[EM] Ways for MTA & MCA as Approval options. AERLO in MTA or MCA.

[MIKE OSSIPOFF]

First, the reason I talk about MCA, MTA and ABucklin is because they can be used
with the conditional-middle-ratings provisions that I've been describing.

...And of course, also, they're extensions of Approval, which, itself, is a freedom-extension of
Plurality. And of course they can be used as options in an Approval election.

I should say something about the conditional-middle-ratings provisions:

Any one of them could be automatic in a method's rule, or the voter could have the option to use
one of them, or maybe any one of them, as the voter chooses. That conditionality could be 
separately optional for each candidate to whom the voter gives a middle-rating--in other words,
any middle rating could be conditional. And the voter could even choose which conditionality
s/he wants to use in hir conditional middle ratings.

Here are at least some of the kinds of conditionality that I've described:

1. Mutuality requirement as in MTAOC.

2. Mutuality requirement by mutual-approval set, as in MMTA.

3. Faction-size: Give the middle rating only if the other candidate has at
least as many top-ratings as one (or all?) of your top-rated candidates.

4. Hypothetical co-operation (or noncooperation): If all middle ratings were
unconditional; and if all the ballots rating one of your top candidates, and not candidate B
at top, rated (or didn't rate) candidate B above bottom; and if all the ballots rating
candidate  B, but none of your top-rated candidates, at top, rated (or didn't rate) 
any of your top-rated candidates above bottom, then give the middle rating only if
, under those conditions, B  would  have more above-bottom ratings than any
of your top-rated candidates.

[end of list of conditionality provisions]

Obviously #4 is a bit wordy, and maybe therefore not so good in a public proposal.

Second, I said that MCA is 2-stage ABucklin. That's true, when:


1. It's used alone

or 

2. It's used as an Approval option without ABucklin being offered as an option.

But, when MCA and ABucklin are both offered as options in an Approval election, MCA is different
from 2-stage ABucklin, because MCA immediately counts all the middle ratings as soon as
it's determined that no one has a top-majority.

Of course, when MCA and ABucklin are offered as options in an Approval election, the voter should
be able to choose whether to call hir ballot an ABucklin ballot or an MCA ballot. Of course if it
has more than two rank (or rating) levels, it's not an MCA ballot.

Ways for MTA and MCA as options in an Approval election:

There are two ways those methods could be offered as options in an Approval election:

1. Bucklin-like

2. Separate top-ratings

What those mean:

1. Bucklin-like means that MTA's and MCA's top-ratings, only, are counted at first, 
and only as approvals.

So, MTA and MCA only give an approval to their top-rated candidates at first.

Of course, if no candidate yet has approvals (votes on Approval ballots, and top-ratings in 
MTA & MTA) greater in number than half the number of voters, then MCA and MTA ballots give
approvals to their middle-rated candidates too. Then the candidate with the most approvals wins.

Say one or more candidates have approvals greater in number than half the number of voters:

For the MCA ballots, nothing changes. They've given all they will, to their top-rated candidates.

MTA ballots give a middle rating (counted, of course, as approvals) to all of their middle-rated
candidates who have a majority, as described above. 

The candidate with the most approvals wins.

I've assumed that MCA and MTA ballots couldn't or wouldn't be options, together in the same
Approval election, but maybe they could be, when MCA and MTA are offered as options Bucklin-
like.

2. Separate top-ratings:

The top-ratings of MCA and MTA ballots are all that are counted when looking for majority
candidates.

If one or more candidates have top ratings greater in number than half the number of voters,
then, if the option is MCA, the candidate with the most top-ratings wins. If the option is 
MTA, then the majority-top candidate with the most approvals wins (where an approval is a vote on an
Approval ballot, or an MTA top or middle rating).

If no candidates have top-ratings greater in number than half the number of voters, then the
winner is the candidate with the most approvals (where an approval is a vote on an Approval
ballot, or an MCA or MTA top or middle rating).

[end of definitions of Bucklin-like and separate top-ratings]

I'd probably suggest, when using MCA as an option with Approval, that it only be used
Bucklin-like. 

In fact, Bucklin-like would probably be better for MTA too, when used as an option with Approval.

For both methods, that's because separate top-ratings gives less role to the Approval ballots.

If only MTA or MCA were used as an added option in an Approval election, I'd prefer MTA.

But it seems to me that Bucklin-like MTA and MCA could both optionally be used in the same Approval election.

If ABucklin is to also be an option in the Approval election, then the advantage of MCA over MTA is
that MCA is compatible with ABucklin.

But maybe an MTA-compatible ABucklin modification could be written.

AERLO in MTA or MCA:

Though MTA and MCA don't use a full ranking, AERLO could still be used as it would be used
in a rank-method.

One's MTA or MCA ballot could look like this:

Top-rated: Candidates A and B.

Middle-rated:

Candidate C

Candidate D

AERLO

Candidate D

Candidate E 

If it were an optional conditional MCA or MTA ballot, it might look like this:

Top-rated: Candidates A and B.

Middle-rated:

Candidate C

Candidate D

AERLO

Candidate D

Candidate E (conditional by mutual-approval set)

Mike Ossipoff