Medians (was Re: [EM] Absolute Utilities)

[Bart Ingles]

Forest Simmons wrote:
> 
> Medians are more democratic measures of general utility than are means.


A problem regarding medians was pointed out to me a couple of years ago,
when I had claimed that,

>> 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*.  


The response I received pretty well convinced me otherwise.  Claiming
that medians are more democratic than averages probably runs into the
same problem (depending on what you mean by 'democratic':


> From:  "Steve Eppley" <SEppley at a...>
> Date:  Tue May 18, 1999  4:49 pm
> Subject:  [EM] Bart's "Median Rating" method?
>
> 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.