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

[Bart Ingles]

Ken Johnson wrote:
> 
> >Date: Mon, 01 Mar 2004 12:37:08 +0100
> >From: Markus Schulze <markus.schulze at alumni.tu-berlin.de>
> >...
> >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.
> >
> >All four properties are needed to get an incompatibility.
> >For example, RandomDictatorship is a paretian rank method that
> >satisfies IIA, RandomCandidate is a non-dictatorial rank method
> >that satisfies IIA, Approval Voting is a paretian non-dictatorial
> >method that satisfies IIA, my beatpath method is a paretian
> >non-dictatorial rank method.
> >
> But why did Arrow stipulate #1?

Because he was interested in ranked voting systems.  Also, the
combination of the other three conditions would have been unremarkable.

> If you remove this requirement, does the
> conclusion that "there is no perfect voting system" still follow, and is
> CR an example of a "perfect" system according to Arrow's remaining
> criteria?

"No perfect voting system" didn't follow with condition #1 in place, so
I suppose it doesn't follow if you remove #1.  A hypothetical system
could fail the conditions and still be "perfect" (depending on how
perfect is defined), or it could meet the conditions and be imperfect. 
Arrow merely proved that the four conditions are mutually exclusive.

It's probably more useful to examine what a system accomplishes.  For
example, is it a Duvergerian system (i.e. does it reinforce the
two-party system)?  If so, it's not much use to an independent or
third-party candidate.


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

That's probably included in the formal statement of condition #1.

Bart