[EM] MAMD (Max Assent Min Dissent)

[fsimmons at pcc.edu]

> Date: Mon, 2 Jan 2012 19:44:48 +0000
> From: MIKE OSSIPOFF
> To:
> Subject: [EM] Forest: MAMD

> Forest--
>
> MMPO has several big advantages:
>
> 1. The unmatched brevity of its definition
> 2. Its full-rankings flexibility, which allows the full sincere-
> expressivity benefit of AERLO
> 3. Its ability to elect unfavorite middle CWS better than do
> most or all of the conditional methods
>
> (Of course, though, in fairness to the conditional methods, the
> election of an unfavorite CW would be seen by most people as a
> bad-example)
>
> A modification of MMPO that would avoid Kevin's MMPO bad-
> example, without gaining some other
> un-plurality-like outcome that would bother people, without
> losing FBC or ABE-success, and without
> significant added complication or wording--that would be a good
> thing to find.
>
> Tell me if this is MaxAssentMinDissent (MAMD):
>
> MMPO, except that each ballot that doesn't rank x is counted as
> voting x over himself, which is treated
> as any other pairwise opposition in the MMPO count
>
> [end of definition of MAMD?]

Pretty close. The other difference from regular MMPO is due to symmetric
completion of the truncations.  This counts half of the ballots in which x and y
are both truncated as opposition of x against y and as opposition of y against x.

>
> Because MAMD has just been posted, I haven't yet had the
> opportunity to evaluate it. Tell anything
> you find out about MAMD and the matters discussed above.
>
> In your post, you mentioned symmetric completion, at bottom, and
> everywhere but top. That isn't used in
> MAMD, is it?

Actually MAMD does make use of one of these symmetric completion options. Which
one you use makes no difference in examples with only three candidates.  If you
like MMPO better than MinMax(margins), then you should use symmetric completion
only at bottom.  Otherwise, you should use symmetric completion for all levels
except top.  A compromise version might use symmetric completion only below the
approval cutoff, which would reduce to the first option in the case of implicit
approval.

>
> MMPO with symmetric completion at bottom, while avoiding Kevin's
> bad-example, also sometimes loses
> MMPO's ABE-success:
>
> 60: A>B
> 55: B
> 100: C

Here is the pairwise opposition matrix for MAMD:

[[155, 110, 87.5],
 [105, 100, 115],
 [127.5, 100, 115]] .

The max dissent against B is from the 110 A supporters.  This is the minimum of
the max dissents, since A has is disapproved by 155, and B has a complaint of
115 against  C , not to mention the 115 disapproval against C.

So yes, B wins.


>
> B wins.
>
> Maybe MAMD is what can make MMPO one of the best, criticism-
> invulnerable, FBC/ABE methods.

I hope so. 

INow here's what I meant about the MinMax(margins) clone problem:

17 A>B>C>D
17 B>C>A>D
17 C>A>B>D
16 D>A>B>C
16 D>B>C>A
16 D>C>A>B

The clone cycle {A, B, C} beats  D by a margin of three.

But the pairwise defeats within the clone cycle are all by margins of 33, so the
MinMax(margins) winner is the  Condorcet Loser D.

It's not nice to have a CL be the method winner is the failure of the Clone
Winner property:  If the clone cycle were replaced by a single candidate, that
candidate would be the method winner.

That's why there should be no more than two slots on either side of the approval
cutoff.  True clones would then be restricted to two adjacent slots per ballot.
 In that case a clone cycle becomes impossible.  The problem disappears.

If the method holds up to critical scrutiny, then the big problem is in
"packaging" for public consumption.

The method must be stated as simply, positively, and clearly as possible with
reasonable heuristic motivations for its peculiar characteristics, such as
including the disapprovals among the dissents, and the symmetric completion
feature at the bottom ... something beyond saying that these are kludges to make
the method work in Kevin's bad examples, etc.

Forest