Oops! Some on this list might know to be sceptical when I suggest a new
method meets FBC.
37: W>F
25: F>C
07: C (sincere is F>C)
31: C>W
Approvals: W68, C63, F62. Top-rating scores: C38, W37, F 25.
Winning threshold T =50.
No candidate has a TR score equal or above the threshold, so the least
approved candidate F is eliminated
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.
But if the 7C voters stop "betraying" their sincere favourite and change
to C=F, we get:
37: W>F
25: F>C
07: C=F
31: C>W
Approvals: F69, W68, C63. Top-rating scores: C38, W37, F 32.
Winning threshold T =50.
This has the effect of boosting F's approval score so now C is
eliminated and W is promoted to top rating on
the 31C>W ballots so giving W a winning score.
So this method clearly fails FBC. I withdraw my support for this method
because I don't like single-winner
methods that fail Independence from Irrelevant Ballots (IIB) without
meeting FBC.
Sorry about that,
Chris Benham
Chris Benham wrote:
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.)
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).
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.
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