[EM] Reverse - Symetrical Weighted Median Approval

[Forest Simmons]

On Thu, 19 Feb 2004, Chris Benham wrote:

>   Participants,
>
> I have been inspired  by this post  by  Forest Simmons (Th.Feb.5, 2004)
>
> http://groups.yahoo.com/group/election-methods-list/message/13475
>
> which  contains some discussion of   Joe Weinstein's  "weighted median
> approval method":
>
> Voters rank the candidates, equal preferences ok.
> Each candidate is given a weight  of  1  for each ballot on which that
> candidate is ranked  alone in first place,  1/2  for each ballot  on
> which that candidate is equal ranked  first with one other candidate,
> 1/3 for each ballot on which that candidate is ranked equal first with
> two other candidates, and so on so that the  total of  all  the weights
> equals  the number of ballots.
> Then  approval scores  for each candidate is  derived  thus: each ballot
> approves all candidates that are ranked in first or equal  first place
> (and does not approve all candidates that are ranked last or equal
> last). Subject to that, if the total weight of the approved candidates
> is less than half  the total of number of ballots, then the candidate/s
> on the second preference-level are also approved, and the third, and so
> on; stopping as soon as  the  total weight of the approved candidates
> equals or exceeds half the total mumber of ballots.
> Then the candidate with the highest approval score wins.
>
> This method  always picks a CW if  there are three candidates, and  I

Perhaps you meant to say that this method always picks the CW if the
voters vote in a pattern consistent with a one dimensional spectrum of
candidates, which is true.

However, on 21 January Dave Gamble gave the following three candidate
non-linear example in which this method gives the win to candidate C
rather than candidate B which is the CW.  It would be interesting to see
what the symmetrized version does.

215 ABC
169 ACB
109 BAC
177 BCA
115 CAB
215 CBA
1000 ballots

I like your idea of reversing the ballots, etc. to bring the method into
compliance with reverse symmetry.

Thanks for your great contributions.

Forest