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<div class="moz-cite-prefix">Greg,<br>
<br>
I'm glad you like my idea.<br>
<br>
I'm sure the definition could be polished and/or made more
succinct. At the moment I don't have a strong view on your
suggestion<br>
on how that should be done. In general I don't mind the odd
redundancy if it makes it more likely that more people will
understand it.<br>
<br>
I won't be dying in a ditch for the "Mutual Plurality" name, but I
think your "Undefeated coalition" suggestion is a bit misleading<br>
and vague.<br>
<br>
It was conceived as an irrelevant-ballot independent version of
Mutual Majority, so I suppose it could be called
"Irrelevant-Ballot<br>
Independent Mutual Majority". Another possible clumsy name:
"Mutual Dominant Relative Majority"?<br>
<br>
<blockquote type="cite">It's clear to me that the Smith set is
always a subset of every "mutual plurality" set, right?</blockquote>
<br>
Yes, but of course there isn't always a "Mutual Plurality" set (or
subset) while there is always a Smith set.<br>
<br>
Chris Benham<br>
<br>
<br>
On 6/05/2018 6:52 AM, Greg Dennis wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAOaqmjpO2e2vr+ScRn-5bt_ydVn1ECzuuN_cNstzFdr=DSDZsQ@mail.gmail.com">
<div dir="ltr">
<div>Chris, I think this is an excellent improvement over mutual
majority. My only suggestions are around how it's phrased and
named.</div>
<div><br>
</div>
<div>I'd probably drop the "smallest S" when describing it,
since it's implied, i.e. just "If there exists a set S
... then the winner must come from S." Mutual majority has the
same "smallest" implication but I think is usually omitted
from descriptions.</div>
<div><br>
</div>
<div>I'm concerned that the name "mutual plurality" makes it
sound like a weaker condition than "mutual majority." Maybe
something like "Undefeated coalition," not sure.</div>
<div><br>
</div>
<div>It's clear to me that the Smith set is always a subset of
every "mutual plurality" set, right?</div>
<div><br>
</div>
<div><br>
<div class="gmail_extra">
<div class="gmail_quote">On Tue, Apr 24, 2018 at 9:11 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:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">The Majority for
Solid Coalitions (aka Mutual Majority) criterion
reflects a strong standard of mine, but I'm not happy<br>
that the concept is vulnerable to irrelevant ballots. In
other words in some election the criterion might insist
that A must<br>
win but then if we add a handful of ballots that vote
for no-one the criterion says that it's now ok for A to
not win.<br>
<br>
To address this I've come up with a somewhat stronger
and more generally useful criterion that implies
compliance<br>
with Majority for Solid Coalitions.<br>
<br>
*If there exists one or more sets S of at least one
candidate that is voted above (together in any order)
above all other<br>
candidates on a greater number of ballots than any
outside-S candidate is voted above any member of S (in
any positions)<br>
then the winner must come from the smallest S.*<br>
<br>
In other words if a candidate or set S of candidates
need only the ballots on which they are voted above all
others to win<br>
all their pairwise contests versus all the other
(outside-S) candidates, then that is good enough.<br>
<br>
The brief and I hope adequate name I suggest is the
"Mutual Plurality" criterion.<br>
<br>
As I earlier implied, everything that meets this also
meets Majority for Solid Coalitions but vice versa isn't
the case.<br>
<br>
49: A>B<br>
41: B<br>
10: C<br>
<br>
Here my suggested criterion says A must win, but
Majority for Solid Coalitions says nothing but will
agree if we remove<br>
two or more of the C ballots.<br>
<br>
Bucklin (and some similar methods) meet Majority for
Solid Coalitions but elect B.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
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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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