MMPO
Here's an idea for fixing MMPO's lack of Plurality compliabnce:
Include the opposition of the Implicit Approval Cutoff Candidate, the
virtual candidate on the truncation boundary.
Example:
40 A
10 C>A
10 C>B
40 B
In regular MMPO, the max opposition to C is 40. But when the number of
ballots on which C is truncated is counted among the oppositions, the max
opposition becomes 80. Thus Plurality is rescued.
How about the Chicken problem?
Consider
49 C
3 A (sincere A>B)
24 A>B
24 B (sincere B>A)
Regular MMPO gives A the win contrary to Plurality.
Taking the truncation opposition into account we have max oppositions for
A, B, and C, respectively, as 73, 52, and 51. Candidate C wins, punishing
B's defection. This only required three of the A supporters to truncate B.
Unfortunately, even this new version of MMPO fails Condorcet Loser and
Clone Winner.
Yes, avoiding the Plurality criticism could be worth requiring 1/8 of the A
voters to truncate B.
There could be an agreement between A & B voters, to rank eachother's
candidate with 7/8 probability.
"Flip a coin 4 times. If it comes down the same way every time, then don't
rank them."
That reminds me of the Srategic-Fractional-Support anti-defection
strategy-suggestion that you made some time ago, & which I've been
advocating.
It's for methods without built-in chicken-dilemma protection, such as
Approval.
In one version, faction A could try to probabilistically give faction B
just enough votes to make B win if the B faction is bigger than the A
faction believes itself to be.
Sure, it's a guess, but the A faction's guess is as good as the B faction's
guess. They both have access to the same predictive information.
So the fact that the A faction is trying that should deter defection by
the B faction.
It, too, could be done probabilistically, but it's one reason why I like 0
to 99 or 0 to 999 Score voting.
Also, in Approval, amicable factions could probabilistically give
eachother's candidate some near-unity fraction of an approval. They're
effectively fully helping eachother, but the bigger faction will
automatically outpoll the other.
Michael Ossipoff
On Oct 1, 2016 12:09 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Here's an idea for fixing MMPO's lack of Plurality compliabnce:
Include the opposition of the Implicit Approval Cutoff Candidate, the
virtual candidate on the truncation boundary.
Example:
40 A
10 C>A
10 C>B
40 B
In regular MMPO, the max opposition to C is 40. But when the number of
ballots on which C is truncated is counted among the oppositions, the max
opposition becomes 80. Thus Plurality is rescued.
How about the Chicken problem?
Consider
49 C
3 A (sincere A>B)
24 A>B
24 B (sincere B>A)
Regular MMPO gives A the win contrary to Plurality.
Taking the truncation opposition into account we have max oppositions for
A, B, and C, respectively, as 73, 52, and 51. Candidate C wins, punishing
B's defection. This only required three of the A supporters to truncate B.
Unfortunately, even this new version of MMPO fails Condorcet Loser and
Clone Winner.
Michael,
You have a good memory.
Zero to ten might be enough resolution for this technique to work for
typical levels of information.
Here's another criterion idea for use with Score style ballots:
We could say that candidate X strongly covers candidate Y iff X pairwise
beats every candidate that Y beats including the virtual candidates (if
any) that Y beats.
In particular, if Y beats a certain score level by having its median score
higher than that level, then so should X.
Forest
On Sat, Oct 1, 2016 at 3:16 PM, Michael Ossipoff email9648742@gmail.com
wrote:
Yes, avoiding the Plurality criticism could be worth requiring 1/8 of the
A voters to truncate B.
There could be an agreement between A & B voters, to rank eachother's
candidate with 7/8 probability.
"Flip a coin 4 times. If it comes down the same way every time, then don't
rank them."
That reminds me of the Srategic-Fractional-Support anti-defection
strategy-suggestion that you made some time ago, & which I've been
advocating.
It's for methods without built-in chicken-dilemma protection, such as
Approval.
In one version, faction A could try to probabilistically give faction B
just enough votes to make B win if the B faction is bigger than the A
faction believes itself to be.
Sure, it's a guess, but the A faction's guess is as good as the B
faction's guess. They both have access to the same predictive information.
So the fact that the A faction is trying that should deter defection by
the B faction.
It, too, could be done probabilistically, but it's one reason why I like 0
to 99 or 0 to 999 Score voting.
Also, in Approval, amicable factions could probabilistically give
eachother's candidate some near-unity fraction of an approval. They're
effectively fully helping eachother, but the bigger faction will
automatically outpoll the other.
Michael Ossipoff
On Oct 1, 2016 12:09 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Here's an idea for fixing MMPO's lack of Plurality compliabnce:
Include the opposition of the Implicit Approval Cutoff Candidate, the
virtual candidate on the truncation boundary.
Example:
40 A
10 C>A
10 C>B
40 B
In regular MMPO, the max opposition to C is 40. But when the number of
ballots on which C is truncated is counted among the oppositions, the max
opposition becomes 80. Thus Plurality is rescued.
How about the Chicken problem?
Consider
49 C
3 A (sincere A>B)
24 A>B
24 B (sincere B>A)
Regular MMPO gives A the win contrary to Plurality.
Taking the truncation opposition into account we have max oppositions
for A, B, and C, respectively, as 73, 52, and 51. Candidate C wins,
punishing B's defection. This only required three of the A supporters to
truncate B.
Unfortunately, even this new version of MMPO fails Condorcet Loser and
Clone Winner.
info
Yes, now that you mention it, 0-10 or 0-9 Score probably has enough
resolution for the anti-defection fractional-vote strategy.
But, for amicable factions to effectively fully help eachother, while still
ensuring that the bigger faction outpolls the other, it has to be possible
to give a near-unity fraction of a vote.
Michael Ossipoff
On Oct 2, 2016 4:26 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Michael,
You have a good memory.
Zero to ten might be enough resolution for this technique to work for
typical levels of information.
Here's another criterion idea for use with Score style ballots:
We could say that candidate X strongly covers candidate Y iff X pairwise
beats every candidate that Y beats including the virtual candidates (if
any) that Y beats.
In particular, if Y beats a certain score level by having its median score
higher than that level, then so should X.
Forest
On Sat, Oct 1, 2016 at 3:16 PM, Michael Ossipoff email9648742@gmail.com
wrote:
Yes, avoiding the Plurality criticism could be worth requiring 1/8 of the
A voters to truncate B.
There could be an agreement between A & B voters, to rank eachother's
candidate with 7/8 probability.
"Flip a coin 4 times. If it comes down the same way every time, then
don't rank them."
That reminds me of the Srategic-Fractional-Support anti-defection
strategy-suggestion that you made some time ago, & which I've been
advocating.
It's for methods without built-in chicken-dilemma protection, such as
Approval.
In one version, faction A could try to probabilistically give faction B
just enough votes to make B win if the B faction is bigger than the A
faction believes itself to be.
Sure, it's a guess, but the A faction's guess is as good as the B
faction's guess. They both have access to the same predictive information.
So the fact that the A faction is trying that should deter defection by
the B faction.
It, too, could be done probabilistically, but it's one reason why I like
0 to 99 or 0 to 999 Score voting.
Also, in Approval, amicable factions could probabilistically give
eachother's candidate some near-unity fraction of an approval. They're
effectively fully helping eachother, but the bigger faction will
automatically outpoll the other.
Michael Ossipoff
On Oct 1, 2016 12:09 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Here's an idea for fixing MMPO's lack of Plurality compliabnce:
Include the opposition of the Implicit Approval Cutoff Candidate, the
virtual candidate on the truncation boundary.
Example:
40 A
10 C>A
10 C>B
40 B
In regular MMPO, the max opposition to C is 40. But when the number of
ballots on which C is truncated is counted among the oppositions, the max
opposition becomes 80. Thus Plurality is rescued.
How about the Chicken problem?
Consider
49 C
3 A (sincere A>B)
24 A>B
24 B (sincere B>A)
Regular MMPO gives A the win contrary to Plurality.
Taking the truncation opposition into account we have max oppositions
for A, B, and C, respectively, as 73, 52, and 51. Candidate C wins,
punishing B's defection. This only required three of the A supporters to
truncate B.
Unfortunately, even this new version of MMPO fails Condorcet Loser and
Clone Winner.
info