Date: Thu, 17 Mar 2005 13:14:10 -0800 From: Araucaria Araucana <[EMAIL PROTECTED]> 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!
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