# [EM] New 3-slot FBC method (not)

Chris Benham chrisjbenham at optusnet.com.au
Mon Jan 15 07:20:43 PST 2007

```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.

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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