[EM] The MCA page

[Kevin Venzke]

I thought MCA was supposed to become an umbrella term for MCA and Bucklin.
If those in favor of that have backed off of that plan then... good, in
my opinion, but then I don't quite get what the plan is. I guess MCA is
now a generic term for all median rating methods?

The intro paragraph says MCA is a ratings method sometimes called 
ER-Bucklin. That should probably be fixed since ER-Bucklin is a rank
method (or two) and doesn't treat equality the same way as MCA /
median rating.

Why does the note on terminology say that MCA originally referred to
3-slot MCA-AR-M?? There are not two rounds in standard MCA. The method
was just MCA-M.

Regarding this:
"Clone independence is satisfied along with the weaker and related ISDA by 
MCA-IR and MCA-AR, if ISDA-compliant Condorcet methods (ie, Schulze) are 
used to choose the two "finalists". Using simpler methods (such as MCA 
itself) to decide the finalists, MCA-IR and MCA-AR are not strictly clone 
independent."

First of all how is ISDA weaker than Clone Independence? Neither seems to
imply the other.

It strikes me as obviously false that using an ISDA method in the runoff
will result in the MCA method satisfying ISDA, unless you want to somehow
argue that MCA-AR satisfies ISDA when it doesn't require a runoff.

Also with Condorcet: How can you say that MCA-AR picks the Condorcet
winner when he has majority approval? That doesn't guarantee he will
appear in the final runoff.

Later-no-help: I'm pretty sure all of the runoff-less MCA methods satisfy
this.

FBC: Same, but also I don't believe FBC will be retained with any kind of
runoff.

This page would be a lot better if -IR and -AR were dumped. They are not
fully defined, and whatever properties these methods do possess will
likely be very different from what standard median rating offers.

The categorization of MCA-M, MCA-A, MCA-P doesn't make much sense to me
either, unless everybody uses three slots. If you have a 50-slot ballot
and the tie is at slot 13, nobody's going to want to use MCA-A or MCA-P.
You can break the tie as the score *at* the place where it occurred, or
at the slot right before it, or break the tie as Woodall does with QLTD.
And any of these methods should result in the same properties being
satisfied.

Kevin Venzke