[EM] TSA/DMC, etc. (was Total Approval Ranked Pairs)

[Forest Simmons]

Date: Thu, 17 Mar 2005 13:14:10 -0800
From: Araucaria Araucana <araucaria.araucana at gmail.com>
Subject: [EM] Re: Total Approval Ranked Pairs

Ted wrote:

About the Approval Cutoff Candidate, as both name and concept.  In
general I think it is an excellent idea, but I would still suggest
using graded ballots (grades A through F, more if you prefer), but
without fixing the approval cutoff below C.  Then instead of calling
the approval cutoff "ACC", you could call it the "Lowest Passing
Grade".  If not entered, it would default to the lowest assigned
grade.

Forest replies:


I like grade ballots, and LPG is very intuitive in that context.


Ted went on to say ...


If you still want to call it "ACC", you could use this analogy to
explain it: a long time back, I read an article which judged any movie
by comparing it to "The Truth about Cats and Dogs" (which I have never
seen).  The premise was that if it's better, it's a good movie ;-),
and if not, it's a bad movie.  Substitute candidates for movies,
mutatis mutandi ;-).


Forest asks ...

And use Gerald Ford as the standard of comparison?


...

Ted:

The key advantage here is that the remaining set of non-DMC losers
("P") will have no cycles.  There will be no inconsistencies for
IRVists to object to.

Forest: precisely!



Ted:

Let's compare this method to Pairwise Sorted Approval.  In PSA,
starting with the Approval ordering (highest to lowest), candidates
are bubbled up as they defeat any higher-seeded opponents above them.
Denote by Q the final set of candidates ranked by PSA above the
Approval Winner.  Q includes your remaining set P of non-DMC losers.
I.e., if you eliminate from Q any candidates defeated by a
higher-approved (seeded) candidate, you get P.  The resulting PSA
social ranking among P candidates is in non-decreasing order of
approval.

So if you rank your P candidates in non-decreasing order of approval,
you should automatically get their corresponding PSA ordering (minus
the eliminated losers).  In fact the DMC winner will be the least
approved member of set P, right?

Forest: right, and that's another reason to not mention the set P or Q 
unless you are going to choose from it by random ballot; "least approved 
from P" doesn't sound so hot.

Ted:

In any case, your algorithm gets the same winner as PSA.

Forest: Yes.

Ted:

The winner by any of these equivalent formulations is equivalent to
the Ranked Pairs (and Beatpath, too!) winner, when the defeat strength
is measured by the approval of the pairwise winner in a pair.

Forest:

I'm not totally convinced of this, but I hope it is true.

...

Ted:

I'm satisfied with DMC as a first round proposal.  Eliminating DMC
losers is as easy to describe as IRV, and there will be no cycles
among remaining candidates.

To digress slightly -- Forest, what are your thoughts about seeding
with Cardinal Ratings vs. Approval?  If the proposal is passed, the
voters could be given the option of either initial ranking method.

Forest:

If we have grade ballots we might as well try to use the extra CR 
information if it doesn't cause strategy problems.

Did you get my email suggesting using dyadic approval to avoid bunching of 
candidates near the extreme ratings?

Ted:

One way to implement it could be by using extra candidates like the
ACC (aka LPG).  You could have 10 CR 'extra candidates' just like the
ACC, say with ratings from 100,90,...,10.

Default rating for ranked candidates, if no CR candidate is ranked, is
100 points.  Default rating below the lowest ranked CR candidate is 0.

Say CR100 is assigned 3rd place (or grade C)) -- anybody at or above
CR100's rank gets 100 points.  If CR40 is ranked at 5th place (grade
E), candidates in 4th and 5th place get 40 points.  If CR40 is the
lowest ranked CR candidate, any 6th-place or lower-ranked candidates
would get 0 points.

Inconsistent CR candidate ranking (e.g.,CR10 ranked at 1st choice in
example above) would be ignored.

This could very well be too complex for voters, but do you have
philosophical objections as well?

Forest:

Simplicity is part of philosophy :']

Your idea is ingenious, and may lead somewhere interesting.

I think using A to Z graded ballots with the approval cutoff fixed between 
letters M and N would be adequate and simpler, but thinking of other 
possibilities can lead to other interesting ideas, so keep forging ahead!

Forest