<div dir="ltr">I've been thinking about this property more recently, and I'd like to offer what I believe is an equivalent formulation of it. I'm not saying this is _the_ way it should be expressed, but this formulation helps me see the importance of the property:<div><br><div>Consider a set S of candidates such that the following is true. For every candidate C outside of S, exclude all the ballots that express indifference between C and all the candidates in S (i.e. C+S all equally ranked, perhaps left off the ballot altogether), more than half of the remaining ballots (aka the "relevant ballots"), prefer every member of S to C. If there exists an S, the winner must come from S.</div></div><div><br></div><div>Do you agree this is equivalent or have I missed something? If so, I like how this formulation reveals the "majority" threshold lurking inside the original formulation, and to me makes the name Mutual Relevant Majority tempting.</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Sat, May 12, 2018 at 1:17 PM, Chris Benham <span dir="ltr"><<a href="mailto:cbenhamau@yahoo.com.au" target="_blank">cbenhamau@yahoo.com.au</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Greg,<br>
<br>
I did have, but that wasn't it. For the purpose of applying the test to methods, I think I defined it thus:<br>
<br>
*If there is some losing candidate X with fewer above-bottom votes than any other candidate, and all the ballots either<br>
vote X below all other candidates (or ignore/truncate X) or vote X above all other candidates and all the other candidates equal bottom<br>
(or ignored/truncated), then removing any number of the X-supporting ballots can't change the result.*<br>
<br>
Maybe a better version is possible. My idea is that those ballots contain no information about any of the remotely competitive<br>
candidates, but would normally (in jurisdictions that allow truncation or voting candidates equal-bottom)) be counted as valid, which<br>
might not be the case if the criterion just talked about "blank" ballots.<span class="HOEnZb"><font color="#888888"><br>
<br>
Chris Benham</font></span><span class="im HOEnZb"><br>
<br>
<br>
On 11/05/2018 7:44 PM, Greg Dennis wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Chris, do you have a precise definition of "irrelevant ballot"? Just a ballot that expresses indifference between the smallest mutual majority set?<br>
</blockquote>
<br>
<br></span><div class="HOEnZb"><div class="h5">
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</div></div></blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><b style="font-size:12.8px">Greg Dennis, Ph.D. :: Policy Director</b><div style="font-size:12.8px">Voter Choice Massachusetts</div><div style="font-size:12.8px"><br></div><div style="font-size:12.8px">e :: <a href="mailto:greg.dennis@voterchoicema.org" target="_blank">greg.dennis@voterchoicema.org</a><br><div>p :: <a href="tel:617.863.0746" value="+16177848993" style="color:rgb(17,85,204)" target="_blank">617.863.0746</a><br></div></div><div style="font-size:12.8px">w :: <a href="http://voterchoicema.org/" style="color:rgb(17,85,204)" target="_blank">voterchoicema.org</a></div><div style="font-size:12.8px"><br></div><div style="font-size:12.8px">:: Follow us on <a href="https://www.facebook.com/voterchoicema" style="color:rgb(17,85,204)" target="_blank">Facebook</a> and <a href="https://twitter.com/voterchoicema" style="color:rgb(17,85,204)" target="_blank">Twitter</a> ::<br></div></div></div></div></div></div></div></div></div></div></div>
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