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<p><br>
<font size="4">One of the candidates for the poll is Majority
Judgement (a "category" ).<br>
<br>
A few months ago I posted something about a version of Bucklin
that is also a Median Ratings method.<br>
<br>
I reproduce it here to explain why in the poll I will be voting
it below Hare and all the reasonable Condorcet<br>
methods:</font><br>
</p>
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style="font-family: -moz-fixed; font-size: 14px;" lang="x-unicode">
<font size="5"><br>
I think it is now generally agreed that least bad is to use some
sort of limited-slot grading/rating ballot,
<br>
with voters There has been more than one version of Bucklin that
has been used or proposed.
free to give as many <br>
or as few candidates as they like the same grade and to skip
grades if
they want.(So it is just a version of Average Ratings)
<br>
</font>
<font size="5"><br>
If ranking ballots are used then above-bottom equal ranking
should get the whole (not fractional) votes
<br>
interpretation, but if say a ballot equal top-ranks 3 candidates
that ballot gives a whole vote to each in
<br>
the first "round" but then "sits out" rounds 2 and 3.
<br>
</font>
<font size="5"><br>
(Not doing that was shown to make the method fail mono-raise).
<br>
</font>
<font size="5"><br>
If we are talking about one of these versions then we are
talking about a method that meets Favorite Betrayal
<br>
and Majority for Solid Coalitions and Later-no-Help.
<br>
</font>
<font size="5"><br>
But there is a very strong incentive for voters to just submit
approval ballots, and in a competitive election with
<br>
informed voters the extra complexity versus simple Approval
doesn't seem to buy much.
<br>
</font>
<font size="5"><br>
40 A>B
<br>
30 B
<br>
09 C
<br>
02 X
<br>
</font>
<font size="5"><br>
81 ballots.
<br>
</font>
<font size="5"><br>
This example highlights the method's disadvantages compared with
Hare (aka IRV).
<br>
</font>
<font size="5"><br>
I don't consider meeting Majority for Solid Coalitions to be an
adequate standard of majoritarian representative goodness.
<br>
</font>
<font size="5"><br>
I propose the "Dominant Coalition" criterion:
<br>
</font>
<font size="5"><br>
*If a the number of ballots on which a set S of candidates is
ranked/voted all below no outside-S candidate is greater than
the maximum
<br>
pairwise opposition that any inside-S candidate gets from any
outside-S candidate, then the winner must come from set S.*
<br>
</font>
<font size="5"><br>
The single-candidate version (that could be relevant for a
method that fails Clone-Winner) is "Dominant Candidate".
<br>
</font>
<font size="5"><br>
*If the number of ballots on which candidate X is ranked/voted
below no other candidate is greater than X's maximum pairwise
opposition,
<br>
then X must win.*
<br>
</font>
<font size="5"><br>
Another criterion I like (and I think I coined) is Irrelevant
Ballots Independence: adding or removing ballots that contain no
information
<br>
relevant to any of the remotely competitive candidates should
not change the result.
<br>
</font>
<font size="5"><br>
Another criterion met by IRV/RCV but not Bucklin is Mutual
Dominant Third : "if a set S of candidates that pairwise beat
all the outside-S
<br>
candidates are voted above all the outside-S candidates on at
least one third of the ballots then the winner must come from
S."
<br>
</font>
<font size="5"><br>
In the example A is the Dominant Candidate and the Mutual
Dominant Third candidate (and so of course the CW) but the
Bucklin winner
<br>
is B.
<br>
(A lot of people like Hare's compliance with Later-no-Harm. Of
course here if the A>B voters had truncated then A would have
won.)
<br>
</font>
<font size="5"><br>
But if we remove the 2 X ballots the winner changes from B to A,
(because the majority threshold lowers from 41 to 40, so now
there is no
<br>
second round) a failure of Irrelevant Ballots independence.
<br>
</font>
<font size="5"><br>
Chris B.
</font><br>
<br>
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