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<div class="moz-cite-prefix">Forest,<br>
<br>
I've been meaning to remind you: for IRV and Benham (and
Woodall and similar) I'm strongly opposed to allowing voters to do
any equal-ranking<br>
apart from truncating because it makes Push-over strategizing much
less risky and more likely to succeed. <br>
<br>
Two versions of ER-IRV have been discussed, one where an A=B
ballot gives a "whole vote" to each and one where it gives half a
vote to each, i.e,<br>
ER-IRV(whole) and ER-IRV(fractional). The problem I referred to
is much worse for the former and so I consider the latter to less
bad.<br>
<br>
But if we insist on allowing above-bottom equal-ranking and don't
mind a lot of extra complexity, I have this suggestion:<br>
<br>
*Before each elimination, order the candidates according to their
ER-IRV(fractional), (so that among continuing candidates a ballot
that equal-top<br>
ranks n candidates give 1/n of a vote to each). <br>
<br>
Then assign each of the ballots that equal-top rank more than one
candidate to whichever of them is highest in that order. <br>
<br>
Then eliminate the candidate with the fewest ballots assigned to
hir.*<br>
<br>
<div>34 A=B<br>
</div>
<div>31 B<br>
</div>
35 C<br>
<br>
So in this example of Forest's, to create the initial order the 34
A=B ballots give half a vote each to A and B, to give the scores <br>
B (31+17=48) > C35 > A17. <br>
<br>
B is above A in this order, so all of the A=B ballots are assigned
to B. This gives the scores B65 > C35 > A0. A has the
lowest score so <br>
A is eliminated and B wins.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
On 5/20/2014 4:45 AM, Forest Simmons wrote:<br>
</div>
<blockquote
cite="mid:CAP29ondyTCzka0XSxp5-9uuQQ6OX8Wdob82_q_pVi7kU96P98Q@mail.gmail.com"
type="cite">
<div dir="ltr">
<div>
<div>Chris and Mike,<br>
<br>
</div>
your combined comments gave me an idea for a more practical
version of semi-sincerity:<br>
<br>
</div>
<div>A method satisfies Semi-Sincerity Relative to MAM or
SS(MAM) if and only if a semi-sincere modification of the
sincere preferences leads to a strategic equilibrium ballot
set from which the method elects the the sincere MAM winner.<br>
<br>
</div>
<div>This criterion recognizes the superiority of MAM under
ideal conditions while allowing the method in question to
comply with CD, for example.<br>
<br>
</div>
<div>Suppose our method is Benham, and sincere votes are<br>
</div>
<div><br>
</div>
<div>34 A>B<br>
</div>
<div>31 B<br>
</div>
<div>35 C<br>
<br>
</div>
<div>A semi-sincere ballot modification results in a Nash
equilibrium for Benham that elects B, the MAM winner of the
sincere ballot set (not to mention the modified set).<br>
<br>
</div>
<div class="gmail_extra">
<div>34 A=B<br>
</div>
<div>31 B<br>
</div>
35 C<br>
<br>
</div>
<div class="gmail_extra">Forest<br>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote"><br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
Date: Sun, 18 May 2014 14:46:30 -0400<br>
From: Michael Ossipoff <<a moz-do-not-send="true"
href="mailto:email9648742@gmail.com">email9648742@gmail.com</a>><br>
To: <a moz-do-not-send="true"
href="mailto:cbenham@adam.com.au">cbenham@adam.com.au</a>,
"<a moz-do-not-send="true"
href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>"<br>
<<a moz-do-not-send="true"
href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>><br>
Subject: Re: [EM] New Criterion<br>
Message-ID:<br>
<<a moz-do-not-send="true"
href="mailto:CAOKDY5DYQZtEnaoxoV8NG3OxyFBsw%2B59x2vpZU8maFZZEuJiqA@mail.gmail.com">CAOKDY5DYQZtEnaoxoV8NG3OxyFBsw+59x2vpZU8maFZZEuJiqA@mail.gmail.com</a>><br>
Content-Type: text/plain; charset="utf-8"<br>
<br>
Chris--<br>
<br>
One comment that I can make right away is that FBC is
almost surely<br>
incompatible with CD + MMC. ...just as FBC is
incompatible with Condorcet.<br>
So, in Green scenario or ideal majoritarian conditions,
FBC would be too<br>
costly. So, if the 2nd of Forest's criteria, too, is
incompatible with the<br>
criteria desirable for the Green scenario, that's
favorable to a likening<br>
of that criterion to FBC. Sure, the differences are great
too..<br>
<br>
Of course you have a point about the desirability of
sacrificing one's<br>
favorite in order to save the winner under sincere voting.<br>
<br>
It could be argued that the thing being measured for is
the _possibiity_ of<br>
easily (without reversal) preserving the sincere winner,
whether or not<br>
it's always desirable, and that that's a matter of
interest, just because<br>
it _could_ be desirable.<br>
<br>
Mike<br>
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