[EM] Bart's "Median Rating" method?

[Bart Ingles]

Steve Eppley wrote:
> 
> Bart wrote:
> > Steve Eppley wrote:
> > > I think the definition of Bart's Median rating method needs
> > > clarification, since Bart's claim about highest median rating
> > > and majority appears dubious.  Here's an example to illustrate
> > > the problem:
> > >
> > >    voter 1:  A=95, B=65
> > >    voter 2:  A=85, B=60
> > >    voter 3:  A=50, B=20
> > >    voter 4:  A=40, B= 0
> > >    voter 5:  A=45, B=55
> > >
> > >    There is a majority (80%) who rank A ahead of B.
> > >
> > >    Average rating for A = 63
> > >    Average rating for B = 40
> > >
> > >    Median rating for A  = 50?
> > >    Median rating for B  = 55?
> > >
> > > If I've interpreted correctly how Bart intends it to be
> > > tallied, B is the candidate with the highest "median rating."
> > > But I wouldn't agree that B is rated higher than A by a
> > > majority of voters.
> >
> > Correction:  A majority rate the Median winner (B) higher
> > than any majority rates the opponent (A).
> 
> There are two problems with that overly terse reply:
> 
> 1. It appears false.
> 
> How do we calculate how "a majority rate an alternative"?
> Since Bart hasn't bothered to explain how he intends this to
> be calculated, I'll guess that it's the average of the ratings
> of the alternative, considering just the members of the given
> majority.

For the record, a majority rates B 55 or above.  No majority rates A
higher than 50, although you can say that a majority rates B 50 or
below.

If my reply was overly terse, it was because I wasn't very interested in
Median Ratings either.  I had intended it as a sort of cross-check on
Average Ratings, in answer to Blake's concerns about sensitivity to
extreme voting by minorities.  I think there are better ways of
addressing that issue, however.

You are right, as a method by itself Median Ratings is not very good
even when strategy considerations are excluded.


> We can now conclude that Medians are not a natural way to
> evaluate rated examples, any more than it would be natural for
> humans to walk on all fours.  Median Rating is a terrible way
> to evaluate rated examples, as the example above shows.
> Here's an example which may make this even clearer:
> 
>    voter 1:  A=99, B=51
>    voter 2:  A=99, B=51
>    voter 3:  A=50, B=51
>    voter 4:  A=49, B= 0
>    voter 5:  A=49, B= 0
> 
>    One voter (#3) has a tiny preference for B.
>    All the other voters "strongly" prefer A more than B.


Here's another bad Median Rating winner:

votes   candidate=rating
  4     A=100  B=0  C=0
 45     A=100  B=5  C=0
  6     B=100  A=0  C=0
 45     C=100  A=0  B=0


> Demorep wrote:
> > I suggested that if medians are to be used, then (1) only the
> > choices getting above 50 medians (on a 0 to 100 scale) should 
> > (2) go head to head 
> -snip-
> 
> No, Bart's median method is totally different from Demorep's.
> Demorep has simply grabbed the buzzword "median" and used it 
> in an inappropriate way.  To Demorep, 50 is the median.  To 
> Bart and to me, the median refers to the middle of the actual 
> votes cast.  Demorep should have read more carefully.
> 
> Perhaps instead of "median" Demorep should use the term 
> "mid-scale."

I believe the actual method proposed at the end of last year required
candidates to have a median rating higher than 50 or be disqualified. 
The method of computing the candidates' median ratings was the same as
was used here.