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Participants,<br>
I've recently had the idea that ER-Bucklin (whole) could be improved
by combining it with the <br>
"Majority-Defeat Disqualification" (MDD) component from MDD//Approval
(MDDA).<br>
<br>
So I suggest MDD,ER-Bucklin(whole) as my favourite method that
meets FBC.<br>
<br>
"Voters rank the candidates, truncation and equal-ranking allowed.<br>
If not all candidates are majority-strength pairwise beaten
(i.e."dominated") by some other candidate,<br>
then "disqualify" (but not drop from the ballots) those that
are. <br>
If only one candidate remains, that candidate wins.<br>
If more than one candidate remains, commence the ER-Bucklin(whole)
process until (at least) one of<br>
the not-disqualified candidates has a vote tally greater than (or equal
to) half the total number of valid<br>
ballots.<br>
At that point elect the not-disqualified candidate with the highest
vote tally."<br>
<br>
[The "(or equal to)" bit isn't traditional, but I suspect as a fine
point it is good.]<br>
<br>
To explain "the ER-Bucklin(whole) process":<br>
"In the first round each ballot contributes a whole vote each to the
tallies of those candidates they rank top or <br>
equal-top.<br>
In the second round, ballots that have contributed to the tallies of
less than two candidates each contribute<br>
a whole vote each to the tallies of candidates they rank second or
equal-second. <br>
(Ballots that in the first round contributed to the tallies of more
than one candidate do nothing in the second round)<br>
In the third round, if there is one, ballots that have contributed to
the tallies of less than three candidates now <br>
contribute a whole vote each to the tallies of candidates they rank
third or equal-third.<br>
And so on."<br>
<br>
Or as it is better explained at the Electowiki:<br>
<blockquote type="cite">
<p><i>If a ballot lists n candidates as tied in kth place, count that
ballot as a whole point for all n candidates beginning in the kth round.</i>
</p>
<p>Note: A candidate is ranked in kth place on a given ballot if
there are k-1 candidates who are ranked strictly higher. For exampe, a
ballot marked A>B=C=D>E>F=G=H=I>J should be considered to
rank A to in 1st place, B, C, and D in 2nd place, E in 5th place, F, G,
H, and I in 6th place, and J in 10th place. Thus, the ballot would not
count in favor of E until the 5th round, and it would not count in
favor of J until the 10th round. </p>
<p>This rule is perhaps unique in that it satisfies both the "<a
title="Favorite betrayal" href="/wiki/Favorite_betrayal">favorite
betrayal</a>" criterion and the <a
title="Majority criterion for solid coalitions"
href="/wiki/Majority_criterion_for_solid_coalitions">Majority
criterion for solid coalitions</a>. </p>
</blockquote>
If the majority-disqualified candidates were dropped from the
ballots, then Bucklin's compliance with Mono-raise would (I presume)
be lost.<br>
(If I'm wrong about, then there probably isn't any reason not to just
first drop them from the ballots, making the method the simpler and
more <br>
"intuitive" MDD//ER-Bucklin(whole).)<br>
<br>
I think the only criterion compliance of plain ER-Bucklin(whole) that
we lose is "Later-no-Help", which I don't expect anyone will miss.<br>
<br>
What we gain is "Smith-Condorcet (Gross)" (which means that the winner
comes from the smallest non-empty set of candidates that all <br>
majority-strength pairwise beat any and all outside-the-set
candidates) and the Strategy-Free Criterion (SFC) .<br>
Electowiki definition of SFC:<br>
<br>
<blockquote type="cite">
<p><i>If a Condorcet candidate exists, and if a majority prefers this
candidate to another candidate, then the other candidate should not win
if that majority votes sincerely and no other voter falsifies</i> any
preferences. </p>
<p>In a ranked method, it is nearly equivalent to say: <i>If more
than half of the voters rank </i>x<i> above </i>y<i>, and there is no
candidate </i>z<i> whom more than half of the voters rank above </i>x<i>,
then </i>y<i> must not be elected.</i> </p>
</blockquote>
<br>
<br>
<br>
The method meets FBC/Sincere Favourite, Majority for solid
coalitions/Mutual Majority, the Plurality criterion, Smith(Gross), SFC<br>
(and GSFC?).<br>
<br>
It fails Clone Independence (doubtless both Clone-Winner and
Clone-Loser), Later-no-Harm, Independence from Irrelevant Ballots,<br>
No Zero-Information Strategy.<br>
<br>
Compared to plain ER-Bucklin(whole), this method would have a less
severe Later-no-Harm problem. In ER-Bucklin(whole), if the voter <br>
has a big sincere approval cutoff, the s/he should equal-rank above it
and truncate below it. <br>
In MDD,ER-Bucklin(whole), if the voter's sincere approval cutoff is
above the most preferred member of the anticipated sincere Smith <br>
set then it is probably safe to truncate below that candidate.<br>
<br>
In my view the worst feature of this method is its bad clone problem.
Also I dislike methods that fail Irrelevant Ballots (in the same spirit<br>
as the "Blank Ballots Criterion").<br>
<br>
But combining FBC with Majority for solid coalitions and Smith(Gross)
in my view makes it an ok package, better than MDDA.<br>
<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
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