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

[Steve Eppley]

In the recent conversation between Bart and Blake about 
voters' ratings of candidates, Bart wrote:
-snip-
>> Medians are a natural way of evaluating rated examples,
>> since a candidate with the highest median rating is by
>> definition the candidate rated higher than all others 
>> *by a majority of voters*.    
-snip-  

Blake replied:
>If I understand you correctly, you are referring to the fact 
>that if a single candidate is given the highest rating by a 
>majority of voters, that candidate will win.  Many methods 
>(including plurality) also give a victory to a majority 
>favourite, so although this is true of Median Ratings, it 
>hardly defines it.   
-snip-  

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.


---Steve     (Steve Eppley    seppley at alumni.caltech.edu)