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<blockquote type="cite">"ME(et-eb) is chicken proof,..."</blockquote>
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35 A>B<br>
25 B<br>
40 C<br>
<br>
B>C>A>B et-eb scores: B-15 > C-20 > A-30<br>
<br>
Forest's suggested ME(et-eb) method elects B, but the Chicken
Dilemma criterion says that the winner must not be B.<br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion">http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion</a><br>
<br>
Also this method can fail to elect a candidate that is voted below
no other on more than half the ballots.<br>
<br>
46 A>C<br>
10 B>A<br>
10 B>C<br>
34 B=C<br>
<br>
C>B>A>C et-eb scores: C24 > B8 > A2 100
ballots, e-t scores B54 > A46 > C34<br>
<br>
ME(et-eb) elects C.<br>
<br>
Also it fails Unburiable Mutual Dominant Third.<br>
<br>
34 A>B<br>
17 C>A<br>
16 B>C<br>
31 B<br>
02 B>C (sincere is B or B>A)<br>
<br>
B>C>A>B et-eb scores: B32 > A-15 > C-48<br>
<br>
A is the sincere MDT winner, but ME(et-eb) easily elects the
buriers' favourite B.<br>
<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
On 5/10/2014 9:27 AM, Forest Simmons wrote:<br>
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cite="mid:CAP29ond8DLzN==MY_y_Tmqi6FX=qvZU4N6a5c+8dv2V91QkJ_Q@mail.gmail.com"
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<div>Here's how majority
enhanced approval works: It
elects the approval winner
unless she is covered by some
other candidate. In that case
from among those that cover
her it elects the one with the
most approval. Unless she
also is covered, in which case
from among those that cover
her, it elects the one with
the most approval, etc.<br>
<br>
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Another fancier way to
articulate this goes like this:
First initialize a list with the
name of the approval winner.
Then while at least one
candidate covers every candidate
named on the list, from among
such candidates add to the list
the one with the greatest
approval. Elect the candidate
whose name was added last.<br>
<br>
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Obviously, the MEA winner is
uncovered. This means that to
every other candidate she has a
short beat path, i.e. if she
doesn't beat him, she beats
someone who does. Since she has a
beatpath to every other candidate
she is a member of Smith.<br>
<br>
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We can majority enhance other kinds
of methods that generate a social
order. For example, we could list
the candidates in order of max
pairwise opposition, initialize the
list with the name of the candidate
with the best score, etc. While some
candidate covers all candidates
listed, from among those covering
candidates add to the list the one
with the best score, etc.<br>
<br>
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Currently the score that I like best
because of simplicity and other
properties is what I call et-eb, Equal
Top minus Equal Bottom.<br>
<br>
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A candidate's et-eb score is the
difference in the number of ballots on
which she is ranked below no other
candidate and the number of ballots on
which she is ranked above no other
candidate.<br>
<br>
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ME(et-eb) is chicken proof, monotone,
clone proof, and elects an uncovered
candidate from Smith. It satisfies
Independence from Pareto Dominated
Alternatives and the Plurality criterion.
It does all of these things seamlessly
from the et-eb order and the pairwise
defeat graph, which are easily assembled
from a summable matrix..<br>
<br>
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Here's how it works on Kevin's famous
chicken example:<br>
<br>
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49 C<br>
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27 A>B<br>
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24 B<br>
<br>
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The et-eb scores are
C(49-51)>B(24-49)>A(27-73)<br>
<br>
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Candidate C is elected because she has the best score
and is uncovered (because she has a short beatpath to
each of the other candidates).<br>
<br>
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Notice that when there are only three candidates in
Smith, this method always gives the same result as
Smith//(et-eb), but is more seamless. . Furthermore (in
the case of three candidates) the et-eb scores yield the
same order as the Borda scores, so in the case of three
candidates this method is equivalent to Black (provided
Black allows equal ranking and truncation)..<br>
<br>
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With any number of candidates you can think of there being
three levels: equal bottom, equal top, and in between.
The in between ranks do not affect the score, but they do
contribute to the pairwise matrix, and thereby help
determine the covering relation.<br>
<br>
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Note that (by definition) candidate X covers candidate Y iff
for each candidate Z, whenever Y defeats Z, then so does X.
<br>
<br>
So if Y is not covered by X, there is some Z that if beaten
by Y but not by X, which gives a short beatpath from Y to X,
namely Y>Z>X .<br>
<br>
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This short beatpath idea allows for an alternative definition
of covering:<br>
<br>
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Candidate X covers candidate Y iff there is no short beatpath
from Y to X.<br>
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