[EM] majorities and ordinal-only pairwise methods

[Jobst Heitzig]

Dear Kevin!

You replied to Russ:
> I would also like to hear again the benefit *inherent* to combining ordinal 
> and cardinal information. It seems to me that you, Jobst, and James all have
> different purposes in doing this.

I have to correct you: I don't think at all that we should base a method
ordinal information since I don't believe there can be sincere cardinal
information. You probably refer to approval information as cardinal
information, but that is only your interpretation of approval, not mine.
I wonder what should be cardinal about a yes-no question...

Anyway, here's why I think a (sincere) method should make use of all
forms of preference information a voter *can* give in a sincere way
(pairwise preferences, favourite, approval): In my opinion, the main
benefit of combining different kinds of preference information is that
it probably will give a more reliable result than when we just
arbitrarily focus on some specific kind of information and ignore the
others.

As I understand James, his main point is strategic considerations, and I
welcome any evidence that a particular approval-aware method has good
anti-strategical properties.

Russ' main point seems to be that a publicly proposed method should be
much more simple than most of the defeat-strength-based methods. I also
welcome if a method is very simple, like DFC or DMC/RAV are.

You also wrote:
> Of course RAV just substitutes an approval measure for WV or Margins.
> It's unchanged, that increasing the strength of one candidate's wins can
> cancel another candidate's wins.

That is also a strange interpretation. Of course, as some of us
including me realized or proved, DMC/RAV is *logically equivalent* to a
number of well-known defeat dropping methods when defeat strength is
defined in a certain way. But defeat strengths are not at all the idea
of neither RAV or DMC, and those methods don't "cancel" any wins.

Yours, Jobst