Re: [EM] Agenda Based Banks
It turns out that this method as it stands is not monotonic, but if you omit the downward part, then the remaining simpler version is monotonic:
First initialize a set named "TheBank" with the most promising agenda item.
Then, as long as even one agenda item pairwise beats every member ofTheBank, deposit the least promising of these into TheBank.
Elect the final deposit.
This simple Banks compliant method is a generalization of TACC (Total Approval Chain Climbing).
The only thing I don't like about it is that even when the most promising agenda item is in the Banks set, as likely as not it will elect a different member of that set. My tweak was designed to overcome that "defect" while preserving Banks efficiency. But it's not worth the loss of monotonicity.
Furthermore, it may turn out that the supposed "defect" actually confers burial resistance ... for example ...
45 A>B (sincere A>C)
25 B>C
30 C>A
Ballot pairwise beat cycle: A>B>C>A
Agenda: C<B<A
(based on implicit approval, for example)
TheBank deposits are C, then B... so B wins.... the A faction burial of C backfires by getting its least favorite B elected!
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Susan Simmons suzerainsimmons@outlook.com
Fecha: 1/8/21 2:15 p. m. (GMT-08:00)
A: election-methods@lists.electorama.com
Asunto: Agenda Based Banks
First initialize a set named "TheBank" with the most promising agenda item.
Then, as long as even one agenda item is beaten pairwise by every member of TheBank, add the most promising of these to TheBank.
After that, as long as even one agenda item pairwise beats every member ofTheBank, deposit the least promising of these into TheBank.
Finally, elect the member of TheBank that pairwise beats all of its other members.
I believe that this method satisfies mono-raise as long as the agenda does.
If so, then this is the best agenda based method so far, because (1) no other agenda based method is simpler to describe or compute, and (2) it always elects from a proper subclass of Landau called "Banks", without need for any mention of "covering" or for that matter, "Condorcet", "Landau", or "maximal chain".
If this is true, then there is no good excuse for continuing to propose make-shift tweaks of second and third rate election methods. In particular, ignorance and misplaced zeal are not good excuses!
Sent from my MetroPCS 4G LTE Android Device
On 02.08.2021 21:31, Susan Simmons wrote:
It turns out that this method as it stands is not monotonic, but if you
omit the downward part, then the remaining simpler version is monotonic:
First initialize a set named "TheBank" with the most promising agenda item.
Then, as long as even one agenda item pairwise beats every member
ofTheBank, deposit the least promising of these into TheBank.
Elect the final deposit.
This simple Banks compliant method is a generalization of TACC (Total
Approval Chain Climbing).
The only thing I don't like about it is that even when the most
promising agenda item is in the Banks set, as likely as not it will
elect a different member of that set. My tweak was designed to overcome
that "defect" while preserving Banks efficiency. But it's not worth the
loss of monotonicity.
Furthermore, it may turn out that the supposed "defect" actually confers
burial resistance ... for example ...
45 A>B (sincere A>C)
25 B>C
30 C>A
Ballot pairwise beat cycle: A>B>C>A
Agenda: C<B<A
(based on implicit approval, for example)
That feels like it's a general feature. Consider e.g. Benham with a
preset ordering as an agenda method (remove the loser until there's a CW
among the remaining candidates). Then raising W puts more candidates
between W and the end of the list, which means that in the worst case,
more candidates have to be eliminated before W wins.
It seems like there's some kind of tension where, on the one hand, being
ranked more highly should be advantageous (which it is if the pairwise
preferences don't change, because it saves W from early elimination),
but on the other hand, being ranked more highly with pairwise
preferences changing has a higher chance of being detrimental (because
more candidates have to be eliminated before W becomes a CW).
-km
So here is ABB (Agenda Based Banks):
First initialize a set named "TheBank" with the most promising agenda item as its only member.
Then, as long as even one agenda item pairwise beats every member of TheBank, deposit the least promising of these into TheBank.
Elect the final deposit.
This is even simpler to state and understand than Sequential Pairwise Elimination (SPE) based on the same agenda ...or any other elimination method for that matter.
Note that just as SPE has no need to explain or even mention "Condorcet Winner" or "Smith Set", this method ABB has no need to explain or even mention "Banks Set", except perhaps for historic background.
Similarly, here is a definition of ABL (Agenda Based Landau) that needs no explanation or even mention of "uncovered" or "Landau Set":
First initialize a set named "JJ" with the most promising agenda item together with all of the other items that do not beat it pairwise.
Then, while there remains even one item that is not beaten pairwise by any member of JJ, include into JJ the most promising such item X together with all other items that do not beat X.
Finally elect the last such X to be included into the set JJ.
So ABB is slightly simpler than ABL, but ABL has more respect for the most promising agenda item when that item has a short beat path to each of the other items.
Is this property of ABL more desirable than the (alleged) increased burial resistance of ABB?
Is it worth the (slight) loss of simplicity?
Although I have an emotional attachment to ABL, it seems to me that simple ABB is the better public proposal.
STAR/MJ style score/grade ballots would be adequate for constructing the pairwise win/loss/tie matrix, as well as for computing the agenda order once the basis for that order has been agreed upon ... whether above midrange approval, or a simple variant of that... like the one Ted Stern has suggested for use with Approval Sorted Margins (ASM):
Speaking of ASM, after SPE, ABB and ABL, it is one of the simplest and most intuitive ways to process an agenda. For comparison with ASM we reformulate SPE to output an entire ordered list of the candidates by sorting the agenda:
While there are still adjacent agenda items that are out of order pairwise, transpose the pair closest to the bad end of the agenda. Once sorted, the list has the first place winner at the good extreme.
That was SPE extended to full social order.
Now for ASM:
While there are still adjacent agenda items out of order pairwise, transpose the pair whose members are closest together in approval. Once sorted, the list has the first place winner at the good end of the list.
Like Kemeny-Young this method satisfies the Reverse Symmetry Property. Beyond that, unlike K-Y, it is marginally clone free, i.e. to the degree that the approval cutoff is treated as a virtual candidate.
Furthermore, K-Y is NP hard computationally, unlike ASM.
So whenever the agenda order is based on a score, grade-point, or other numerical system, ASM is infinitely superior to K-Y!
IMHO, these are the methods we should be considering .... ASM, SPE, ABL, and ABB, as defined above:-)
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Susan Simmons suzerainsimmons@outlook.com
Fecha: 2/8/21 12:31 p. m. (GMT-08:00)
A: election-methods@lists.electorama.com
Asunto: Re: Agenda Based Banks
It turns out that this method as it stands is not monotonic, but if you omit the downward part, then the remaining simpler version is monotonic:
First initialize a set named "TheBank" with the most promising agenda item.
Then, as long as even one agenda item pairwise beats every member ofTheBank, deposit the least promising of these into TheBank.
Elect the final deposit.
This simple Banks compliant method is a generalization of TACC (Total Approval Chain Climbing).
The only thing I don't like about it is that even when the most promising agenda item is in the Banks set, as likely as not it will elect a different member of that set. My tweak was designed to overcome that "defect" while preserving Banks efficiency. But it's not worth the loss of monotonicity.
Furthermore, it may turn out that the supposed "defect" actually confers burial resistance ... for example ...
45 A>B (sincere A>C)
25 B>C
30 C>A
Ballot pairwise beat cycle: A>B>C>A
Agenda: C<B<A
(based on implicit approval, for example)
TheBank deposits are C, then B... so B wins.... the A faction burial of C backfires by getting its least favorite B elected!
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Susan Simmons suzerainsimmons@outlook.com
Fecha: 1/8/21 2:15 p. m. (GMT-08:00)
A: election-methods@lists.electorama.com
Asunto: Agenda Based Banks
First initialize a set named "TheBank" with the most promising agenda item.
Then, as long as even one agenda item is beaten pairwise by every member of TheBank, add the most promising of these to TheBank.
After that, as long as even one agenda item pairwise beats every member ofTheBank, deposit the least promising of these into TheBank.
Finally, elect the member of TheBank that pairwise beats all of its other members.
I believe that this method satisfies mono-raise as long as the agenda does.
If so, then this is the best agenda based method so far, because (1) no other agenda based method is simpler to describe or compute, and (2) it always elects from a proper subclass of Landau called "Banks", without need for any mention of "covering" or for that matter, "Condorcet", "Landau", or "maximal chain".
If this is true, then there is no good excuse for continuing to propose make-shift tweaks of second and third rate election methods. In particular, ignorance and misplaced zeal are not good excuses!
Sent from my MetroPCS 4G LTE Android Device
Great explanatory insight!
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Kristofer Munsterhjelm km_elmet@t-online.de
Fecha: 2/8/21 2:13 p. m. (GMT-08:00)
A: Susan Simmons suzerainsimmons@outlook.com, election-methods@lists.electorama.com
Asunto: Re: [EM] Agenda Based Banks
On 02.08.2021 21:31, Susan Simmons wrote:
It turns out that this method as it stands is not monotonic, but if you
omit the downward part, then the remaining simpler version is monotonic:
First initialize a set named "TheBank" with the most promising agenda item.
Then, as long as even one agenda item pairwise beats every member
ofTheBank, deposit the least promising of these into TheBank.
Elect the final deposit.
This simple Banks compliant method is a generalization of TACC (Total
Approval Chain Climbing).
The only thing I don't like about it is that even when the most
promising agenda item is in the Banks set, as likely as not it will
elect a different member of that set. My tweak was designed to overcome
that "defect" while preserving Banks efficiency. But it's not worth the
loss of monotonicity.
Furthermore, it may turn out that the supposed "defect" actually confers
burial resistance ... for example ...
45 A>B (sincere A>C)
25 B>C
30 C>A
Ballot pairwise beat cycle: A>B>C>A
Agenda: C<B<A
(based on implicit approval, for example)
That feels like it's a general feature. Consider e.g. Benham with a
preset ordering as an agenda method (remove the loser until there's a CW
among the remaining candidates). Then raising W puts more candidates
between W and the end of the list, which means that in the worst case,
more candidates have to be eliminated before W wins.
It seems like there's some kind of tension where, on the one hand, being
ranked more highly should be advantageous (which it is if the pairwise
preferences don't change, because it saves W from early elimination),
but on the other hand, being ranked more highly with pairwise
preferences changing has a higher chance of being detrimental (because
more candidates have to be eliminated before W becomes a CW).
-km
Suppose that A has high approval or high first place support .... whatever is likely to put him at the good end of the agenda ... but knows that C has the broad & deep support necessary to be the sincere CW... in particular beating A pairwise.. and that there is some candidate B that A beats pairwise ... and the sincere preference order of the A faction is (mostly) A>C>B, (among these 3 major candidates)
Then A (emboldened by his presumed favorable agenda standing) gets the bright idea of convincing his supporters to bury C under B to create an artificial Condorcet cycle A>B>C>A.
Without this artificial cycle C would win no matter the agenda order ... but now A, at the top of the agenda has a good chance. In fact, the three members of this Smith set are the only possible winners under ISDA (Independence from Smith Dominated Alternatives).
When Smith has only three candidates, some agenda based methods, like SPE and ABL always elect the cycle member with the best agenda position... in this case A.
Another method DMC (Definite Majority Choice), elects the item in the worst agenda position that pairwise beats every item in a higher position ... which in this case is A if the agenda order of favor is (1) C<B<A, but is C if the order is (2) B<C<A.
How about ABB?
In case (1) C is the first bank deposit, and B is the last, hence the winner.
In case (2) B is the first deposit and A is the last, hence winner.
Both DMC and ABB make A's gambit somewhat risky, and if C's supporters take the standard CW precaution of truncating below C, then A's agenda status becomes least favorable of the three, in which case A loses by any reasonable agenda based method.
How do DMC and ABB compare under Chicken attack?
49 B
26 C>A
25 A (sincere is A>B)
Given implicit approval as the agenda setting criterion, A has the favored agenda spot, which makes A win under SPE and ABL.
Candidate C has the worst agenda position, so the agenda order is C<B<A, which makes Chicken attacker A win under DMC.
So our last hope is ABB. It comes through by electing B... fortunately NOT electing the most favored Banks agenda item!
[When Smith is a triple, Banks = Smith]
The very thing that turned me off about ABB years ago (when it was just TACC) made it impervious to Chicken!
ABB (Agenda Based Banks) looks Better and Better Actually (BBA).
... Forest (sharing Sue's phone)
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Kristofer Munsterhjelm km_elmet@t-online.de
Fecha: 2/8/21 2:13 p. m. (GMT-08:00)
A: Susan Simmons suzerainsimmons@outlook.com, election-methods@lists.electorama.com
Asunto: Re: [EM] Agenda Based Banks
On 02.08.2021 21:31, Susan Simmons wrote:
It turns out that this method as it stands is not monotonic, but if you
omit the downward part, then the remaining simpler version is monotonic:
First initialize a set named "TheBank" with the most promising agenda item.
Then, as long as even one agenda item pairwise beats every member
ofTheBank, deposit the least promising of these into TheBank.
Elect the final deposit.
This simple Banks compliant method is a generalization of TACC (Total
Approval Chain Climbing).
The only thing I don't like about it is that even when the most
promising agenda item is in the Banks set, as likely as not it will
elect a different member of that set. My tweak was designed to overcome
that "defect" while preserving Banks efficiency. But it's not worth the
loss of monotonicity.
Furthermore, it may turn out that the supposed "defect" actually confers
burial resistance ... for example ...
45 A>B (sincere A>C)
25 B>C
30 C>A
Ballot pairwise beat cycle: A>B>C>A
Agenda: C<B<A
(based on implicit approval, for example)
That feels like it's a general feature. Consider e.g. Benham with a
preset ordering as an agenda method (remove the loser until there's a CW
among the remaining candidates). Then raising W puts more candidates
between W and the end of the list, which means that in the worst case,
more candidates have to be eliminated before W wins.
It seems like there's some kind of tension where, on the one hand, being
ranked more highly should be advantageous (which it is if the pairwise
preferences don't change, because it saves W from early elimination),
but on the other hand, being ranked more highly with pairwise
preferences changing has a higher chance of being detrimental (because
more candidates have to be eliminated before W becomes a CW).
-km
Actually, in the burial example below, ABB performs strictly better than DMC because under DMC, the burial of C by A either rewards A with a win, or leaves intact A's sincere 2nd choice as winner ... a zero risk gambit.
By way of contrast, if A's gambit fails under ABB, then A's least preferred, B, wins ... a big risk, because A's raising of B enough to introduce the necessary cycle might also be enough to move B to the necessary agenda level (if it was not already there).
In summary, ABB has both the best burial resistance and the best chicken attack resistance of any agenda based Condorcet method that we know of (and we know of oodles!).
It seems doubtful that any simpler, monotone, clone free, ISDA, burial and chicken resistant method exists ... except perhaps Asset Voting, which is too far ahead of its time (and our time ...first promoted only 150 years ago by Charles L Dodgson) even for Steven J Brams the great academic promoter of Approval, another simple method too far ahead of its time.
Have I over-looked something?
Why are people still talking IRV (and its tweaks), STAR, MJ, etc?
Now we have a method ABB simpler than any of these somewhat popular proposals, and equal (in criteria compliances) to any of the academically respectable methods like CSSD, Ranked Pairs, River, etc ... and far superior to classical methods like Copeland, Borda, Bucklin, MinMax, Kemeny-Young, etc.
Why can't we get off dead center and start moving forward instead of backwards?
We know why ... zeal without knowledge, and big egos among movers and shakers.
But what can we do about it?
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Susan Simmons suzerainsimmons@outlook.com
Fecha: 3/8/21 12:08 p. m. (GMT-08:00)
A: Kristofer Munsterhjelm km_elmet@t-online.de, election-methods@lists.electorama.com
Asunto: Re: [EM] Agenda Based Banks
Suppose that A has high approval or high first place support .... whatever is likely to put him at the good end of the agenda ... but knows that C has the broad & deep support necessary to be the sincere CW... in particular beating A pairwise.. and that there is some candidate B that A beats pairwise ... and the sincere preference order of the A faction is (mostly) A>C>B, (among these 3 major candidates)
Then A (emboldened by his presumed favorable agenda standing) gets the bright idea of convincing his supporters to bury C under B to create an artificial Condorcet cycle A>B>C>A.
Without this artificial cycle C would win no matter the agenda order ... but now A, at the top of the agenda has a good chance. In fact, the three members of this Smith set are the only possible winners under ISDA (Independence from Smith Dominated Alternatives).
When Smith has only three candidates, some agenda based methods, like SPE and ABL always elect the cycle member with the best agenda position... in this case A.
Another method DMC (Definite Majority Choice), elects the item in the worst agenda position that pairwise beats every item in a higher position ... which in this case is A if the agenda order of favor is (1) C<B<A, but is C if the order is (2) B<C<A.
How about ABB?
In case (1) C is the first bank deposit, and B is the last, hence the winner.
In case (2) B is the first deposit and A is the last, hence winner.
Both DMC and ABB make A's gambit somewhat risky, and if C's supporters take the standard CW precaution of truncating below C, then A's agenda status becomes least favorable of the three, in which case A loses by any reasonable agenda based method.
How do DMC and ABB compare under Chicken attack?
49 B
26 C>A
25 A (sincere is A>B)
Given implicit approval as the agenda setting criterion, A has the favored agenda spot, which makes A win under SPE and ABL.
Candidate C has the worst agenda position, so the agenda order is C<B<A, which makes Chicken attacker A win under DMC.
So our last hope is ABB. It comes through by electing B... fortunately NOT electing the most favored Banks agenda item!
[When Smith is a triple, Banks = Smith]
The very thing that turned me off about ABB years ago (when it was just TACC) made it impervious to Chicken!
ABB (Agenda Based Banks) looks Better and Better Actually (BBA).
... Forest (sharing Sue's phone)
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Kristofer Munsterhjelm km_elmet@t-online.de
Fecha: 2/8/21 2:13 p. m. (GMT-08:00)
A: Susan Simmons suzerainsimmons@outlook.com, election-methods@lists.electorama.com
Asunto: Re: [EM] Agenda Based Banks
On 02.08.2021 21:31, Susan Simmons wrote:
It turns out that this method as it stands is not monotonic, but if you
omit the downward part, then the remaining simpler version is monotonic:
First initialize a set named "TheBank" with the most promising agenda item.
Then, as long as even one agenda item pairwise beats every member
ofTheBank, deposit the least promising of these into TheBank.
Elect the final deposit.
This simple Banks compliant method is a generalization of TACC (Total
Approval Chain Climbing).
The only thing I don't like about it is that even when the most
promising agenda item is in the Banks set, as likely as not it will
elect a different member of that set. My tweak was designed to overcome
that "defect" while preserving Banks efficiency. But it's not worth the
loss of monotonicity.
Furthermore, it may turn out that the supposed "defect" actually confers
burial resistance ... for example ...
45 A>B (sincere A>C)
25 B>C
30 C>A
Ballot pairwise beat cycle: A>B>C>A
Agenda: C<B<A
(based on implicit approval, for example)
That feels like it's a general feature. Consider e.g. Benham with a
preset ordering as an agenda method (remove the loser until there's a CW
among the remaining candidates). Then raising W puts more candidates
between W and the end of the list, which means that in the worst case,
more candidates have to be eliminated before W wins.
It seems like there's some kind of tension where, on the one hand, being
ranked more highly should be advantageous (which it is if the pairwise
preferences don't change, because it saves W from early elimination),
but on the other hand, being ranked more highly with pairwise
preferences changing has a higher chance of being detrimental (because
more candidates have to be eliminated before W becomes a CW).
-km
On 04.08.2021 00:29, Susan Simmons wrote:
Actually, in the burial example below, ABB performs strictly better than
DMC because under DMC, the burial of C by A either rewards A with a win,
or leaves intact A's sincere 2nd choice as winner ... a zero risk gambit.
By way of contrast, if A's gambit fails under ABB, then A's least
preferred, B, wins ... a big risk, because A's raising of B enough to
introduce the necessary cycle might also be enough to move B to the
necessary agenda level (if it was not already there).
In summary, ABB has both the best burial resistance and the best chicken
attack resistance of any agenda based Condorcet method that we know of
(and we know of oodles!).
It seems doubtful that any simpler, monotone, clone free, ISDA, burial
and chicken resistant method exists ... except perhaps Asset Voting,
which is too far ahead of its time (and our time ...first promoted only
150 years ago by Charles L Dodgson) even for Steven J Brams the great
academic promoter of Approval, another simple method too far ahead of
its time.
As the perennial cold shower man, I must ask if this is actually
monotone for all monotone base methods :-)
Suppose that the base method is Plurality. In this election:
5: A>B>C
2: A>C>B
6: B>C>A
1: C>A>B
1: C>B>A
there's an ABCA cycle and the Plurality order is A>B>C. If I understand
correctly, ABB would first deposit A and then find the candidate that
beats A pairwise, i.e. C, and then terminate, giving C as the winner.
Now let 3 of the A>B>C voters raise C to C>A>B:
2: A>B>C
2: A>C>B
6: B>C>A
4: C>A>B
1: C>B>A
Now the Plurality order is B>C>A. B is first deposited, and then the
candidate who beats B (i.e.) A is deposited and wins.
So raising C made C lose. Looks like we need strong mono-raise.
With Plurality as the base method, I think ABB reduces to Eivind
Stensholt's BPW - or in my ABCA jargon, the method where candidate A's
score is "-fpC". If we just had a way of making it fpA-fpC, then all
would be well, at least in the case of Smith set equals three!
(Here's an ugly hack: The inner procedure takes a "tentative first
candidate" A. It inserts A, then it inserts the candidate that beats
everybody in the list, whose [first preference count - the last inserted
candidate's first preference count] is maximized. The inner procedure is
over once nobody beats everybody inside pairwise; the candidate last
inserted is the winner, and his score is the (first pref - last guy's
first pref) count.[1]
The outer procedure runs the inner procedure with every candidate as
tentative first, and elects the winning outcome with the greatest score.
But it's extremely ugly and I have no idea if it's strategy resistant or
monotone beyond a Smith cycle of three.)
In general, it seems that in a three-cycle, ABB elects the candidate who
beats the winner of the base method pairwise.
-km
[1] One could imagine other score functions as well, as long as they
specialize properly. E.g. Q's score is min P: fpQ - fpP, where P is a
candidate from the current chain. But I suspect that properly
generalizing fpA-fpC (so that it preserves DMTBR) will require some kind
of solid coalition logic -- or eliminations.
On 8/3/2021 3:29 PM, Susan Simmons (or Forest?) wrote:
...
Why are people still talking IRV (and its tweaks), STAR, MJ, etc?
Now we have a method ABB simpler than any of these somewhat popular
proposals, and equal (in criteria compliances) to any of the
academically respectable methods like CSSD, Ranked Pairs, River, etc ...
and far superior to classical methods like Copeland, Borda, Bucklin,
MinMax, Kemeny-Young, etc.
Why can't we get off dead center and start moving forward instead of
backwards?
...
But what can we do about it?
Please start by describing the method on Electowiki.
Speaking personally I need to see it described in order to evaluate how
easy or hard it is to understand -- from the perspective of voters.
The next step would be to convey it to voters. But keep in mind that a
simple-to-explain-in-words method can be difficult to understand by
people who are moved by feelings rather than words.
We know why ... zeal without knowledge, and big egos among movers and
shakers.
Indeed zeal and money are behind:
-
The FairVote organization
-
STAR voting
-
Center for Election Science
Ironically those of us who promote Condorcet methods don't have money
behind us. The money is behind methods that dismiss Condorcet methods.
Sigh, ...
Richard Fobes
The VoteFair guy
On 8/3/2021 3:29 PM, Susan Simmons wrote:
Actually, in the burial example below, ABB performs strictly better than
DMC because under DMC, the burial of C by A either rewards A with a win,
or leaves intact A's sincere 2nd choice as winner ... a zero risk gambit.
By way of contrast, if A's gambit fails under ABB, then A's least
preferred, B, wins ... a big risk, because A's raising of B enough to
introduce the necessary cycle might also be enough to move B to the
necessary agenda level (if it was not already there).
In summary, ABB has both the best burial resistance and the best chicken
attack resistance of any agenda based Condorcet method that we know of
(and we know of oodles!).
It seems doubtful that any simpler, monotone, clone free, ISDA, burial
and chicken resistant method exists ... except perhaps Asset Voting,
which is too far ahead of its time (and our time ...first promoted only
150 years ago by Charles L Dodgson) even for Steven J Brams the great
academic promoter of Approval, another simple method too far ahead of
its time.
Have I over-looked something?
Why are people still talking IRV (and its tweaks), STAR, MJ, etc?
Now we have a method ABB simpler than any of these somewhat popular
proposals, and equal (in criteria compliances) to any of the
academically respectable methods like CSSD, Ranked Pairs, River, etc ...
and far superior to classical methods like Copeland, Borda, Bucklin,
MinMax, Kemeny-Young, etc.
Why can't we get off dead center and start moving forward instead of
backwards?
We know why ... zeal without knowledge, and big egos among movers and
shakers.
But what can we do about it?
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Susan Simmons suzerainsimmons@outlook.com
Fecha: 3/8/21 12:08 p. m. (GMT-08:00)
A: Kristofer Munsterhjelm km_elmet@t-online.de,
election-methods@lists.electorama.com
Asunto: Re: [EM] Agenda Based Banks
Suppose that A has high approval or high first place support ....
whatever is likely to put him at the good end of the agenda ... but
knows that C has the broad & deep support necessary to be the sincere
CW... in particular beating A pairwise.. and that there is some
candidate B that A beats pairwise ... and the sincere preference order
of the A faction is (mostly) A>C>B, (among these 3 major candidates)
Then A (emboldened by his presumed favorable agenda standing) gets the
bright idea of convincing his supporters to bury C under B to create an
artificial Condorcet cycle A>B>C>A.
Without this artificial cycle C would win no matter the agenda order ...
but now A, at the top of the agenda has a good chance. In fact, the
three members of this Smith set are the only possible winners under ISDA
(Independence from Smith Dominated Alternatives).
When Smith has only three candidates, some agenda based methods, like
SPE and ABL always elect the cycle member with the best agenda
position... in this case A.
Another method DMC (Definite Majority Choice), elects the item in the
worst agenda position that pairwise beats every item in a higher
position ... which in this case is A if the agenda order of favor is (1)
C<B<A, but is C if the order is (2) B<C<A.
How about ABB?
In case (1) C is the first bank deposit, and B is the last, hence the
winner.
In case (2) B is the first deposit and A is the last, hence winner.
Both DMC and ABB make A's gambit somewhat risky, and if C's supporters
take the standard CW precaution of truncating below C, then A's agenda
status becomes least favorable of the three, in which case A loses by
any reasonable agenda based method.
How do DMC and ABB compare under Chicken attack?
49 B
26 C>A
25 A (sincere is A>B)
Given implicit approval as the agenda setting criterion, A has the
favored agenda spot, which makes A win under SPE and ABL.
Candidate C has the worst agenda position, so the agenda order is C<B<A,
which makes Chicken attacker A win under DMC.
So our last hope is ABB. It comes through by electing B... fortunately
NOT electing the most favored Banks agenda item!
[When Smith is a triple, Banks = Smith]
The very thing that turned me off about ABB years ago (when it was just
TACC) made it impervious to Chicken!
ABB (Agenda Based Banks) looks Better and Better Actually (BBA).
... Forest (sharing Sue's phone)
Sent from my MetroPCS 4G LTE Android Device
-------- Mensaje original --------
De: Kristofer Munsterhjelm km_elmet@t-online.de
Fecha: 2/8/21 2:13 p. m. (GMT-08:00)
A: Susan Simmons suzerainsimmons@outlook.com,
election-methods@lists.electorama.com
Asunto: Re: [EM] Agenda Based Banks
On 02.08.2021 21:31, Susan Simmons wrote:
It turns out that this method as it stands is not monotonic, but if you
omit the downward part, then the remaining simpler version is monotonic:
First initialize a set named "TheBank" with the most promising agenda item.
Then, as long as even one agenda item pairwise beats every member
ofTheBank, deposit the least promising of these into TheBank.
Elect the final deposit.
This simple Banks compliant method is a generalization of TACC (Total
Approval Chain Climbing).
The only thing I don't like about it is that even when the most
promising agenda item is in the Banks set, as likely as not it will
elect a different member of that set. My tweak was designed to overcome
that "defect" while preserving Banks efficiency. But it's not worth the
loss of monotonicity.
Furthermore, it may turn out that the supposed "defect" actually confers
burial resistance ... for example ...
45 A>B (sincere A>C)
25 B>C
30 C>A
Ballot pairwise beat cycle: A>B>C>A
Agenda: C<B<A
(based on implicit approval, for example)
That feels like it's a general feature. Consider e.g. Benham with a
preset ordering as an agenda method (remove the loser until there's a CW
among the remaining candidates). Then raising W puts more candidates
between W and the end of the list, which means that in the worst case,
more candidates have to be eliminated before W wins.
It seems like there's some kind of tension where, on the one hand, being
ranked more highly should be advantageous (which it is if the pairwise
preferences don't change, because it saves W from early elimination),
but on the other hand, being ranked more highly with pairwise
preferences changing has a higher chance of being detrimental (because
more candidates have to be eliminated before W becomes a CW).
-km
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