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

[Monkey Puzzle]

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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