<div dir="ltr"><div>It seems to me that _this_ is the method that you'd rather have named after you, if it meets FBC, CD, Mono-Add-Plump, and resists truncation & burial.<br><br></div>Michael Ossipoff<br><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Sat, Nov 19, 2016 at 4:49 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>Well, this looks like the sought-after method that meets FBC & CD, and has wv strategy. ...and without a major criticism.<br><br></div>My first impression is that MDDA(pt/2) would be easier to explain & propose.<br><br></div><div>Thanks for what seems to be the method with the sought-after properties-combination!<span class="HOEnZb"><font color="#888888"><br><br></font></span></div><span class="HOEnZb"><font color="#888888"><div>Michael Ossipoff<br></div></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_-3210881506502165346HOEnZb"><font color="#888888"><br><br></font></span></div><span class="m_-3210881506502165346HOEnZb"><font color="#888888"><div class="gmail_extra">Forest<br></div></font></span></div>
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