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
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@gmail.com>
À : EM election-methods@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
Election-Methods mailing list - see http://electorama.com/em for list info
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@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@gmail.com
À : EM election-methods@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
Election-Methods mailing list - see http://electorama.com/em for list info
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
On Thu, Nov 10, 2016 at 2:31 PM, Monkey Puzzle <araucaria.araucana@gmail.com
wrote:
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
Election-Methods mailing list - see http://electorama.com/em for list info
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 <araucaria.araucana@gmail.com>
À : Kevin Venzke stepjak@yahoo.fr
Cc : EM election-methods@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 stepjak@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@gmail.com>
À : EM <election-methods@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
Election-Methods mailing list - see http://electorama.com/em for list info
Election-Methods mailing list - see http://electorama.com/em for list info