[EM] Top-two Approval Pairwise Runoff (TTAPR)

[Kevin Venzke]

Hello,
I'm mainly saying that (purely in theory) the runoff method shouldn't behave any differently from Approval (i.e. if the nominators know what they are doing and voters don't mind clones). I don't see an advantage to having the voters pick between two clones when (in theory, again) those clones wouldn't even be there, save for the incentives of the method. You could counter my criticism by saying a mechanism is allowed to be "theoretically" pointless if in practice it would be OK. Harder to sell such a method though, I think.
The method doesn't satisfy Participation or IIA. Notice that deleting the loser of the final runoff does not necessarily preserve the original winner. And adding ballots that approve the winner can change who the winner is up against, making him lose.
Kevin

      De : Monkey Puzzle <araucaria.araucana at gmail.com>
 À : EM <election-methods at lists.electorama.com> 
 Envoyé le : Jeudi 10 novembre 2016 13h31
 Objet : [EM] Top-two Approval Pairwise Runoff (TTAPR)
   
Back in 2005, Russ Paielli proposed the following to this list:(https://www.mail-archive.com/election-methods-electorama.com@electorama.com/msg06164.html)


I'm up too late again, and I just had an interesting idea. If the
following method has been proposed before, please let me know.
The voters rank the candidates and specify an Approval cutoff. The
winner is then the pairwise winner of the top-two most-approved candidates.
If it doesn't have a name already, let me tentatively call it ATTPR for
Approval Top-Two Pairwise Runoff.
A simpler variation would be to let the voter rank only the approved
candidates, thereby eliminating the need for an explicit Approval cutoff.
Good night, or good morning, whichever the case may be.

I'd like to revive this proposal, in the following form, still basically what Russ proposed:

Voters grade the candidates on a 6 level scale, A>B>C>D>E>F.
Grades A, B, or C are approved; D, E, or F are disapproved.
Rank preferences are inferred from ratings, and the pairwise winner of the top two approved candidates is the winner.
I'd like to defend this method against the two objections posed at the time:
Kevin Venzke raised the following objection:
This fails Clone-Loser pretty badly: if the faction commanding the most
approval runs two candidates, they can win regardless of the pairwise
comparison.

My take on this is that you would have the same problem with straight Approval.   The full pairwise comparison ensures that the least objectionable of the clones (to both winning and losing factions) is the one who wins.  Since my primary metric is finding the candidate who minimizes variance, there is better variance-minimizing when those disagreeing with the top-two approved candidates are able to have a voice in the comparison between the two.
Chris Benham responded with the following objection:
This would be a strategy farce. Voters who are only interested in
electing their favourite would all have incentive to approve, besides
their favourite, any and all candidates
that they think that their favourite can beat in the runoff. The net
effect of this strategising could be that that the two candidates in
the runoff could be the two *least* popular
(sincerely approved).
As well of course, as Kevin pointed out, well-resourced parties would
have incentive to each run two candidates to try to capture both runoff
spots.

I disagree with the supposed strategic incentive.  This seems to be a combination of pushover strategy plus Chicken Dilemma.  The very fact that one might promote more than one sincerely disapproved candidate into the top-two set is itself a disincentive to the attempt, since you get only one coarse-grained shot at the top two.  I think pairwise runoff is an incentive to avoid CD, but possibly not.
And again, I'm not worried about a runoff between clones.  The advantage of TTA is that if the larger faction is going to win anyway, the losing factions can at least have a voice in deciding the lesser of two evils.
I'm primarily concerned about participation, monotonicity and independence from irrelevant alternatives.  It seems to me that participation is satisfied as it would be with straight approval, since adding an approved vote for your favorite would never decrease approval, and adding a preference between favorite and any other compromise should never hurt either favorite or compromise.  
IIA seems like it should be satisfied because adding or removing a non-top-two candidate should never have an effect on the top-two pairwise comparison.
The latter is interesting to me because one would expect that a method with ranking would fall under Arrow Impossibility conditions.
It is apparent that TTAPR can fail Condorcet when the sincere CW is not in the top-two approved, but there is less chance of that occurring than would happen in simple Approval, so I see an improvement.  Of course, it would still fail Smith and other full set Condorcet criteria also.
In an ideal world, I would like to reduce the weight of the pairwise vote between two disapproved candidates, but in a USA-type election, it seems like one has to ensure that ballot weight is always 1 when making candidate comparisons to satisfy constitutional requirements.
Finally, I think this satisfies all the monotonicity criteria satisfied by Approval.  Are there any counterexamples?
Ted--  Frango ut patefaciam -- I break so that I may reveal

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