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

[Monkey Puzzle]

Thank you for your reply, Kevin.  It is nice to get clarification on an
11-year-old thread :-).

If you have by now seen subsequent replies, you will note that Jameson
Quinn proposed a refinement which I think might be better than the original
method.  Call it Reweighted Approval Pairwise (RAP) to avoid potentially
derogatory acronyms:

Graded ballots with approval cutoff (A > B > C approved > D disapproved > E
> F).

Pick approval winner X for first runoff seat.

Reweight all X-approving ballots by 1/2 (D'Hondt) or 1/3 (Sainte-Laguë) [at
the moment I'm leaning toward 1/2].

Pick reweighted approval winner Y for second runoff seat.

Kristofer Munsterhjelm noted that a second n^2 array could be accumulated
summably at the same time as the pairwise array to assist in the Y choice.

The winner is the pairwise winner (PW) of X vs. Y.  Call the pairwise loser
PL.

Adding any ballot that approves PW but does not approve PL should only add
to PW's approval or the PW>PL pairwise vote.  So this ballot should never
be eliminated by reweighted approval.  The ballot increases or does not
change PW vs. PL pairwise.  Therefore this method meets a weak
participation criterion.

The method could fail strong participation if the additional ballot
approved both PW and PL, causing one or the other to lose to a third
candidate.  However, I would argue that the clone independence conferred by
reweighted approval voting would tend to discourage this in most cases.

Similarly, I believe the method passes a weak IIA if the irrelevant
candidate is neither X or Y.  Most voters would consider even the pairwise
loser to be relevant, in my opinion.

Ted

 Frango ut patefaciam -- I break so that I may reveal

On Thu, Nov 10, 2016 at 2:21 PM, Kevin Venzke <stepjak at yahoo.fr> wrote:

> 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 at 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
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20161110/e17cc676/attachment-0001.htm>