[EM] Re: Total Approval Ranked Pairs

[Araucaria Araucana]

On 16 Mar 2005 at 17:32 PST, Forest Simmons wrote:
> Russ worried that putting in an approval cutoff might be too costly.
>
> The cost is the same as adding one extra candidate, the ACC
> (Approval Cutoff Candidate).
>
> Voters that truncate the ACC candidate are implicitly approving all
> of their ranked candidates, since any ranked candidate is considered
> to be ranked above all truncated candidates.

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.

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 ;-).

>
> Russ went on to say that he wasn't too crazy about any of the
> proposed names for ARC/RAV.
>
> If we want to beat IRV we have to get "majority" into the title.
>
> I suggest that we call it "Definite Majority Choice" which would be
> consistent with the following description:

I like this name.  I abbreviate it as DMC below.

>
> 1. Rank as many candidates as you want. One of these candidates is
>    the Approval Cutoff Candidate (the ACC).

Or Lowest Passing Grade ;-).

>
> 2. For each candidate X (besides the ACC) count how many of the
>    ballots rank X above the Approval Cutoff Candidate. This number is
>    candidate X's approval score.
>
> 3. Now withdraw the ACC, which has served its purpose.

>
> 4. For each candidate X determine if there is another candidate Y
> with higher approval score than X, such that Y is also ranked higher
> than X by a majority.  If this is the case, we say that Y is
> definitely preferred over X, and that X is a definite majority
> choice loser.
>
> [In Fine Print] By "majority" we mean a majority of those voters that
> express a preference between X and Y.
>
> 5. Eliminate all definite majority choice losers.

This step might be slightly questionable, but only to theorists.  It
could eliminate members of the Smith Set.  But (I think) such a Smith
Set member would be the Pairwise-Sorted Approval (PSA) loser of a
cycle and would never win in PSA anyway.

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.

>
> 6. Choose as winner the candidate that is ranked above each of the
> other remaining candidates by a majority.

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?

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

The winner by any of these equivalent formulations is 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.

>
> [In each case it is to be understood that the majority is a majority
> of those that express a preference.]
>
> [End of method description]
>
> What do you think?

I'm convinced.

>
> Personally, I would rather see the last step replaced with
>
> 6'. Of the remaining candidates, pick as winner the one which is
> ranked highest on a randomly chosen ballot.
>
> But I realize that the advantage of this version over the
> deterministic version is too subtle for the general voting public to
> appreciate.
>
> But just for the record, I would call this stochastic version
> "Majority Fair Chance."
>
> Perhaps the citizens of a country like Rwanda could appreciate the
> method.
>
> Forest

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.

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?

Ted
-- 
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