[EM] There's nothing wrong with Average Rating.

[wclark at xoom.org]

Markus Schulze wrote:

>>Arrow proved that there is no single-winner election method with
>>the following four properties:

>>   1) It is a rank method (= a ranked-preference method).
>>   2) It satisfies Pareto.
>>   3) It is non-dictatorial.
>>   4) It satisfies IIA.

Ken Johnson wrote:

> But why did Arrow stipulate #1?

Because it was necessary for his method of proof.  Arrow demonstrated
that, given assumptions 1, 2, and 4, there was no method of resolving
disagreements between ballots, except to give one ballot priority over all
others (i.e. to be dictatorial.)

If you allow cardinal methods, then you can use the strength of
preferences to resolve such disagreements without letting the system
become dictatorial.  (This isn't to say that cardinal methods don't suffer
from their own problems -- just that they don't suffer from the particular
problems Arrow highlighted.)

Here's a rather straightforward graphical proof that might make it more
clear why restriction #1 plays such a crucial role:

http://www.indiana.edu/~econed/pdffiles/summer02/phansen.pdf

> (By the way, shouldn't the criteria also include transitivity, or does
> that follow from the other criteria?)

It follows from Pareto.

-Bill Clark

-- 
Ralph Nader for US President in 2004
http://votenader.org/