[EM] Utilities and CR terminology [Was: Efforts to improve on CR's strategy]

[Gervase Lam]

> Date: Thu, 20 May 2004 16:46:02 -0700
> From: Ken Johnson
> To: election-methods-electorama.com at electorama.com
> Subject: [EM] Efforts to improve on CR's strategy

>     SincereCR: A(0.7), B(0.5), C(0.3), D(0.1), E(-0.1), F(-0.3)
> (This assumes signed CR's, with an approval cutoff of zero.) What I call
> "ExaggerateCR" simply applies a linear transformation so that the max
> and min CR's are +1 and -1:
>     ExaggerateCR: A(1.0), B(0.6), C(0.2), D(-0.2), E(-0.6), F(-1.0)

Ignoring the names of any voting methods for a brief moment, here are some 
what I think are correct definitions in terms of candidates:

Cardinal Ratings are a set of scores that range from 0 to 1.  1 means 
perfect, 0 means the EXTREME worst.  By definition, it is possible for no 
candidate to get a 0 or 1.  This is your SincereCR.

Cardinal Utilities (i.e. Social Utilities) are a set of scores that range 
from 0 to 1.  1 is given to the best candidate and 0 to the worst.  The 
other candidates are given scores in between the best and worst candidates 
as appropriate.  This is your ExaggerateCR.

Ordinal Utilities is the same as ranking.

See <http://en.wikipedia.org/wiki/Utility> for details.

Note that when the Cardinal Ratings Method is talked about, it is assumed 
that the ballots cast are Cardinal Utilities!

By the way, can anybody explain the following statement from the above 
Wikipedia web page:

"The concept of cardinal utility suffers from the absence of an objective 
measure of utility when comparing the utility gained from consumption of a 
particular good by one individual as opposed to another individual.  For 
this reason, neoclassical economics abandoned utility as a foundation for 
the analysis of economic behaviour, in favour of an analysis based upon 
preferences [i.e. rankings]."
 
In the terms of my definition of Cardinal Ratings, does this mean that 
"perfect" cannot really be defined?

Thanks,
Gervase.