[EM] Winners or representation?

[Kristofer Munsterhjelm]

On 11.04.2022 20:48, Richard Lung wrote:
> 
> On 11/04/2022 09:22, Richard Lung wrote:
>
>
> Kristofer,
>
> “election criteria” are to be found in the four scales of measurement,
> which I have been discussing. They are the criteria not just of
> “electics” but of the sciences in general. STV has essentially
> satisfied the main four scales, for nearly one and a half centuries.

I think we're talking about very different things in that case.

My definition of an election (method) criterion, and I think one shared
by the EM list, is that an election criterion is a statement about the
behavior of a method.

With the exception of the summability criterion, a criterion is either a
statement about outcomes for particular elections (e.g. the majority
criterion or Droop proportionality criterion) or about how the outcome
changes or doesn't change when something about the election changes
(e.g. the monotonicity criterion).

A method is then said to pass the criterion if the statement is true
when referring to that method (otherwise false if it doesn't, or
inapplicable).

(I could provide a more rigorous mathematical definition if required.)

Since this concept is very general about the behavior of election
methods (it can be used for rated methods, ranked ones, etc.), it
doesn't seem like different scales come into play.

As an example, let's choose Range voting as a typical cardinal method,
and IRV as a typical ordinal one, and reweighted range and STV as their
multi-winner versions.

Then it seems to me that we can just as easily ask if Range satisfies
the majority criterion (it does not) as we can ask whether IRV does (it
does). And similarly, we can just as easily ask if Reweighted Range
Voting satisfies Droop proportionality (it doesn't) as whether STV does
(it does).

It might be the case that *proving* that a particular method passes a
particular criterion requires considerations into just how the algorithm
works. But whether it's meaningful to speak of a criterion in isolation
does not seem to.

Properties like universal suffrage are more about voting in general than
about election methods.

-km