yes, that 2/3 majority rule would avoid having to say:<br><br></div>"(If each candidate has someone rated over hir by a majority, then the winner is the most top-rated candidate.)"<br><br></div>Tantalizingly greater simplicity, regrettably not workable, as you said.<br><br></div>ICT would avoid the Mono-Add-Plump criticism, but at the cost of truncation-vulnerability.<br></div>I'd rather have the Mono-Add-Plump criticism and truncation-proofness.<br><br></div>The ICT wording you described comes closer to the brevity of MDDTR, but MDDTR doesn't need a separate "beat" definition at all. ...just the use of the already-understood majority.<br><br></div>I suggested the 3-slot version of MDDTR because I felt that it should be used only as an Approval-version, with the Middle rating reserved for the special chicken-dilemma situation. ...because I felt that MDDTR, with its complete vulnerability to burial (like every pairwise-count method), wouldn't be good as a rank-method.<br><br></div><div>But maybe that should be reconsidered. Why would it be worse to rank your inbetween candidates in order of preference, than to rate them all together at middle? <br><br>The burial-vulnerability, the fact that "wv-like" didn't mean as much as I'd believed it did, was such a disappointment that it at first made me not appreciate the fact that MDDTR still has truncation-resistance. Burial vulnerability isn't a complete disaster:<br><br></div><div>For one thing, to bury the CWs, you have to know who is the CWs. And if you know it, then the defending wing knows it too, because the same predictive information is available to everyone. <br><br></div><div>If the CWs is more with your wing, and it's the opposite wing that dislikes the CWs, and is likely to bury, you can prevent successful burial by equal-top-ranking the CWs. That was pointed out a long time ago, as general pairwise-count defensive strategy.<br><br></div><div>You could protect the CWs in that way in Bucklin too. (in case people might rank past the CWs).<br><br></div><div>Of course the difference is that, in Buclin you & the others in your wing can also just avoid ranking past the CWse (expected or evident CWs).<br><br></div><div>MDDTR, and pairwise-count methods in general, don't have that protection, and you only have the defensive strategy of equal-top-ranking the CWse.<br><br></div><div>So, as regards protection of the CWs, Bucklin is better than the pairwise-count methods. MDDTR's tradeoff-advantage is its CD. ...in return for being able to protect the CWs only by equal-top-ranking.<br><br></div><div>Conditional Bucklin's and Conditional Approval's FBC failure is of a different kind than Condorcet's FBC failure, it seems to me. With Conditional Bucklin, the effectiveness of my equal-top-ranking isn't diminished by the FBC failure. The FBC failure merely gives me a trick that I could use, with sufficient predictive information, to gain advantage. Not a problem. But the problem is that the serious overcompromiser would still have incentive to rank Hillary alone at top, over the overompromiser's favorite. So I guess I reluctantly have to not advocate Conditional Bucklin or Conditional Approval. <br><br></div><div>...meaning that evidently Bucklin can't have CD, and MDDTR's CD is an advantage for MDDTR over Bucklin. So it's MDDTR's CD vs Bucklin's easier protection of the CWs.<br><br></div><div>All that time I was calling wv burial-deterrent, because of the 3-candidate example, where deterrence is achieved by merely not ranking the would-be buriers' candidate, I never considered a 4-candidate example.<br><br></div><div>It's easy to make a 4-candidate example where, in wv (& in MDDTR), that defense won't work: If B is the CWs, and the A voters are going to bury by insincerely ranking C over B, then just add D, between B and C. <br><br></div><div>The halfway point between D & C is of course way C-ward from the median, and so D will have a majority against C, if voters are uniformly-distributed. (...and probably could, with suitable distance-relations, even if the voter-distribution is Gaussian).<br><br></div><div>So, when the A voters make B majority-beaten, by ranking C over B, C remains majority-beaten (by D), and so now everyone is majority-beaten, and A wins if s/he's the most top-rated.<br><br></div><div>I haven't looked at what it would take for A to win in wv, because I no longer propose wv for official public political elections (or any where offensive strategy is likely). That would be something for a wv advocate to discuss.<br><br></div><div>Maybe I should list, together, some relative advantages of Bucklin & MDDTR:<br><br></div><div>Bucklin:<br><br></div><div>* Easier protection of the CWs (relevant if one of your inbetween might be the CWs)<br><br></div><div>* Use-precedence<br><br></div><div>MDDTR:<br><br></div><div>* CD<br><br></div><div>* LNHa<br><br></div><div>* Precinct-Summability<br><br>------------------------------<wbr>------------------------------<wbr>----<br><br></div><div>As for Bucklin's easier protection of the CWs, I'm not entirely sure, because there's some reason for the individual to rank all of the best candidates (instead of only ranking down to the CWse), to improve, somewhat, the probabiliy of electing one of them (but not as much as equal-top-ranking them all). So I don't know if Bucklin's easier protection of the CWs would materialize..<br><br></div><div>Michael Ossipoff<br><br></div><div><br><br></div><div><br><br></div><div><br><br></div><div>Michael Ossipoff<br><br></div><div><br> <br></div><div><br><br></div><div>Maybe a toss-up. Bucklin has the use-precedence advantage, but MDDTR has the precinct-summability adantage. And I consider MDDTR's LNHa an advantage too, when you don't have to hesitate to append less-liked inbetweens to your ranking for fear that you'll help the beat better candidaes.<br><br></div><div>In Bucklin, when skipping is permitted, you could make sure that, above some inbetween, you skip enough levels that the better candidates will have enough rounds to accumulate the coalescing lower-choices that are coming to them from other candidates' preferrers.<br><br></div><div>In MDDTR, & maybe in Bucklin, I'd likely top-rate the CWse, along with the very best of the strong top-set, even if s/he isn't really among those, and even if I felt like down-rating some of that top-set a bit because of some fault, or because of likely defection-inclination of their voters.<br><br><br></div><div><br></div><div><br><br></div></div><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">On Sat, Nov 12, 2016 at 2:56 PM, Forest Simmons <span dir="ltr"><<a href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div><div><div><div><div><div>Perhaps we could modify (non-symmetric) ICT in order to have a less wordy definition of "strongly beat."<br><br></div>Candidate X <b>strongly beats</b> candidate Y iff X is preferred over Y on more ballots than Y is<i> <u><b>ranked</b></u></i> equal to or above X.<br><br></div>All strongly beaten candidates are disqualified unless that would disqualify all of them.<br><br></div>Elect the qualified candidate ranked top on the most ballots.<br><br></div>This definition makes it slightly harder for X to strongly beat Y than in standard ICT, because all equal rankings have to be overcome, not only those at the top.<br><br></div>But it changes nothing in our standard CD examples, because in those examples there are no equal rankings (only equal truncations, which don't contribute to the strongly beat definition).<br><br></div>It should preserve the FBC and perhaps even introduce a stronger property: if some candidate X is raised to the level of the winner on some ballots, then the winner is unchanged unless the new winner is X.<br><br></div><div>I see the wisdom in saying "disqualified" instead of "eliminated." If we said "eliminated," then some people would wrongly think that "favorite" refers to the highest among the remaining candidates (after their original favorite was stricken from the ballot).<br></div><div><br></div><div>Also a comment about three slot methods in general:<br><br></div><div>With three slots it is impossible for every candidate to be eliminated by a two-thirds majority. So the following method would be even simpler to define in the context of 3 slot ballots:<br><br></div><div>Elect the favorite candidate who is not beaten by a two-thirds majority.<br><br></div><div>Of course, for all practical purposes that would be the same as "elect the candidate ranked top on the greatest number of ballots," which doesn't satisfy the CD criterion.<br></div><div><div class="m_2335114804577517422h5"><br><div class="gmail_extra"><br><div class="gmail_quote">On Sat, Nov 12, 2016 at 9:07 AM, Michael Ossipoff <span dir="ltr"><<a href="mailto:email9648742@gmail.com" target="_blank">email9648742@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><p dir="ltr">Yes, but ICT defines "beat" in a wordier way, that people hear as complicated.</p>
<p dir="ltr">For people who are into voting-systems, I can say "majority-beaten", & they know what I mean...that I'm talking about pairwise defeats.</p>
<p dir="ltr">So, here's how I'd define 3-Slot MDDTR, to the public:</p>
<p dir="ltr">You rate each candidate as "Top", "Middle", or "Bottom". If you don't rate someone, that counts as rating hir at Bottom.</p>
<p dir="ltr">The winner is the most favorite candidate who doesn't have anyone rated over hir by a majority.</p>
<p dir="ltr">(If everyone has someone rated over hir by a majority, then the winner is the most favorite candidate.)<br></p>
<p dir="ltr">(end of definition)</p>
<p dir="ltr">I'd just call it " Majority Disqualification".</p><span class="m_2335114804577517422m_6973034429649062176HOEnZb"><font color="#888888">
<p dir="ltr">Michael Ossipoff</p></font></span><div class="m_2335114804577517422m_6973034429649062176HOEnZb"><div class="m_2335114804577517422m_6973034429649062176h5">
<div class="gmail_quote">On Nov 11, 2016 4:39 PM, "Forest Simmons" <<a href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>> wrote:<br type="attribution"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">You wrote in part ...<br><div><div class="gmail_extra"><br><div class="gmail_quote"><div>>Another advantage that it has over 3-Slot ICT is that 3-Slot MDDTR has a much >simpler definition:<br><br></div>>The winner is the most favorite candidate who isn't majority-beaten.</div><br></div><div class="gmail_extra">Three slot ICT could be defined in the same way;<br><br></div><div class="gmail_extra">Elect the most favorite candidate who isn't strongly beaten.<br><br></div><div class="gmail_extra">Neither definition tells what to do when every candidate is beaten (majority beaten or strongly beaten, respectively). But that is just a detail of the definition that doesn't have to be mentioned immediately.<br><br></div><div class="gmail_extra">Here's a more complete definition that works in both cases:<br><br></div><div class="gmail_extra">Eliminate all candidates that are {majority, strongly} beaten unless that would eliminate all candidates. Elect the most favorite among the remaining.<br><br></div><div class="gmail_extra">So ordinary ICT and MDDTR are equally easy to define. It's a matter of which has the best properties.<br></div></div></div>
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