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<br>
Oops! Some on this list might know to be sceptical when I suggest a
new method meets FBC.<br>
<br>
37: W>F<br>
25: F>C<br>
07: C (sincere is F>C)<br>
31: C>W<br>
<br>
Approvals: W68, C63, F62. Top-rating scores: C38, W37, F 25.
Winning threshold T =50.<br>
<br>
No candidate has a TR score equal or above the threshold, so the least
approved candidate F is eliminated<br>
and then on the 25F>C ballots C is promoted to top rating, boosting
C's TR score to 56, above T so C wins.<br>
<br>
But if the 7C voters stop "betraying" their sincere favourite and
change to C=F, we get:<br>
<br>
37: W>F<br>
25: F>C<br>
07: C=F<br>
31: C>W<br>
<br>
Approvals: F69, W68, C63. Top-rating scores: C38, W37, F 32.
Winning threshold T =50.<br>
<br>
This has the effect of boosting F's approval score so now C is
eliminated and W is promoted to top rating on<br>
the 31C>W ballots so giving W a winning score.<br>
<br>
So this method clearly fails FBC. I withdraw my support for this method
because I don't like single-winner<br>
methods that fail Independence from Irrelevant Ballots (IIB) without
meeting FBC.<br>
<br>
Sorry about that,<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
Chris Benham wrote:
<blockquote cite="mid45AAA43D.2030503@optusnet.com.au" type="cite">
<pre wrap="">I have an idea for a new 3-slot method, and if people like it I'm open
to suggestions for a name.
(It is similar to and partly inspired by Douglas Woodall's "ApAV" method.)
</pre>
<blockquote type="cite">
<pre wrap="">1. Voters give each candidate a top rating , a middle rating or no
rating.
2. Fix the winning threshold T at 50% of the total valid ballots. Give
each candidate a score equal to
the number of ballots on which it is top-rated. If the candidate X
with the highest score has a score
equal or greater than T, elect X.
3. If not, eliminate the (remaining) candidate which is given a top or
middle rating on the fewest ballots, and
on ballots that now top-rate none of the remaining candidates promote
all the middle-rated candidates to "top-rated"
and accordingly amend the scores.
4. Again, if the now highest scoring candidate X has a score of at
least T then elect X. (T does not shrink
as ballots 'exhaust').
5. Repeat steps 3 and 4 until there is a winner. If no candidate ever
reaches a score of T, elect the candidate
that is top or middle rated on the most ballots (i.e. the Approval
winner).
</pre>
</blockquote>
<pre wrap=""><!---->
Note that in the course of the count no candidates are ever "demoted" on
any ballots from middle-rated to
unrated. Both the winning threshold and the elimination order is fixed
at the start and don't change.
</pre>
<pre wrap="">
</pre>
</blockquote>
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