<div dir="ltr"><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div>I've unsuccessfully looked for an exception to this statement of mine:<br><br>"It's probably impossible in principle, with any possible method, to both
protect from chicken-defection by a candidate's voters, and also give
hir full truncation & burial protection."<br><br></div>Here's what I tried:<br><br></div>I know of 3 ways of avoiding chicken-dilemma:<br><br></div>1. IRV does it by not sharing any votes unless your top-ranked candidate is eliminated.<br><br></div>2. MDDA(p/2) does it by the A voters denying an approval to B, in the chicken-dilemma example.<br><br></div>3. MMPO does it by the fact that, with C voters treating A & B equally, B can't do better than A, because the A faction is larger.<br><br></div>It could appear as if #3 is promising, because there's no need for A voters to deny support to B.<br><br></div>The trouble is that, though the A voters don't need to deny support to B, the support that they give to _anyone_ is iffy. MMPO doesn't really have burial-resistance for _anyone_ you middle-rank. Truncation of the buriers' candidate doesn't prevent hir from successfully burying, any more than it does in MDDTR.<br><br></div>Well, the best that can be said for MMPO, in regards to burial resistance, is that burial isn't quite as easy & safe as it can be in MDDTR.<br><br></div>In MDDTR, the buriers merely need for everyone to be majority-beaten, & for their candidate to have a plurality. In MMPO, the buriers need for all the other candidates to be _more_ beaten than their candidate. So the requirement is a bit harder, making the burial a little less safe & dependable.<br><br></div><div>The pt/2 provision seems to avoid MMPO's "Hitler with 2 votes" bad-example.<br></div><div><br></div>So, between MDDA(pt/2) and MMPO(pt/2), it's a choice between fully protecting middle-ranked candidates whom you don't deny approval to, vs making burial a little harder & less reliable & less safe than in MDDTR (but not really resisted), for all of your middle-ranked candidates.<br><br></div>...Complete protection to all of your middle-ranked to whom you don't deny approval, vs some questionable maybe-protection to all of your middle-ranked.<br><br></div>MDDA(pt/2) gives the choice to the voter, regarding support vs chicken-deterrence, instead of being a crapshoot-compromise like MMPO(pt/2).<br><br>-------------------------------------------------<br><br></div>I also considered IC-Smith//MMPO.<br><br></div>Maybe it fails FBC, but I didn't find where it does. It share's MMPO's (& MDDTR's) usual lack of real anti-burial support for any of your middle-ranked candidates.<br><br></div>I guess its advantage over MMPO(pt/2) would be its limitation to the IC-Smith set, if that's really achieved without losing FBC.<br><br>---------------------------------------------------<br><br></div>I wanted to mention these possibilities, but I don't regard either of these gamble-support methods as a rival to MDDA(pt/2).<br><br>---------------------------------------------------<br><br></div>Michael Ossipoff<br><div><div><div><div><div><br><br><div><br><div><div><br><br></div></div></div></div></div></div></div></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Sun, Nov 20, 2016 at 2:42 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><div>Voting, using this method, I might often want to deny approval to a high-ranked candidate (even top?), without denying to the rest of my ranking, approval & full protection from burial & truncation.<br><br></div>Maybe I just don't trust to voters of an excellent candidate whom I rank high, but I have no reason to not want to protect the rest of my ranking from burial or truncation by my unranked candidates' voters.<br><br></div>So I suggest that, in addition to an approval cutoff, a voter should also be able to individually deny approval to any individual candidate(s).<br><br></div>It's probably impossible in principle, with any possible method, to both protect from chicken-defection by a candidate's voters, and also give hir full truncation & burial protection.<span class="HOEnZb"><font color="#888888"><br><br></font></span></div><span class="HOEnZb"><font color="#888888">Michael Ossipoff<br></font></span></div><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">On Fri, Nov 18, 2016 at 6:56 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><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div>Does optional approval cutoff wreck burial protection?<br><br></div>Suppose we have a sincere scenario<br><br></div>40 C>B<br></div>35 A>B<br></div>25 B>C<br><br></div>and the C faction decides to bury the CWs B. The B faction anticipates this and responds by truncating C. It is in the interest of the A faction to leave the default implicit approval cutoff in place. The C faction doesn't want to give A too much support so they use the explicit cutoff option:<br><br></div>40 C>>A<br></div>35 A>B<br></div>25 B<br><br></div>The approval winner is B the CWs.<br><br></div><div>If they left the implicit cutoff in place it would be worse for them; their last choice would be elected.<br></div><div><br></div>So I think MDDA with optional explicit cutoff is fine with respect to truncation and burial.<br><br></div>How about the CD?<br><br></div>In this case the sincere profile is<br><br></div>40 C<br></div>35 A>B<br></div>25 B>A<br><br></div>The B>A faction threatens to defect from the AB coalition.<br></div>The A faction responds by using the explicit cutoff:<br><br></div>40 C<br></div>35 A>>B<br></div>25 B<br><br></div>The approval winner is C, so the threatened defection back-fires.<br><br></div>It seems to me like that is plenty of chicken defection insurance.<br><br></div>The obvious equilibrium position (for the chicken scenario) is<br><br>40 C<br>35 A>>B<br>25 B>>A<br><br></div>Under MDDA(pt/2) the only uneliminated candidate is A.<br><br></div>But if the B faction defects, all candidates are eliminated, and the approval winner C is elected.<br><br></div>This is why I like MDDA(pt/2).<br><br></div>An interesting fact is that MDDA(pt/2) is just another formulation of my version of ICA. They are precisely equivalent. Here's why:<br><br></div>In my version of ICA, X beats Y iff <br><br></div>[X>Y] > [Y>X] + [X=Y=T] + [X=Y=between] , in other words,<br><br></div>[X>Y] > [Y:>=X] - [X=Y=Bottom],<br><br></div>which in turn equals<br><br></div>100% - [X>Y] - [X=Y=Bottom], since 100%= [X>Y] + [Y>=X].<br><br></div>So X beats Y iff<br><br></div>[X>Y] > 100% - [X>Y] - [X=Y=Bottom].<br><br></div>If you add [X.Y] to both sides and divide by 2, you get<br><br></div>[X>Y] +[X=Y=Bottom]/2 > 50%, <br><br></div>precisely the "majority-with- half-power-truncation" rule.<br><br></div>So (my version of) ICA is precisely equivalent to MDDA(pt/2).<br><br></div>I believe it to be completely adequate for defending against burial, truncation, and Chicken Defection.<br><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><div><br></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><div class="gmail_extra"><br><div class="gmail_quote">Now suppose that p<q<r, and p+q+r=100%, and we have three factions of respective sizes p, q, and r:, with r + q > 50%.<br><br></div><div class="gmail_quote">p: C<br></div><div class="gmail_quote">q: A>>B<br></div><div class="gmail_quote">r: B>>A<br></div><br></div><div class="gmail_extra">Then under the pt/2 rule both C and B are eliminated, but not A, so A is elected.<br><br></div><div class="gmail_extra">Suppose that the B factions defects.<br><br></div><div class="gmail_extra">Then A is also eliminated, and the approval winner C is elected.<br><br></div><div class="gmail_extra">Etc.<br><br></div><div class="gmail_extra">So which of the two equivalent formulations is easier to sell? ICA or MDDA(pt/2) ?<span class="m_102490877655208587HOEnZb"><font color="#888888"><br><br></font></span></div><span class="m_102490877655208587HOEnZb"><font color="#888888"><div class="gmail_extra">Forest<br></div></font></span></div>
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