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Simmons, Forest wrote:<br>
<blockquote type="cite">
<pre wrap="">Here's a version that is both clone proof and monotonic:
The winner is the alternative A with the smallest number of ballots on which alternatives that beat A pairwise are ranked in first place. [shared first place slots are counted fractionally]
That's it.
This method satisfies the Smith Criterion, Monotonicity, and Clone Independence.
</pre>
</blockquote>
Warren Smith wrote:<br>
<blockquote type="cite">
<pre wrap="">this is an elegant method!
Note that it is IMMUNE to my "DH3 pathology!<a class="moz-txt-link-rfc2396E" href="http://rangevoting.org/DH3.htmlItisstrategicallypointlessto">"
http://rangevoting.org/DH3.html
It is strategically pointless to "</a>bury" (lower artificially) a rival
to your favorite below some non-entities, because if those nonentitites are never
ranked top, doing so makes no difference.
And it satisfies mono-add-plump and mono-append (two Woodall criteria)!
And it is simple!</pre>
</blockquote>
<br>
Assuming these criterion compliance claims are right , so far I am very
very impressed. Congratulations Forest!<br>
<br>
It seems to completely dominate Schwartz,IRV which until now was one
of my favourite Condorcet methods. I am convinced that it has an<br>
anti-burial property stronger than I suspected it was a possible for
an unadorned Condorcet method to have. One of the reasons I liked<br>
Schwartz,IRV was that it met what I called "Dominant Mutual Third
Burial Resistance", a criterion that said that if there are three
candidates<br>
X,Y,Z and X wins, then changing some ballots from Y>X to Y>Z
can't make Y the winner.<br>
<br>
Well I'm quite sure this Simmons method meets "Dominant Mutual
*Quarter* Burial Resistance"!<br>
<br>
26: A>B<br>
25: C>A<br>
49: B>C (sincere is B>A or B)<br>
<br>
A>B>C>A. "Simmons" scores: A25, B26, C49. A has the lowest
score and so narrowly wins.<br>
<br>
On top of that it has the advantage over Schwartz,IRV of meeting
mono-raise (and so isn't vulnerable to Pushover strategy), and doesn't<br>
seem to have any disadvantage.<br>
<br>
It definitely fails two of Steve Eppley's criteria: Minimal Defense
and "Truncation Resistance" (not ones I rate highly).<br>
<br>
<blockquote type="cite"><a
href="Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm"><i>truncation
resistance</i></a>: Define the "sincere top set" as the smallest
subset <br>
<i> </i> of alternatives such that, for each alternative in the
subset, say <i>x</i>, and <br>
<i> </i> each alternative outside the subset, say <i>y</i>,
the number of voters who <br>
<i> </i> sincerely prefer <i>x</i> over <i>y</i> exceeds the
number who sincerely prefer <i>y</i> <br>
over <i>x</i>. If no voter votes the reverse of any sincere
preference regarding <br>
any pair of alternatives, and more than half of the voters rank
some <i>x</i> in <br>
the sincere top set over some <i>y</i> outside the sincere top
set, then <i>y</i> must <br>
not be elected. (This is a strengthening of a criterion having
the same name <br>
promoted by Mike Ossipoff, whose weaker version applies only
when <br>
the sincere top set contains only one alternative, a Condorcet
winner.)<i><br>
</i></blockquote>
<br>
<br>
I'm not sure about his "Non-Drastic Defense" criterion, (the version)
that says that if Y is ranked no lower than equal-top on more than
half the ballots and Y<br>
pairwise beats X, then X can't win.<br>
<br>
It has Woodall's Symmetric Completion property, and it certainly meets
his Plurality criterion when there are three candidates (and probably
meets it period).<br>
<br>
I'm happy with its performance in this old example:<br>
<br>
101: A<br>
001: B>A<br>
101: C>B<br>
<br>
It easily elects A. Schulze (like the other Winning Votes "defeat
dropper" methods) elects B.<br>
<br>
It meets my "No Zero-Information Strategy" criterion, which means that
the voter with no idea how others will vote does best to simply rank
sincerely.<br>
<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
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