<div dir="ltr"><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div>Uh-oh...<br><br></div>When I first proposed wv, and when I've evaluated pairwise-count methods' properties for protection from truncation, I always looked only at 3-candidate examples. By that, wv, MMPO, & MDDTR looked pretty good in that regard.<br></div>wv-like strategy.<br><br></div>Well, they still meet SFC, and are fully resistant to truncation. That's the good news...<br><br></div>But, when looked at in 2D issue-space (with Euclidean distances), and a voter-distribution that is uniform or the same in every direction from the all-dimensions median...MDDTR is completely vulnerable and un-defendable from burial.<br><br></div>I haven't looked at 1D. I looked at 2D. Maybe, in 1D, it will turn out to not have that problem. But if the method has a problem in one dimensionality, I guess one would expect it in all dimensionalities.<br><br></div><div>Maybe the problem doesn't happen with city-block distance, but I guess the likely presumption is that it does.<br></div><div><br></div>SFC is a very good thing, and its premises are well-met, by the assumptions I used. But the burial vulnerability spoils MDDTR, at least in 2D.<br><br></div>I have no idea whether wv, which I began proposing in the late '80s, has the same thoroughgoing vulnerability to burial. I no longer propose wv--except that I like MAM for CIVS polls, where the burial problem isn't a problem, because there evidently is no offensive strategy used at CIVS.<br><br></div>In 2D, with the voter-distribution assumptions I described, the CWs has a preference majority over everyone, and, with sincere voting majority pair-beats everyone. <br><br></div>Of course burial could make someone beat hir. The closer to the voter-median point a candidate is, the fewer burriers are needed to make that candidate majority-beat the CWs. <br><br></div>In MDDTR, if you can make someone majority-beat the CWs, then everyone is majority-beaten, and so no one is disqualified. Then, if your candidate is the most favorite, & your burial is successful.<br><br></div>...unless the candidate you're burying the CWs with isn't majority-beaten by someone else, other than the CWs..<br><br></div>By the assumptions that I described, a candidate has a "beat-region", such that a candidate in that region of issue-space will majority-beat hir.<br><br></div>The closer the candidate is to the voter-median point, the smaller hir beat-region is.<br><br></div>It consists of the circle that just fits between the candidate and the median.<br><br></div><div>I guess maybe in 3-space it would be a sphere.<br></div><div><br></div>If you want to bury the CWs in MDDTR, just bury hir under a candidate who has 1 or more candidates in hir beat-region.<br><br></div>There's no way to defend against that if your wing has a number of such candidates and you don't know which one will be used for the burial of the CWs.<br><br></div>Of course maybe you just havve 0 or 1 such candidate, and then there isn't a problem. But, in general there is. At least in 2D.<br><br></div>It seems likely that wv has the same problem, because the burial deterrence depends on a threat to keep the candidate used in the burial from being beaten. That's easy in the 3-candidate example: Just don't rank the buriers' candidate. It's nothing like that in 2D issue-space with continuously-distributed voters.<br><br></div>There's an enouraging fact: The larger beat-regions belong to candidates farther from the voter-median point, where it takes more buriers to make the candidate majority-beat the CWs. But the distance only varies with the square-root of the size of the beat-region.<br><br></div>But these mitigations that I've mentioned don't seem enough to justify a pairwise-count method.<br><br></div>I guess Bucklin is the only rank method that can be recommended..<br><div><div><div><br></div><div>Michael Ossipoff<br></div><div><div><div><div><div><div><div><div><div><br><br><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Nov 10, 2016 at 11:26 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"><div dir="ltr"><div><div><div>Regarding the statement about burial deterrence, the majority preferring the CWs to the buriers' candidate can of course, being a majority, ensure that some candidate of their choice doesn't have a majority pairwise vote against hir, because such a majority is impossible if a majority of the voters decline to be part of it.<br><br></div>So the buriers' candidate has a majority against hir because, by assumption, those preferring the CWs to hir vote the CWs over hir. And there's a candidate whom the buriers like less thaln the CWs who _doesn't_ have a majority pairwise vote against hir.<br><br></div>So the burial is thwarted & penalized.<span class="HOEnZb"><font color="#888888"><br><br></font></span></div><span class="HOEnZb"><font color="#888888">Michael Ossipoff<br><br></font></span></div><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Nov 10, 2016 at 9:15 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"><div dir="ltr"><div>Well, by the definition of a CWs, the CWs is preferred to each other candidate by more people than vice-versa, and that doesn't depend on how many dimensions there are.<br><br></div><div>With n dimensions, of course the dimensions might not all share a common median for the distribution, but, for the purpose of wv-like properties, I assume that they do, and that there's always a CWs.<br><br>But if the voters are uniformly-distributed, or if they're continuously, symmetrically distributed about that common median (I assusme that at least one of those is so) then, not only is the CWs preferred to each of other candidates by more voters than vice-versa, but s/he also has a pairwise preference-majority over each of the other candidates.<br><br></div><div>When I say "the median", I mean the common distribution-median for all of the dimensions.<br><br></div><div>Regarding the line that connects the median to a candidate who is away from the median, and regarding the plane that perpendicularly bisects that line, a majority of the points in the distribution are on the median side of that plane.<br><br></div><div>I suggest that the n-dimensional generalization of a "wing" is the set of candidates on one side of a plane that includes the median.<br><br></div><div>Of course, because the CWs has a pairwise preference majority over each of the other candidates, no candidate can have a preference majority over the CWs.<br><br></div><div>As I was saying, for the purpose of defining wv-like strategy properties, I stipulate that only one wing stratgegizes, and the other wing votes sincerely.<br><br>So, by these assumptions, with wv, or MMPO, or MDDTR, truncation from one side can't take the win from the CWs, because the truncators' candidate has a voted majority against him (The CWs is voted over hir by a majority), and the CWs doesn't have a majority against hir (because no candidate has a pairwise preference majority against hir, and no one is burying).<br><br></div><div>And if some candidate's preferrers bury against the CWs, making a voted pairwise majority against hir, and if all the people preferring the CWs to the buriers' candidate (those people are a majority, for the reason that I stated)<br></div><div>decline to vote the buriers' candidate over anyone, then the burier's candidate can't hava a majoriity over anyone, including the candidate they've insincerely ranked over the CWs.<br><br></div><div>So the wv's, MMPO's & MDDTR's automatic protection against truncation, and their deterrence of burial, apply regardless of the dimensionality.<span class="m_3502408520872552199HOEnZb"><font color="#888888"><br><br></font></span></div><span class="m_3502408520872552199HOEnZb"><font color="#888888"><div>Michael Ossipoff<br><br></div></font></span><div><div class="m_3502408520872552199h5"><div><br></div><div><br><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Nov 9, 2016 at 10:57 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">(Replying farther down)<br><br><div><div class="gmail_extra"><div class="gmail_quote"><span>On Wed, Nov 9, 2016 at 10:07 PM, C.Benham <span dir="ltr"><<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div class="m_3502408520872552199m_6287866597694490998m_-7563802397097719283m_7872677193537689502moz-cite-prefix"><span>On 11/10/2016 11:48 AM, Michael
Ossipoff wrote:<br>
<br>
<blockquote type="cite">But that doesn't change the fact that all
of my examples of wv's CWs "protection" guarantees had the CWs
preferred from both sides, and supported from one wing, the wing
opposite the truncating or burying wing.<br>
<br>
That's the "wv-like strategy" that I've been referring to.<br>
<br>
...even though wv has an additional anti-burial guarantee, or
even though its anti-burial guarantee is stronger and more
general.</blockquote>
<br></span>
Mike,<br>
<br>
I'm not completely clear on the exact definition of this
property/criterion that you think is worth giving up compliance
with Mono-add-Plump<br>
and Plurality to have.<span><br>
<br></span></div></div></blockquote></span><div>Good question. When I previously said what I meant by "wv-like strategy", I assumed that no one is indifferent between the CWs and any other candidate.<br></div><div>...which means that the CWs has _lots_ of support from the preferrers of other candidates.<br><br></div><div>In fact, I assumed, without explicitly saying so, that voters & candidates were on a 1D spectrum, with 2 "wings" (sets of voters separated by the CWs), and that the truncation (innocent or strategic) or burial all came from one wing, so that one wing all unanimously ranked the CWs over the other wing's candidates.<br><br></div><div>So the CWs has a preference majority against everyone, and has a voted pairwise majority against all of the candidates of the strategizing wing.<br></div><div><br></div><div>I don't know how well that holds up with more dimensions, with Euclidean or city block distance.<br><br></div><div>Maybe the mathematicians can help with that. Forest?<br><br></div><div>In the meantime, maybe I should just say that "wv-like strategy" is only defined for 1D, with the above-stated assumptions as stipulations.<br><br></div><span><div> <br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"><div class="m_3502408520872552199m_6287866597694490998m_-7563802397097719283m_7872677193537689502moz-cite-prefix"><span>
<blockquote type="cite">Yes, in the standard chicken-dilemma
example, MDDTR elects A, and that's a violation of the Plurality
Criterion. Try to forgive MDDTR for electing the most
favorite-popular candidate who isn't majority-beaten :^)</blockquote>
<br></span>
I'm afraid I find the justification "most favorite-popular
candidate who isn't majority-beaten" to be quite oblique and
arbitrary-sounding.<br></div></div></blockquote><div><br></div></span><div>Majority is a familiar notion. Losing to another candidate by a majority is a reasonable enough grounds for disqualification, if not everyone is.<br><br></div><div>Among the non-disqualified candidates, choosing the most favorite one sounds too natural to be called "arbitrary".<br><br></div><div>And the rule to elect the most favorite candidate who doesn't have someone else ranked over hir by a majority has uniquely many of the best properties. ...practical properties that make voting easier & make sincerity safer.<br><br> <br></div><span><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"><div class="m_3502408520872552199m_6287866597694490998m_-7563802397097719283m_7872677193537689502moz-cite-prefix">
<br>
"Majority-beaten" can go away if we add a few ballots that just
plump for nobody, so big deal. </div></div></blockquote><div><br></div></span><div>Fine. So then I recommend that, in an MDDT election: If your candidate is particularly in danger of majority-disqualification, you should recruit as many voters as possible to plump for no one.<br></div><div><br></div><div>...or wait...Better yet, tell them to rank the candidates you like (and suggest that they should like too) over the ones you don't like.<br><br></div><div>But, whatever you do, get the vote out. Giving an incentive to get everyone to vote--Is that a bad thing? We'd have a big turnout. <br><br>And then, when one of those people shows up to vote, are they just going to say to to themselves, "He said that it would be in my best interest to come here & plump for no one."? Would that be in their best interest? Or might they realize that, having come to the polling place, it might be even better to preferentially rank the candidates whom they like more.<br><br></div><div>So, by all means, get the vote out.<br><br></div><div>Michael Ossipoff<br></div><div><br></div><div class="m_3502408520872552199m_6287866597694490998m_-7563802397097719283m_7872677193537689502moz-cite-prefix"> <br>
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