<div dir="ltr">I earlier said that C would win in "PARFBC" in Chris's scenario. I was wrong, as Chris nicely pointed out to me privately:<div><br></div><div><span class="gmail-"><br>43: A<br>03: A>B<br>44: B>C <br></span>10: C</div><div><br></div><div>C is eliminated for having under 25% prefer, and so A wins.</div><div><br></div><div>Honestly, I think that a scenario where the approval winner is eliminated on this basis is not very plausible. If 15 of the B>C voters switched to BC, then C would win. This switch would not stop B from winning if there were more A>B voters, so it's strategically safe; it's not hard to imagine that 1/3 of the honest B>C>A voters might vote like that either naively or strategically.<br><div class="gmail_extra"><br><div class="gmail_quote">2016-11-09 10:09 GMT-05:00 C.Benham <span dir="ltr"><<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
<div class="gmail-m_-3745584437365888725moz-cite-prefix">
<blockquote type="cite"><font id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20463" face="Arial" size="2"><b><span style="font-weight:bold">Envoyé
le :</span></b> Lundi 7 novembre 2016 8h27<br>
<b><span style="font-weight:bold">Objet :</span></b> [EM] Holy
grail: PAR with FBC?<br>
</font>
<div class="gmail-m_-3745584437365888725m_4426200618294732187y_msg_container" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20573">
<div>
<div class="gmail-m_-3745584437365888725h5"><br>
<div id="gmail-m_-3745584437365888725m_4426200618294732187yiv0468842522">
<div dir="ltr" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20572">
<div id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20571"><font id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20570" face="sans-serif" color="#252525"><span style="font-size:14px" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20569">Here's
a new system. It's like PAR, but meets FBC, and
deals with center squeeze correctly in the few
tricky cases where PAR doesn't. I'm considering
using the PAR name for this system, and renaming
the current PAR to something like "<a rel="nofollow" href="http://sr3.wine-searcher.net/images/labels/29/06/grand-old-parr-12-year-old-blended-scotch-whisky-scotland-10152906t.jpg" target="_blank">Old Par</a>". Meanwhile, the
system below is temporarily called <a rel="nofollow" href="http://wiki.electorama.com/wiki/PARFBC_voting" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20635" target="_blank">PARFBC</a>.</span></font></div>
<div id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20574"><font face="sans-serif" color="#252525"><span style="font-size:14px"> </span></font></div>
<ol style="margin:0.3em 0px 0px 3.2em;padding:0px;color:rgb(37,37,37);font-family:sans-serif;font-size:14px" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20576">
<li style="margin-bottom:0.1em" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20762">Voters
can Prefer, Accept, or Reject each candidate.
Default is Accept.</li>
<li style="margin-bottom:0.1em" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20634">Candidates
with a majority of Reject, or with under 25%
Prefer, are eliminated, unless that would
eliminate all candidates.</li>
<li style="margin-bottom:0.1em" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20761">Tally
"prefer" ratings for all non-eliminated
candidates.</li>
<li style="margin-bottom:0.1em" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20575">Find
the leader in this tally, and add in "accept"
ratings on ballots that don't prefer the leader
(if they haven't already been tallied).</li>
<li style="margin-bottom:0.1em" id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20760">Repeat
step 4 until the leader doesn't change. The winner
is the final leader.</li>
</ol>
<div id="gmail-m_-3745584437365888725m_4426200618294732187yui_3_16_0_ym19_1_1478564409045_20633"><font face="sans-serif" color="#252525"><span style="font-size:14px"><br>
</span></font></div>
</div>
</div>
</div>
</div>
</div>
</blockquote><span class="gmail-">
<br>
43: A<br>
03: A>B<br>
44: B>C <br></span>
10: C<span class="gmail-"><br>
<br>
<blockquote type="cite">No, PARHG (PAR Holy Grail) elects C here.</blockquote>
<br></span>
With default being "Accept", no candidate has a "majority of
Reject" but C has "under 25% Prefer" so is eliminated under rule
2. Then I suppose A wins.<br>
<br>
If we assume that the truncators are giving "Rejects" to the
unrated/unranked candidates, then I suppose both A and B have a
"majority of Rejects" and so<br>
none of the candidates are eliminated and then as you say C would
win. (My mistake was that I didn't notice B's "majority of Reject"
so I thought that C and<br>
A would be eliminated).<br>
<br>
Have I now got this right? If so I'll correct my mistake on EM.<br>
<br>
Chris<div><div class="gmail-h5"><br>
On 11/9/2016 5:07 PM, Jameson Quinn wrote:<br>
</div></div></div>
<blockquote type="cite"><div><div class="gmail-h5">
<div dir="ltr"><br>
<div class="gmail_extra"><br>
<div class="gmail_quote">2016-11-08 23:25 GMT-05:00 C.Benham <span dir="ltr"><<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>:<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
<div class="gmail-m_-3745584437365888725m_-5811915833743989738moz-cite-prefix"><span>On 11/9/2016 8:35 AM, Michael Ossipoff
wrote:<br>
<br>
<blockquote type="cite">
<p dir="ltr">(You wrote) :</p>
<p dir="ltr">And it isn't clear to me that
"wv-like strategy" is even something we should
take if it was free.</p>
<p dir="ltr">(endquote)</p>
<p dir="ltr">In Benham, Woodall, ICT, &
probably many or most pairwise-count methods,
the CWs has no protection from burial, or even
from innocent, non-strategic truncation.</p>
<p dir="ltr">With wv-like strategy, truncation
from one side can't take victory from the CWs
& give it to the truncators' candidate.</p>
<p dir="ltr">...and plumping by the CWs's voters
makes it impossible for burial to succeed. In
fact, the mere threat of that plumping can deter
burial.</p>
</blockquote>
<br>
</span> So to "protect" some candidate that some
voters imagine is the sincere CW (when perhaps there
is no sincere CW or some other candidate <br>
is the sincere CW) you want to have a "defensive
truncation" strategy available<i> inside</i> a method
with a very strong random-fill incentive?<br>
<br>
And you should add (and stress) that it needs plumping
by <i>all </i>of the "CWs voters to make it
impossible for burial to succeed", and not ,say, <br>
merely 93% of them (with the other 7% sincerely fully
ranking):<br>
<br>
43: A<br>
03: A>B<br>
44: B>C (sincere may be B or B>A)<br>
10: C<br>
<br>
100 ballots. C>A 54-46, A>B 46-44, B>C
47-10. Top Ratings A46 > B44 > C10.
Approvals: C54 > A46 > B44.<br>
<br>
Here MDDTR (like MDDTA and WV and Margins and MMPO
and Jameson's latest "holy grail") all elect the
possibly burying voters' favourite, B.<br>
</div>
</div>
</blockquote>
<div><br>
</div>
<div>No, PARHG (PAR Holy Grail) elects C here.</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
<div class="gmail-m_-3745584437365888725m_-5811915833743989738moz-cite-prefix"> <br>
Viewing the ballots from the top, A is the strongest
candidate (and possibly the sincere CW) and viewing
the ballots from the bottom C is the<br>
strongest candidate. And electing B is simply a very
bad (and flagrant) failure of Later-no-Help. And B is
both pairwise beaten and positionally <br>
dominated by A.<br>
<br>
So I can't accept any method that in this scenario
elects B.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
</div>
<br>
</div>
<br>
----<br>
Election-Methods mailing list - see <a href="http://electorama.com/em" rel="noreferrer" target="_blank">http://electorama.com/em</a>
for list info<br>
<br>
</blockquote>
</div>
<br>
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</blockquote></div><br></div></div></div>