[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/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.

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.

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

[Monkey Puzzle]

Re-weighted Approval Voting would lose summability, but it might be worth
considering.

To fill out your proposal, the Approval winner and the reweighted approval
winner after reweighting are matched using the original ballot rank
preferences.

This amounts to a two-seat multiwinner primary (satisfying some PR rule)
with pairwise instant runoff.

I worry that introducing multiwinner strategy would still lead to two-party
factionalism.

Would this still satisfy IIA?

Ted

It would be relatively easy to modify this method so that it was
reasonably cloneproof. To wit: "Rank preferences are inferred from
ratings, and the pairwise winner between the top two candidates from
reweighted approval voting (that is: pick the top approval candidate,
reweight all ballots which approved them at 1/2, and then pick the new top
approval candidate)."
1/2 (D'Hondt) could be replaced by 1/3 (Sainte-Laguë) if you preferred.

(https://www.mail-archive.com/election-methods-electorama.co
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
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.

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.

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

[Kristofer Munsterhjelm]

Post by Monkey Puzzle
Re-weighted Approval Voting would lose summability, but it might be
worth considering.
To fill out your proposal, the Approval winner and the reweighted
approval winner after reweighting are matched using the original ballot
rank preferences.
This amounts to a two-seat multiwinner primary (satisfying some PR rule)
with pairwise instant runoff.
I worry that introducing multiwinner strategy would still lead to
two-party factionalism.
Would this still satisfy IIA?

It should be summable with order n^2. For each candidate C, keep a
"C-penalized Approval count" that is counted as usual except that where
every ballot that approves of C only counts 1/2 (or 1/3), instead of a
full point, towards the candidates that ballot approves.

Then you use the unpenalized Approval count to determine the ordinary
Approval Winner. Suppose the winner is x. Then you look up the winner in
x's penalized Approval count (say it's y). Finally, you determine the
pairwise winner between x and y based on non-penalized pairwise preferences.

You can't do better than O(n^2) since you'd presumably need the full
pairwise matrix anyway, so as far as asymptotics go, including the n
C-penalized Approval counts is essentially free.

Or am I missing something?
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Monkey Puzzle]

Thanks Kristofer, that does sound correct, and still O(n^2) as you note.

This is looking quite interesting. You get clone independence from the PR
round. Does it now avoid pushover strategy? Quite possibly, because
elevating your weakest opponent could also weaken your hoped-for favorite.

How about IIA and monotonicity criteria?

Ted

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

On Thu, Nov 10, 2016 at 1:01 PM, Kristofer Munsterhjelm <

Post by Kristofer Munsterhjelm

Post by Monkey Puzzle
Re-weighted Approval Voting would lose summability, but it might be
worth considering.
To fill out your proposal, the Approval winner and the reweighted
approval winner after reweighting are matched using the original ballot
rank preferences.
This amounts to a two-seat multiwinner primary (satisfying some PR rule)
with pairwise instant runoff.
I worry that introducing multiwinner strategy would still lead to
two-party factionalism.
Would this still satisfy IIA?

It should be summable with order n^2. For each candidate C, keep a
"C-penalized Approval count" that is counted as usual except that where
every ballot that approves of C only counts 1/2 (or 1/3), instead of a
full point, towards the candidates that ballot approves.
Then you use the unpenalized Approval count to determine the ordinary
Approval Winner. Suppose the winner is x. Then you look up the winner in
x's penalized Approval count (say it's y). Finally, you determine the
pairwise winner between x and y based on non-penalized pairwise preferences.
You can't do better than O(n^2) since you'd presumably need the full
pairwise matrix anyway, so as far as asymptotics go, including the n
C-penalized Approval counts is essentially free.
Or am I missing something?

[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 <***@gmail.com>
À : EM <election-***@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/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

[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

Post by Kevin Venzke
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

Post by 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
------------------------------
*Envoyé le :* Jeudi 10 novembre 2016 13h31
*Objet :* [EM] Top-two Approval Pairwise Runoff (TTAPR)
(https://www.mail-archive.com/election-methods-electorama.
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
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.
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.
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

[Kevin Venzke]

Ok. I notice from your description that it's not clear how to decide whether a different method would satisfy the weak IIA. It seems like it will be really hard to define it, because your definition of the second "relevant" candidate is very specific to this method.
Incidentally I feel even the methods that fully satisfy the letter of IIA don't seem to do anything of value stemming from that fact. E.g. we expect real Approval voters to generally approve at least one and disapprove at least one candidate of those offered. But that assumption already means we can't safely delete losers without fear of changing the winner.
I'm not too optimistic about Participation, either, as all the (non-random?) methods that satisfy it just sum points. DAC and DSC seem like the upper limit of complexity so far, and they are not that great.
My take on the general concept of TTAPR is to start by checking for a majority favorite, and then have the pairwise comparison between the two candidates who minimize the number of voters who didn't approve either of them. But that rule could exclude the approval winner from the comparison. A different option could be to compare the approval winner with the candidate most approved on ballots not approving the approval winner. (We've called this measure "approval opposition" I believe.)

Kevin

De : Monkey Puzzle <***@gmail.com>
À : Kevin Venzke <***@yahoo.fr>
Cc : EM <election-***@lists.electorama.com>
Envoyé le : Jeudi 10 novembre 2016 17h16
Objet : Re: [EM] Top-two Approval Pairwise Runoff (TTAPR)

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 <***@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 <***@gmail.com>
À : EM <election-***@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. ***@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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[Michael Ossipoff]

Of course Approval with top-2 runoff has been discussed many times at EM,
and written about a lot.

It's been rejected in EM discussion because, if you decide to approve
Favorite, in addition to Compromise: Favorite can knock Compromise out of
the runoff, when Compromise, but not Favorite can win in the runoff.

Basing the runoff count on rankings voted in the same ballot as the
approvals, instead of by returning later to the polling-place on a
different day, doesn't change that.

Michael Ossipoff

(https://www.mail-archive.com/election-methods-electorama.
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
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.

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.

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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[Forest Simmons]

Some of the replies are taking the subject line too literally. We're not
talking about top two runoff, but two member PR runoff. we find out who
the two member parliament would be then pit those two against each other.

So

40 C
32 A>B
28 B>A

Suppose that we use PAV with implicit approval

The A is the first member in the two member parliament.

The two factions that supported A get their weights cut in half, so C is
the second member.

The runoff is between A and C, not between A and B, as some people are
assuming.

If the B faction defects, then the two members of the pariliament would be
B and C, and the pairwise winner would be B, so the method does not satisfy
CD.


Date: Thu, 10 Nov 2016 22:21:07 +0000 (UTC)

Subject: Re: [EM] Top-two Approval Pairwise Runoff (TTAPR)
Content-Type: text/plain; charset="utf-8"
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
Envoy? 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-
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
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
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.
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
----

[Kevin Venzke]

The very first post quoted and responded to me talking about TTAPR. Thus you get a response about TTAPR
I do understand how this PR method works.
Kevin

De : Forest Simmons <***@pcc.edu>
À : EM <election-***@lists.electorama.com>
Envoyé le : Jeudi 10 novembre 2016 18h48
Objet : Re: [EM] Top-two Approval Pairwise Runoff (TTAPR)

Some of the replies are taking the subject line too literally.  We're not talking about top two runoff, but two member PR runoff.  we find out who the two member parliament would be then pit those two against each other.

So

40 C
32 A>B
28 B>A

Suppose that we use PAV with implicit approval

The A is the first member in the two member parliament.

The two factions that supported A get their weights cut in half, so C is the second member.

The runoff is between A and C, not between A and B, as some people are assuming.

If the B faction defects, then the two members of the pariliament would be B and C, and the pairwise winner would be B, so the method does not satisfy CD.



Date: Thu, 10 Nov 2016 22:21:07 +0000 (UTC)
From: Kevin Venzke <***@yahoo.fr>
To: Monkey Puzzle <***@gmail.com> ,       EM
        <election-***@lists. electorama.com>
Subject: Re: [EM] Top-two Approval Pairwise Runoff (TTAPR)
Message-ID: <610944053.3025054. ***@mail.yahoo.com>
Content-Type: text/plain; charset="utf-8"

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 <***@gmail.com>
 ??: EM <election-***@lists. electorama.com>
 Envoy? 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/ 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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[Kristofer Munsterhjelm]

Post by Forest Simmons
Some of the replies are taking the subject line too literally. We're
not talking about top two runoff, but two member PR runoff. we find out
who the two member parliament would be then pit those two against each
other.
So
40 C
32 A>B
28 B>A
Suppose that we use PAV with implicit approval
The A is the first member in the two member parliament.
The two factions that supported A get their weights cut in half, so C is
the second member.
The runoff is between A and C, not between A and B, as some people are
assuming.
If the B faction defects, then the two members of the pariliament would
be B and C, and the pairwise winner would be B, so the method does not
satisfy CD.

On a more intuitive level, that isn't too surprising. Suppose you have a
Bush-Nader-Gore situation. The runoff doesn't help the voters who want
to know whether to vote {Nader, Gore} or {Nader}, since if they vote
only Nader, Bush and Gore may go to the runoff (i.e. Nader loses). On
the other hand, if they do vote {Nader, Gore}, and Gore is picked for
the first winner, then their ballots will be deweighted and Nader
probably won't come in second anyway.
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[Monkey Puzzle]

In this chicken dilemma defection situation, the As and Bs could add
preferences below the approval cutoff:

40 C
32 A>>B
28 B>>A

Both groups defect from each other, but assign their rival a higher
preference above other disapproved candidates.

C and the larger first choice of A or B are the two parliament seats, and
the disapproved preference helps that candidate win.

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

On Fri, Nov 11, 2016 at 12:21 AM, Kristofer Munsterhjelm <

Post by Kristofer Munsterhjelm

Post by Forest Simmons
Some of the replies are taking the subject line too literally. We're
not talking about top two runoff, but two member PR runoff. we find out
who the two member parliament would be then pit those two against each
other.
So
40 C
32 A>B
28 B>A
Suppose that we use PAV with implicit approval
The A is the first member in the two member parliament.
The two factions that supported A get their weights cut in half, so C is
the second member.
The runoff is between A and C, not between A and B, as some people are
assuming.
If the B faction defects, then the two members of the pariliament would
be B and C, and the pairwise winner would be B, so the method does not
satisfy CD.

On a more intuitive level, that isn't too surprising. Suppose you have a
Bush-Nader-Gore situation. The runoff doesn't help the voters who want
to know whether to vote {Nader, Gore} or {Nader}, since if they vote
only Nader, Bush and Gore may go to the runoff (i.e. Nader loses). On
the other hand, if they do vote {Nader, Gore}, and Gore is picked for
the first winner, then their ballots will be deweighted and Nader
probably won't come in second anyway.
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[Forest Simmons]

Very good! And it works for a variety of Proportional Representation
methods, whether you deweight the ballots to 1/2, 1/3, or even totally
deweight to zero, so that no ballot that approved the first finalist has
any weight at all in deciding who the second finalist is. That may be the
simplest method.


On Fri, Nov 11, 2016 at 10:13 AM, Monkey Puzzle <

Post by Monkey Puzzle
In this chicken dilemma defection situation, the As and Bs could add
40 C
32 A>>B
28 B>>A
Both groups defect from each other, but assign their rival a higher
preference above other disapproved candidates.
C and the larger first choice of A or B are the two parliament seats, and
the disapproved preference helps that candidate win.
Frango ut patefaciam -- I break so that I may reveal
On Fri, Nov 11, 2016 at 12:21 AM, Kristofer Munsterhjelm <

Post by Kristofer Munsterhjelm

Post by Forest Simmons
Some of the replies are taking the subject line too literally. We're
not talking about top two runoff, but two member PR runoff. we find out
who the two member parliament would be then pit those two against each
other.
So
40 C
32 A>B
28 B>A
Suppose that we use PAV with implicit approval
The A is the first member in the two member parliament.
The two factions that supported A get their weights cut in half, so C is
the second member.
The runoff is between A and C, not between A and B, as some people are
assuming.
If the B faction defects, then the two members of the pariliament would
be B and C, and the pairwise winner would be B, so the method does not
satisfy CD.

On a more intuitive level, that isn't too surprising. Suppose you have a
Bush-Nader-Gore situation. The runoff doesn't help the voters who want
to know whether to vote {Nader, Gore} or {Nader}, since if they vote
only Nader, Bush and Gore may go to the runoff (i.e. Nader loses). On
the other hand, if they do vote {Nader, Gore}, and Gore is picked for
the first winner, then their ballots will be deweighted and Nader
probably won't come in second anyway.
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[C.Benham]

The "deweight to zero" option would be best for avoiding an extra easy
Push-over incentive.

With voters being allowed to rank both above and below an approval
threshold, this a one-ballot per voter and one trip
to the polling station version of an earlier suggestion of mine for a 2
trips to the polling station method using simple Approval
ballots.

But then we have a method that can badly fail Condorcet and fails FBC.

I suppose if we don't mind a kludge fix it to meet Condorcet:

*Voters submit rankings with an approval threshold (Default is all
candidates ranked above equal-bottom are interpreted as approved).
Elect the CW if there is one.
Otherwise elect the pairwise winner between (among members of the Smith
set?) the most approved candidate A and the candidate
most approved on ballots that don't approve A.*

Chris Benham

Post by Forest Simmons
Very good! And it works for a variety of Proportional Representation
methods, whether you deweight the ballots to 1/2, 1/3, or even totally
deweight to zero, so that no ballot that approved the first finalist
has any weight at all in deciding who the second finalist is. That
may be the simplest method.
On Fri, Nov 11, 2016 at 10:13 AM, Monkey Puzzle
In this chicken dilemma defection situation, the As and Bs could
40 C
32 A>>B
28 B>>A
Both groups defect from each other, but assign their rival a
higher preference above other disapproved candidates.
C and the larger first choice of A or B are the two parliament
seats, and the disapproved preference helps that candidate win.
Frango ut patefaciam -- I break so that I may reveal
On Fri, Nov 11, 2016 at 12:21 AM, Kristofer Munsterhjelm

Post by Forest Simmons
Some of the replies are taking the subject line too

literally. We're

Post by Forest Simmons
not talking about top two runoff, but two member PR runoff.

we find out

Post by Forest Simmons
who the two member parliament would be then pit those two

against each

Post by Forest Simmons
other.
So
40 C
32 A>B
28 B>A
Suppose that we use PAV with implicit approval
The A is the first member in the two member parliament.
The two factions that supported A get their weights cut in

half, so C is

Post by Forest Simmons
the second member.
The runoff is between A and C, not between A and B, as some

people are

Post by Forest Simmons
assuming.
If the B faction defects, then the two members of the

pariliament would

Post by Forest Simmons
be B and C, and the pairwise winner would be B, so the

method does not

Post by Forest Simmons
satisfy CD.

On a more intuitive level, that isn't too surprising. Suppose you have a
Bush-Nader-Gore situation. The runoff doesn't help the voters who want
to know whether to vote {Nader, Gore} or {Nader}, since if they vote
only Nader, Bush and Gore may go to the runoff (i.e. Nader loses). On
the other hand, if they do vote {Nader, Gore}, and Gore is picked for
the first winner, then their ballots will be deweighted and Nader
probably won't come in second anyway.
----
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----
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[Monkey Puzzle]

Chris's suggestion is a good one, though in some ways the original idea has
come full circle.

His suggestion is now reduced to a form of Condorcet completion.

The primary difference from Smith//Approval is that unless the Smith Set is
explicitly required, the winner could potentially come from outside the
Smith Set.

In the example below,

40 C
32 A >> B
28 B >> A

A is the CW and the completion rule is not necessary. But I can imagine
that there might be situations where a determined CD betrayal by B voters
could force the approval two-seat parliament runoff and prevent A from
being one of the contenders.

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

Post by C.Benham
The "deweight to zero" option would be best for avoiding an extra easy
Push-over incentive.
With voters being allowed to rank both above and below an approval
threshold, this a one-ballot per voter and one trip
to the polling station version of an earlier suggestion of mine for a 2
trips to the polling station method using simple Approval
ballots.
But then we have a method that can badly fail Condorcet and fails FBC.
*Voters submit rankings with an approval threshold (Default is all
candidates ranked above equal-bottom are interpreted as approved).
Elect the CW if there is one.
Otherwise elect the pairwise winner between (among members of the Smith
set?) the most approved candidate A and the candidate
most approved on ballots that don't approve A.*
Chris Benham
Very good! And it works for a variety of Proportional Representation
methods, whether you deweight the ballots to 1/2, 1/3, or even totally
deweight to zero, so that no ballot that approved the first finalist has
any weight at all in deciding who the second finalist is. That may be the
simplest method.
On Fri, Nov 11, 2016 at 10:13 AM, Monkey Puzzle <

Post by Monkey Puzzle
In this chicken dilemma defection situation, the As and Bs could add
40 C
32 A>>B
28 B>>A
Both groups defect from each other, but assign their rival a higher
preference above other disapproved candidates.
C and the larger first choice of A or B are the two parliament seats, and
the disapproved preference helps that candidate win.
Frango ut patefaciam -- I break so that I may reveal
On Fri, Nov 11, 2016 at 12:21 AM, Kristofer Munsterhjelm <

Post by Kristofer Munsterhjelm

Post by Forest Simmons
Some of the replies are taking the subject line too literally. We're
not talking about top two runoff, but two member PR runoff. we find

out

Post by Forest Simmons
who the two member parliament would be then pit those two against each
other.
So
40 C
32 A>B
28 B>A
Suppose that we use PAV with implicit approval
The A is the first member in the two member parliament.
The two factions that supported A get their weights cut in half, so C

is

Post by Forest Simmons
the second member.
The runoff is between A and C, not between A and B, as some people are
assuming.
If the B faction defects, then the two members of the pariliament would
be B and C, and the pairwise winner would be B, so the method does not
satisfy CD.

On a more intuitive level, that isn't too surprising. Suppose you have a
Bush-Nader-Gore situation. The runoff doesn't help the voters who want
to know whether to vote {Nader, Gore} or {Nader}, since if they vote
only Nader, Bush and Gore may go to the runoff (i.e. Nader loses). On
the other hand, if they do vote {Nader, Gore}, and Gore is picked for
the first winner, then their ballots will be deweighted and Nader
probably won't come in second anyway.
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[Forest Simmons]

A suggestion for this class of methods:

Twin clone all of the candidates before computing the two candidate
proportional respresentation parliament.

If the winning parliament consists of a candidate and its twin, then that
candidate wins. Otherwise do the pairwise runoff between the two
parliament members.