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<div class="moz-cite-prefix">Greg,<br>
<br>
Sorry to be so tardy in replying.<br>
<br>
Your idea seems fine to me.<br>
<br>
Chris Benham<br>
<br>
On 7/07/2018 1:10 AM, Greg Dennis wrote:<br>
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<blockquote type="cite"
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<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>
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<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"
moz-do-not-send="true">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>
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<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>
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