FS
Forest Simmons
Sat, Jan 7, 2023 10:06 PM
It is well known that not all nice properties are compatible with each
other in a common single winner voting method. However, we shall see by
example that the following nice features are mutually compatible in a
simple RCV voting method (MGCB defined below). Therefore, excluding any of
them can only be justified by trading in the excluded ones for equally
important ones in an equally simple method.
-
The method should be clone independent like IRV ... therefore not
plagued by the spoiler problem like First Past The Post Plurality or by
"teaming" like the Borda Count.
-
The method should pass the majority Criterion... a majority of first
place votes should always vouchsafe the win.
-
The method should be monotone: if a recount reveals more votes for X
than the initial count, it should not change X from winner to loser.
-
The method should be decisive: ties should be extremely rare under usual
conditions.
-
The method should be computationally efficient with a one pass precinct
summable tally.
-
The method should not elect covered candidates: a covered winner is an
embarrassment ... if X defeats the winner W head to head, and the winner
cannot defend itself in a short beatpath, then X covers W. That's one way
of describing (without mentioning Condorcet) the recent failure of IRV in
Alaska, as well as a previous notable failure of IRV in Burlington, VT.
This sixth feature can be tacked onto any RCV method as a kluge ... but
it's nice when it follows seamlessly from the simple basic tally.
IRV satisfies features 1, 2, and 4.
If you can think of any simple method (besides the one below) that has all
six features (or better ones), please let us know; it will probably be a
significant improvement over every extant public method.
Max Gradient Chain Building (MGCB):
Initialize a pairwise defeat chain with the strongest over-all defeat A>B.
Then ...
... as long as possible, accommodate into the chain (from among the
candidates that defeat all current chain members) the candidate that has
the strongest defeat against the current chain head
Elect the head of the completed chain.
It was a comment of Kristofer that inspired this method. He mentioned that
according to his recent simulations electing the winner of the over-all
strongest defeat A>B is a surprisingly burial resistant stand-alone
method. It seems to me that the burial resistance should carry over to
this MGCB completion of his discovery.
Furthermore, it appears that if defeat strength is gauged by margins, then
the method is Chicken resistant.
A fairly simple modification ... where the chain is built up from both ends
... always giving priority to the end where the new defeat is stronger ....
preserves all six of the nice features in our list while adding a Strong
Reverse Symmetry feature ... reversing all of the ballot rankings precisely
reverses the output chain .... swapping the head and tail of the completed
chain.
So this MGCB method seems pretty promising .... but the proof will be in
its acual performance when it is put through its paces.
Please try it on your favorite test profiles, and report your observations.
Thanks!
Forest
It is well known that not all nice properties are compatible with each
other in a common single winner voting method. However, we shall see by
example that the following nice features are mutually compatible in a
simple RCV voting method (MGCB defined below). Therefore, excluding any of
them can only be justified by trading in the excluded ones for equally
important ones in an equally simple method.
1. The method should be clone independent like IRV ... therefore not
plagued by the spoiler problem like First Past The Post Plurality or by
"teaming" like the Borda Count.
2. The method should pass the majority Criterion... a majority of first
place votes should always vouchsafe the win.
3. The method should be monotone: if a recount reveals more votes for X
than the initial count, it should not change X from winner to loser.
4. The method should be decisive: ties should be extremely rare under usual
conditions.
5. The method should be computationally efficient with a one pass precinct
summable tally.
6. The method should not elect covered candidates: a covered winner is an
embarrassment ... if X defeats the winner W head to head, and the winner
cannot defend itself in a short beatpath, then X covers W. That's one way
of describing (without mentioning Condorcet) the recent failure of IRV in
Alaska, as well as a previous notable failure of IRV in Burlington, VT.
This sixth feature can be tacked onto any RCV method as a kluge ... but
it's nice when it follows seamlessly from the simple basic tally.
IRV satisfies features 1, 2, and 4.
If you can think of any simple method (besides the one below) that has all
six features (or better ones), please let us know; it will probably be a
significant improvement over every extant public method.
Max Gradient Chain Building (MGCB):
Initialize a pairwise defeat chain with the strongest over-all defeat A>B.
Then ...
... as long as possible, accommodate into the chain (from among the
candidates that defeat all current chain members) the candidate that has
the strongest defeat against the current chain head
Elect the head of the completed chain.
It was a comment of Kristofer that inspired this method. He mentioned that
according to his recent simulations electing the winner of the over-all
strongest defeat A>B is a surprisingly burial resistant stand-alone
method. It seems to me that the burial resistance should carry over to
this MGCB completion of his discovery.
Furthermore, it appears that if defeat strength is gauged by margins, then
the method is Chicken resistant.
A fairly simple modification ... where the chain is built up from both ends
... always giving priority to the end where the new defeat is stronger ....
preserves all six of the nice features in our list while adding a Strong
Reverse Symmetry feature ... reversing all of the ballot rankings precisely
reverses the output chain .... swapping the head and tail of the completed
chain.
So this MGCB method seems pretty promising .... but the proof will be in
its acual performance when it is put through its paces.
Please try it on your favorite test profiles, and report your observations.
Thanks!
Forest
KV
Kevin Venzke
Sun, Jan 8, 2023 1:03 AM
Hi Forest, I may give it a look, but a couple of issues.
One thing, I feel a little unsure it will be monotone to pick a new candidate to add to the
chain based on who the current head is. Normally these methods don't actually depend on the
ordering of candidates already in the chain.
It is well known that not all nice properties are compatible with each other in a common
single winner voting method. However, we shall see by example that the following nice
features are mutually compatible in a simple RCV voting method (MGCB defined below).
Therefore, excluding any of them can only be justified by trading in the excluded ones for
equally important ones in an equally simple method.
- The method should be clone independent like IRV ... therefore not plagued by the spoiler
problem like First Past The Post Plurality or by "teaming" like the Borda Count.
Generous of you to imply that IRV is not plagued by a spoiler problem.
It was a comment of Kristofer that inspired this method. He mentioned that according to his
recent simulations electing the winner of the over-all strongest defeat A>B is a
surprisingly burial resistant stand-alone method. It seems to me that the burial resistance
should carry over to this MGCB completion of his discovery.
Well. That kind of method is a stone's throw away from just being approval.
Furthermore, it appears that if defeat strength is gauged by margins, then the method is
Chicken resistant.
If you mean "more" chicken-resistant then OK, but if you mean satisfying the CD criterion,
there's no reason for that to be true. If you want to guarantee CD you need to deliberately
reject some majorities (which is completely in its spirit), not simply be indifferent to
them.
More importantly, I would point out that from a CD criterion standpoint, the Alaska RCV
outcome was probably completely correct.
It seems to me the Alaska race demonstrates that the CD criterion can't deliver on its
promise even under IRV, its most advantageous setting. It's not going to be better under a
method that poses actual incentives to withhold lower preferences.
A fairly simple modification ... where the chain is built up from both ends ... always
giving priority to the end where the new defeat is stronger .... preserves all six of the
nice features in our list while adding a Strong Reverse Symmetry feature ... reversing all
of the ballot rankings precisely reverses the output chain .... swapping the head and tail
of the completed chain.
I don't follow. Are you just saying there's a choice of whether you beat the head or the
tail, but in either case the newly added candidate becomes the new head?
Kevin
votingmethods.net
Hi Forest, I may give it a look, but a couple of issues.
One thing, I feel a little unsure it will be monotone to pick a new candidate to add to the
chain based on who the current head is. Normally these methods don't actually depend on the
ordering of candidates already in the chain.
> It is well known that not all nice properties are compatible with each other in a common
> single winner voting method. However, we shall see by example that the following nice
> features are mutually compatible in a simple RCV voting method (MGCB defined below).
> Therefore, excluding any of them can only be justified by trading in the excluded ones for
> equally important ones in an equally simple method.
>
> 1. The method should be clone independent like IRV ... therefore not plagued by the spoiler
> problem like First Past The Post Plurality or by "teaming" like the Borda Count.
Generous of you to imply that IRV is not plagued by a spoiler problem.
> It was a comment of Kristofer that inspired this method. He mentioned that according to his
> recent simulations electing the winner of the over-all strongest defeat A>B is a
> surprisingly burial resistant stand-alone method. It seems to me that the burial resistance
> should carry over to this MGCB completion of his discovery.
Well. That kind of method is a stone's throw away from just being approval.
> Furthermore, it appears that if defeat strength is gauged by margins, then the method is
> Chicken resistant.
If you mean "more" chicken-resistant then OK, but if you mean satisfying the CD criterion,
there's no reason for that to be true. If you want to guarantee CD you need to deliberately
reject some majorities (which is completely in its spirit), not simply be indifferent to
them.
More importantly, I would point out that from a CD criterion standpoint, the Alaska RCV
outcome was probably completely correct.
It seems to me the Alaska race demonstrates that the CD criterion can't deliver on its
promise even under IRV, its most advantageous setting. It's not going to be better under a
method that poses actual incentives to withhold lower preferences.
> A fairly simple modification ... where the chain is built up from both ends ... always
> giving priority to the end where the new defeat is stronger .... preserves all six of the
> nice features in our list while adding a Strong Reverse Symmetry feature ... reversing all
> of the ballot rankings precisely reverses the output chain .... swapping the head and tail
> of the completed chain.
I don't follow. Are you just saying there's a choice of whether you beat the head or the
tail, but in either case the newly added candidate becomes the new head?
Kevin
votingmethods.net
FS
Forest Simmons
Mon, Jan 9, 2023 8:17 AM
The candidate added to the tail would be the one defeated most strongly by
the current tail. Whether to lengthen the chain forward or backwards at a
given stage would depend on which new direct defeat was stronger.
On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Forest, I may give it a look, but a couple of issues.
One thing, I feel a little unsure it will be monotone to pick a new
candidate to add to the
chain based on who the current head is. Normally these methods don't
actually depend on the
ordering of candidates already in the chain.
It is well known that not all nice properties are compatible with each
single winner voting method. However, we shall see by example that the
features are mutually compatible in a simple RCV voting method (MGCB
Therefore, excluding any of them can only be justified by trading in the
equally important ones in an equally simple method.
- The method should be clone independent like IRV ... therefore not
problem like First Past The Post Plurality or by "teaming" like the
Borda Count.
Generous of you to imply that IRV is not plagued by a spoiler problem.
It was a comment of Kristofer that inspired this method. He mentioned
recent simulations electing the winner of the over-all strongest defeat
surprisingly burial resistant stand-alone method. It seems to me that
should carry over to this MGCB completion of his discovery.
Well. That kind of method is a stone's throw away from just being approval.
Furthermore, it appears that if defeat strength is gauged by margins,
If you mean "more" chicken-resistant then OK, but if you mean satisfying
the CD criterion,
there's no reason for that to be true. If you want to guarantee CD you
need to deliberately
reject some majorities (which is completely in its spirit), not simply be
indifferent to
them.
More importantly, I would point out that from a CD criterion standpoint,
the Alaska RCV
outcome was probably completely correct.
It seems to me the Alaska race demonstrates that the CD criterion can't
deliver on its
promise even under IRV, its most advantageous setting. It's not going to
be better under a
method that poses actual incentives to withhold lower preferences.
A fairly simple modification ... where the chain is built up from both
giving priority to the end where the new defeat is stronger ....
nice features in our list while adding a Strong Reverse Symmetry feature
of the ballot rankings precisely reverses the output chain .... swapping
I don't follow. Are you just saying there's a choice of whether you beat
the head or the
tail, but in either case the newly added candidate becomes the new head?
Kevin
votingmethods.net
The candidate added to the tail would be the one defeated most strongly by
the current tail. Whether to lengthen the chain forward or backwards at a
given stage would depend on which new direct defeat was stronger.
On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke <stepjak@yahoo.fr> wrote:
> Hi Forest, I may give it a look, but a couple of issues.
>
> One thing, I feel a little unsure it will be monotone to pick a new
> candidate to add to the
> chain based on who the current head is. Normally these methods don't
> actually depend on the
> ordering of candidates already in the chain.
>
> > It is well known that not all nice properties are compatible with each
> other in a common
> > single winner voting method. However, we shall see by example that the
> following nice
> > features are mutually compatible in a simple RCV voting method (MGCB
> defined below).
> > Therefore, excluding any of them can only be justified by trading in the
> excluded ones for
> > equally important ones in an equally simple method.
> >
> > 1. The method should be clone independent like IRV ... therefore not
> plagued by the spoiler
> > problem like First Past The Post Plurality or by "teaming" like the
> Borda Count.
>
> Generous of you to imply that IRV is not plagued by a spoiler problem.
>
> > It was a comment of Kristofer that inspired this method. He mentioned
> that according to his
> > recent simulations electing the winner of the over-all strongest defeat
> A>B is a
> > surprisingly burial resistant stand-alone method. It seems to me that
> the burial resistance
> > should carry over to this MGCB completion of his discovery.
>
> Well. That kind of method is a stone's throw away from just being approval.
>
> > Furthermore, it appears that if defeat strength is gauged by margins,
> then the method is
> > Chicken resistant.
>
> If you mean "more" chicken-resistant then OK, but if you mean satisfying
> the CD criterion,
> there's no reason for that to be true. If you want to guarantee CD you
> need to deliberately
> reject some majorities (which is completely in its spirit), not simply be
> indifferent to
> them.
>
> More importantly, I would point out that from a CD criterion standpoint,
> the Alaska RCV
> outcome was probably completely correct.
>
> It seems to me the Alaska race demonstrates that the CD criterion can't
> deliver on its
> promise even under IRV, its most advantageous setting. It's not going to
> be better under a
> method that poses actual incentives to withhold lower preferences.
>
> > A fairly simple modification ... where the chain is built up from both
> ends ... always
> > giving priority to the end where the new defeat is stronger ....
> preserves all six of the
> > nice features in our list while adding a Strong Reverse Symmetry feature
> ... reversing all
> > of the ballot rankings precisely reverses the output chain .... swapping
> the head and tail
> > of the completed chain.
>
> I don't follow. Are you just saying there's a choice of whether you beat
> the head or the
> tail, but in either case the newly added candidate becomes the new head?
>
> Kevin
> votingmethods.net
>
FS
Forest Simmons
Mon, Jan 9, 2023 6:51 PM
Let's see where my proof goes wrong .... my mistaken proof of monotonicity
for the one sided chain where every addition to the chain becomes the new
head:
Suppose the final head (the winner) H increases pairwise relative to some
candidate X while all of the other pairwise relations are undisturbed.
Then before H is added the sequence of additions proceeds exactly as before
... H has no influence.
If X is among those added before H, then the increase in H>X strength has
no relevance unless it allows H to immediately follow X instead of waiting
for Y1,Y2, etc ... where the Y1>X defeat was stronger than the H>X defeat
(but no longer is).
But now none of these Y's can be added because they are still defeated by H.
How about some Z that defeats H but was kept out by one of those Y's? Now
that those Y's are gone, that Z gets admitted.
So H is no longer the final head of the chain.
Back to the drawing board!
On Mon, Jan 9, 2023, 12:17 AM Forest Simmons forest.simmons21@gmail.com
wrote:
The candidate added to the tail would be the one defeated most strongly by
the current tail. Whether to lengthen the chain forward or backwards at a
given stage would depend on which new direct defeat was stronger.
On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Forest, I may give it a look, but a couple of issues.
One thing, I feel a little unsure it will be monotone to pick a new
candidate to add to the
chain based on who the current head is. Normally these methods don't
actually depend on the
ordering of candidates already in the chain.
It is well known that not all nice properties are compatible with each
single winner voting method. However, we shall see by example that the
features are mutually compatible in a simple RCV voting method (MGCB
Therefore, excluding any of them can only be justified by trading in
equally important ones in an equally simple method.
- The method should be clone independent like IRV ... therefore not
problem like First Past The Post Plurality or by "teaming" like the
Borda Count.
Generous of you to imply that IRV is not plagued by a spoiler problem.
It was a comment of Kristofer that inspired this method. He mentioned
recent simulations electing the winner of the over-all strongest defeat
surprisingly burial resistant stand-alone method. It seems to me that
should carry over to this MGCB completion of his discovery.
Well. That kind of method is a stone's throw away from just being
approval.
Furthermore, it appears that if defeat strength is gauged by margins,
If you mean "more" chicken-resistant then OK, but if you mean satisfying
the CD criterion,
there's no reason for that to be true. If you want to guarantee CD you
need to deliberately
reject some majorities (which is completely in its spirit), not simply be
indifferent to
them.
More importantly, I would point out that from a CD criterion standpoint,
the Alaska RCV
outcome was probably completely correct.
It seems to me the Alaska race demonstrates that the CD criterion can't
deliver on its
promise even under IRV, its most advantageous setting. It's not going to
be better under a
method that poses actual incentives to withhold lower preferences.
A fairly simple modification ... where the chain is built up from both
giving priority to the end where the new defeat is stronger ....
nice features in our list while adding a Strong Reverse Symmetry
feature ... reversing all
of the ballot rankings precisely reverses the output chain ....
swapping the head and tail
I don't follow. Are you just saying there's a choice of whether you beat
the head or the
tail, but in either case the newly added candidate becomes the new head?
Kevin
votingmethods.net
Let's see where my proof goes wrong .... my mistaken proof of monotonicity
for the one sided chain where every addition to the chain becomes the new
head:
Suppose the final head (the winner) H increases pairwise relative to some
candidate X while all of the other pairwise relations are undisturbed.
Then before H is added the sequence of additions proceeds exactly as before
... H has no influence.
If X is among those added before H, then the increase in H>X strength has
no relevance unless it allows H to immediately follow X instead of waiting
for Y1,Y2, etc ... where the Y1>X defeat was stronger than the H>X defeat
(but no longer is).
But now none of these Y's can be added because they are still defeated by H.
How about some Z that defeats H but was kept out by one of those Y's? Now
that those Y's are gone, that Z gets admitted.
So H is no longer the final head of the chain.
Back to the drawing board!
On Mon, Jan 9, 2023, 12:17 AM Forest Simmons <forest.simmons21@gmail.com>
wrote:
> The candidate added to the tail would be the one defeated most strongly by
> the current tail. Whether to lengthen the chain forward or backwards at a
> given stage would depend on which new direct defeat was stronger.
>
> On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke <stepjak@yahoo.fr> wrote:
>
>> Hi Forest, I may give it a look, but a couple of issues.
>>
>> One thing, I feel a little unsure it will be monotone to pick a new
>> candidate to add to the
>> chain based on who the current head is. Normally these methods don't
>> actually depend on the
>> ordering of candidates already in the chain.
>>
>> > It is well known that not all nice properties are compatible with each
>> other in a common
>> > single winner voting method. However, we shall see by example that the
>> following nice
>> > features are mutually compatible in a simple RCV voting method (MGCB
>> defined below).
>> > Therefore, excluding any of them can only be justified by trading in
>> the excluded ones for
>> > equally important ones in an equally simple method.
>> >
>> > 1. The method should be clone independent like IRV ... therefore not
>> plagued by the spoiler
>> > problem like First Past The Post Plurality or by "teaming" like the
>> Borda Count.
>>
>> Generous of you to imply that IRV is not plagued by a spoiler problem.
>>
>> > It was a comment of Kristofer that inspired this method. He mentioned
>> that according to his
>> > recent simulations electing the winner of the over-all strongest defeat
>> A>B is a
>> > surprisingly burial resistant stand-alone method. It seems to me that
>> the burial resistance
>> > should carry over to this MGCB completion of his discovery.
>>
>> Well. That kind of method is a stone's throw away from just being
>> approval.
>>
>> > Furthermore, it appears that if defeat strength is gauged by margins,
>> then the method is
>> > Chicken resistant.
>>
>> If you mean "more" chicken-resistant then OK, but if you mean satisfying
>> the CD criterion,
>> there's no reason for that to be true. If you want to guarantee CD you
>> need to deliberately
>> reject some majorities (which is completely in its spirit), not simply be
>> indifferent to
>> them.
>>
>> More importantly, I would point out that from a CD criterion standpoint,
>> the Alaska RCV
>> outcome was probably completely correct.
>>
>> It seems to me the Alaska race demonstrates that the CD criterion can't
>> deliver on its
>> promise even under IRV, its most advantageous setting. It's not going to
>> be better under a
>> method that poses actual incentives to withhold lower preferences.
>>
>> > A fairly simple modification ... where the chain is built up from both
>> ends ... always
>> > giving priority to the end where the new defeat is stronger ....
>> preserves all six of the
>> > nice features in our list while adding a Strong Reverse Symmetry
>> feature ... reversing all
>> > of the ballot rankings precisely reverses the output chain ....
>> swapping the head and tail
>> > of the completed chain.
>>
>> I don't follow. Are you just saying there's a choice of whether you beat
>> the head or the
>> tail, but in either case the newly added candidate becomes the new head?
>>
>> Kevin
>> votingmethods.net
>>
>
FS
Forest Simmons
Thu, Jan 12, 2023 5:29 PM
It seems the way through is to make every step a covering step ... then
when the winner W gets a stronger step ... cutting in front of a bunch of
Y's that it followed before its strength increase ... it still covers all
of those Y's so no Z can be added just because it beats W and the previous
members of the chain.
I think we can get away with the very first step A>B not being a covering:
Make it the single strongest defeat possible so that the first chain head A
is the "Gross Defeat Strength Champ."
Then until the current chain head is uncovered ... at each stage the new
head is the candidate with the strongest possible defeat of the old head by
any candidate covering it (the old head).
Example:
35 A>B>C
25 B>C>A
40 C>A>B
The strongest defeat is A>B (75 to 25).
And since the head A is uncovered, the chain cannot be continued, since by
our new rule all defeats after the first must be coverings.
So A wins.
Now is this monotone?
Shall we call it Max Gradient Ascent MGA?
-Forest
On Mon, Jan 9, 2023, 10:51 AM Forest Simmons forest.simmons21@gmail.com
wrote:
Let's see where my proof goes wrong .... my mistaken proof of monotonicity
for the one sided chain where every addition to the chain becomes the new
head:
Suppose the final head (the winner) H increases pairwise relative to some
candidate X while all of the other pairwise relations are undisturbed.
Then before H is added the sequence of additions proceeds exactly as
before ... H has no influence.
If X is among those added before H, then the increase in H>X strength has
no relevance unless it allows H to immediately follow X instead of waiting
for Y1,Y2, etc ... where the Y1>X defeat was stronger than the H>X defeat
(but no longer is).
But now none of these Y's can be added because they are still defeated by
H.
How about some Z that defeats H but was kept out by one of those Y's? Now
that those Y's are gone, that Z gets admitted.
So H is no longer the final head of the chain.
Back to the drawing board!
On Mon, Jan 9, 2023, 12:17 AM Forest Simmons forest.simmons21@gmail.com
wrote:
The candidate added to the tail would be the one defeated most strongly
by the current tail. Whether to lengthen the chain forward or backwards at
a given stage would depend on which new direct defeat was stronger.
On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Forest, I may give it a look, but a couple of issues.
One thing, I feel a little unsure it will be monotone to pick a new
candidate to add to the
chain based on who the current head is. Normally these methods don't
actually depend on the
ordering of candidates already in the chain.
It is well known that not all nice properties are compatible with each
single winner voting method. However, we shall see by example that the
features are mutually compatible in a simple RCV voting method (MGCB
Therefore, excluding any of them can only be justified by trading in
equally important ones in an equally simple method.
- The method should be clone independent like IRV ... therefore not
problem like First Past The Post Plurality or by "teaming" like the
Borda Count.
Generous of you to imply that IRV is not plagued by a spoiler problem.
It was a comment of Kristofer that inspired this method. He mentioned
recent simulations electing the winner of the over-all strongest
surprisingly burial resistant stand-alone method. It seems to me that
should carry over to this MGCB completion of his discovery.
Well. That kind of method is a stone's throw away from just being
approval.
Furthermore, it appears that if defeat strength is gauged by margins,
If you mean "more" chicken-resistant then OK, but if you mean satisfying
the CD criterion,
there's no reason for that to be true. If you want to guarantee CD you
need to deliberately
reject some majorities (which is completely in its spirit), not simply
be indifferent to
them.
More importantly, I would point out that from a CD criterion standpoint,
the Alaska RCV
outcome was probably completely correct.
It seems to me the Alaska race demonstrates that the CD criterion can't
deliver on its
promise even under IRV, its most advantageous setting. It's not going to
be better under a
method that poses actual incentives to withhold lower preferences.
A fairly simple modification ... where the chain is built up from both
giving priority to the end where the new defeat is stronger ....
nice features in our list while adding a Strong Reverse Symmetry
feature ... reversing all
of the ballot rankings precisely reverses the output chain ....
swapping the head and tail
I don't follow. Are you just saying there's a choice of whether you beat
the head or the
tail, but in either case the newly added candidate becomes the new head?
Kevin
votingmethods.net
It seems the way through is to make every step a covering step ... then
when the winner W gets a stronger step ... cutting in front of a bunch of
Y's that it followed before its strength increase ... it still covers all
of those Y's so no Z can be added just because it beats W and the previous
members of the chain.
I think we can get away with the very first step A>B not being a covering:
Make it the single strongest defeat possible so that the first chain head A
is the "Gross Defeat Strength Champ."
Then until the current chain head is uncovered ... at each stage the new
head is the candidate with the strongest possible defeat of the old head by
any candidate covering it (the old head).
Example:
35 A>B>C
25 B>C>A
40 C>A>B
The strongest defeat is A>B (75 to 25).
And since the head A is uncovered, the chain cannot be continued, since by
our new rule all defeats after the first must be coverings.
So A wins.
Now is this monotone?
Shall we call it Max Gradient Ascent MGA?
-Forest
On Mon, Jan 9, 2023, 10:51 AM Forest Simmons <forest.simmons21@gmail.com>
wrote:
> Let's see where my proof goes wrong .... my mistaken proof of monotonicity
> for the one sided chain where every addition to the chain becomes the new
> head:
>
> Suppose the final head (the winner) H increases pairwise relative to some
> candidate X while all of the other pairwise relations are undisturbed.
>
> Then before H is added the sequence of additions proceeds exactly as
> before ... H has no influence.
>
> If X is among those added before H, then the increase in H>X strength has
> no relevance unless it allows H to immediately follow X instead of waiting
> for Y1,Y2, etc ... where the Y1>X defeat was stronger than the H>X defeat
> (but no longer is).
>
> But now none of these Y's can be added because they are still defeated by
> H.
>
> How about some Z that defeats H but was kept out by one of those Y's? Now
> that those Y's are gone, that Z gets admitted.
>
> So H is no longer the final head of the chain.
>
> Back to the drawing board!
>
> On Mon, Jan 9, 2023, 12:17 AM Forest Simmons <forest.simmons21@gmail.com>
> wrote:
>
>> The candidate added to the tail would be the one defeated most strongly
>> by the current tail. Whether to lengthen the chain forward or backwards at
>> a given stage would depend on which new direct defeat was stronger.
>>
>> On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke <stepjak@yahoo.fr> wrote:
>>
>>> Hi Forest, I may give it a look, but a couple of issues.
>>>
>>> One thing, I feel a little unsure it will be monotone to pick a new
>>> candidate to add to the
>>> chain based on who the current head is. Normally these methods don't
>>> actually depend on the
>>> ordering of candidates already in the chain.
>>>
>>> > It is well known that not all nice properties are compatible with each
>>> other in a common
>>> > single winner voting method. However, we shall see by example that the
>>> following nice
>>> > features are mutually compatible in a simple RCV voting method (MGCB
>>> defined below).
>>> > Therefore, excluding any of them can only be justified by trading in
>>> the excluded ones for
>>> > equally important ones in an equally simple method.
>>> >
>>> > 1. The method should be clone independent like IRV ... therefore not
>>> plagued by the spoiler
>>> > problem like First Past The Post Plurality or by "teaming" like the
>>> Borda Count.
>>>
>>> Generous of you to imply that IRV is not plagued by a spoiler problem.
>>>
>>> > It was a comment of Kristofer that inspired this method. He mentioned
>>> that according to his
>>> > recent simulations electing the winner of the over-all strongest
>>> defeat A>B is a
>>> > surprisingly burial resistant stand-alone method. It seems to me that
>>> the burial resistance
>>> > should carry over to this MGCB completion of his discovery.
>>>
>>> Well. That kind of method is a stone's throw away from just being
>>> approval.
>>>
>>> > Furthermore, it appears that if defeat strength is gauged by margins,
>>> then the method is
>>> > Chicken resistant.
>>>
>>> If you mean "more" chicken-resistant then OK, but if you mean satisfying
>>> the CD criterion,
>>> there's no reason for that to be true. If you want to guarantee CD you
>>> need to deliberately
>>> reject some majorities (which is completely in its spirit), not simply
>>> be indifferent to
>>> them.
>>>
>>> More importantly, I would point out that from a CD criterion standpoint,
>>> the Alaska RCV
>>> outcome was probably completely correct.
>>>
>>> It seems to me the Alaska race demonstrates that the CD criterion can't
>>> deliver on its
>>> promise even under IRV, its most advantageous setting. It's not going to
>>> be better under a
>>> method that poses actual incentives to withhold lower preferences.
>>>
>>> > A fairly simple modification ... where the chain is built up from both
>>> ends ... always
>>> > giving priority to the end where the new defeat is stronger ....
>>> preserves all six of the
>>> > nice features in our list while adding a Strong Reverse Symmetry
>>> feature ... reversing all
>>> > of the ballot rankings precisely reverses the output chain ....
>>> swapping the head and tail
>>> > of the completed chain.
>>>
>>> I don't follow. Are you just saying there's a choice of whether you beat
>>> the head or the
>>> tail, but in either case the newly added candidate becomes the new head?
>>>
>>> Kevin
>>> votingmethods.net
>>>
>>
KV
Kevin Venzke
Thu, Jan 12, 2023 11:53 PM
Hi Forest, I think it satisfies it. Assuming I coded it correctly I didn't see any Mono-raise issues going up to 7 candidates.
It seems like it's broadly in the neighborhood of Condorcet//Approval, with reduced truncation and compromise, but higher burial incentive. Not shabby though probably not Kristofer's type of method.
Kevin
(end)
Le jeudi 12 janvier 2023 à 11:30:13 UTC−6, Forest Simmons forest.simmons21@gmail.com a écrit :
It seems the way through is to make every step a covering step ... then when the winner W gets a stronger step ... cutting in front of a bunch of Y's that it followed before its strength increase ... it still covers all of those Y's so no Z can be added just because it beats W and the previous members of the chain.
I think we can get away with the very first step A>B not being a covering:
Make it the single strongest defeat possible so that the first chain head A is the "Gross Defeat Strength Champ."
Then until the current chain head is uncovered ... at each stage the new head is the candidate with the strongest possible defeat of the old head by any candidate covering it (the old head).
Example:
35 A>B>C
25 B>C>A
40 C>A>B
The strongest defeat is A>B (75 to 25).
And since the head A is uncovered, the chain cannot be continued, since by our new rule all defeats after the first must be coverings.
So A wins.
Now is this monotone?
Shall we call it Max Gradient Ascent MGA?
-Forest
On Mon, Jan 9, 2023, 10:51 AM Forest Simmons forest.simmons21@gmail.com wrote:
Let's see where my proof goes wrong .... my mistaken proof of monotonicity for the one sided chain where every addition to the chain becomes the new head:
Suppose the final head (the winner) H increases pairwise relative to some candidate X while all of the other pairwise relations are undisturbed.
Then before H is added the sequence of additions proceeds exactly as before ... H has no influence.
If X is among those added before H, then the increase in H>X strength has no relevance unless it allows H to immediately follow X instead of waiting for Y1,Y2, etc ... where the Y1>X defeat was stronger than the H>X defeat (but no longer is).
But now none of these Y's can be added because they are still defeated by H.
How about some Z that defeats H but was kept out by one of those Y's? Now that those Y's are gone, that Z gets admitted.
So H is no longer the final head of the chain.
Back to the drawing board!
On Mon, Jan 9, 2023, 12:17 AM Forest Simmons forest.simmons21@gmail.com wrote:
The candidate added to the tail would be the one defeated most strongly by the current tail. Whether to lengthen the chain forward or backwards at a given stage would depend on which new direct defeat was stronger.
On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Forest, I may give it a look, but a couple of issues.
One thing, I feel a little unsure it will be monotone to pick a new candidate to add to the
chain based on who the current head is. Normally these methods don't actually depend on the
ordering of candidates already in the chain.
It is well known that not all nice properties are compatible with each other in a common
single winner voting method. However, we shall see by example that the following nice
features are mutually compatible in a simple RCV voting method (MGCB defined below).
Therefore, excluding any of them can only be justified by trading in the excluded ones for
equally important ones in an equally simple method.
- The method should be clone independent like IRV ... therefore not plagued by the spoiler
problem like First Past The Post Plurality or by "teaming" like the Borda Count.
Generous of you to imply that IRV is not plagued by a spoiler problem.
It was a comment of Kristofer that inspired this method. He mentioned that according to his
recent simulations electing the winner of the over-all strongest defeat A>B is a
surprisingly burial resistant stand-alone method. It seems to me that the burial resistance
should carry over to this MGCB completion of his discovery.
Well. That kind of method is a stone's throw away from just being approval.
Furthermore, it appears that if defeat strength is gauged by margins, then the method is
Chicken resistant.
If you mean "more" chicken-resistant then OK, but if you mean satisfying the CD criterion,
there's no reason for that to be true. If you want to guarantee CD you need to deliberately
reject some majorities (which is completely in its spirit), not simply be indifferent to
them.
More importantly, I would point out that from a CD criterion standpoint, the Alaska RCV
outcome was probably completely correct.
It seems to me the Alaska race demonstrates that the CD criterion can't deliver on its
promise even under IRV, its most advantageous setting. It's not going to be better under a
method that poses actual incentives to withhold lower preferences.
A fairly simple modification ... where the chain is built up from both ends ... always
giving priority to the end where the new defeat is stronger .... preserves all six of the
nice features in our list while adding a Strong Reverse Symmetry feature ... reversing all
of the ballot rankings precisely reverses the output chain .... swapping the head and tail
of the completed chain.
I don't follow. Are you just saying there's a choice of whether you beat the head or the
tail, but in either case the newly added candidate becomes the new head?
Kevin
votingmethods.net
Hi Forest, I think it satisfies it. Assuming I coded it correctly I didn't see any Mono-raise issues going up to 7 candidates.
It seems like it's broadly in the neighborhood of Condorcet//Approval, with reduced truncation and compromise, but higher burial incentive. Not shabby though probably not Kristofer's type of method.
Kevin
(end)
Le jeudi 12 janvier 2023 à 11:30:13 UTC−6, Forest Simmons <forest.simmons21@gmail.com> a écrit :
It seems the way through is to make every step a covering step ... then when the winner W gets a stronger step ... cutting in front of a bunch of Y's that it followed before its strength increase ... it still covers all of those Y's so no Z can be added just because it beats W and the previous members of the chain.
I think we can get away with the very first step A>B not being a covering:
Make it the single strongest defeat possible so that the first chain head A is the "Gross Defeat Strength Champ."
Then until the current chain head is uncovered ... at each stage the new head is the candidate with the strongest possible defeat of the old head by any candidate covering it (the old head).
Example:
35 A>B>C
25 B>C>A
40 C>A>B
The strongest defeat is A>B (75 to 25).
And since the head A is uncovered, the chain cannot be continued, since by our new rule all defeats after the first must be coverings.
So A wins.
Now is this monotone?
Shall we call it Max Gradient Ascent MGA?
-Forest
On Mon, Jan 9, 2023, 10:51 AM Forest Simmons <forest.simmons21@gmail.com> wrote:
> Let's see where my proof goes wrong .... my mistaken proof of monotonicity for the one sided chain where every addition to the chain becomes the new head:
>
> Suppose the final head (the winner) H increases pairwise relative to some candidate X while all of the other pairwise relations are undisturbed.
>
> Then before H is added the sequence of additions proceeds exactly as before ... H has no influence.
>
> If X is among those added before H, then the increase in H>X strength has no relevance unless it allows H to immediately follow X instead of waiting for Y1,Y2, etc ... where the Y1>X defeat was stronger than the H>X defeat (but no longer is).
>
> But now none of these Y's can be added because they are still defeated by H.
>
> How about some Z that defeats H but was kept out by one of those Y's? Now that those Y's are gone, that Z gets admitted.
>
> So H is no longer the final head of the chain.
>
> Back to the drawing board!
>
> On Mon, Jan 9, 2023, 12:17 AM Forest Simmons <forest.simmons21@gmail.com> wrote:
>> The candidate added to the tail would be the one defeated most strongly by the current tail. Whether to lengthen the chain forward or backwards at a given stage would depend on which new direct defeat was stronger.
>>
>> On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke <stepjak@yahoo.fr> wrote:
>>> Hi Forest, I may give it a look, but a couple of issues.
>>>
>>> One thing, I feel a little unsure it will be monotone to pick a new candidate to add to the
>>> chain based on who the current head is. Normally these methods don't actually depend on the
>>> ordering of candidates already in the chain.
>>>
>>>> It is well known that not all nice properties are compatible with each other in a common
>>>> single winner voting method. However, we shall see by example that the following nice
>>>> features are mutually compatible in a simple RCV voting method (MGCB defined below).
>>>> Therefore, excluding any of them can only be justified by trading in the excluded ones for
>>>> equally important ones in an equally simple method.
>>>>
>>>> 1. The method should be clone independent like IRV ... therefore not plagued by the spoiler
>>>> problem like First Past The Post Plurality or by "teaming" like the Borda Count.
>>>
>>> Generous of you to imply that IRV is not plagued by a spoiler problem.
>>>
>>>> It was a comment of Kristofer that inspired this method. He mentioned that according to his
>>>> recent simulations electing the winner of the over-all strongest defeat A>B is a
>>>> surprisingly burial resistant stand-alone method. It seems to me that the burial resistance
>>>> should carry over to this MGCB completion of his discovery.
>>>
>>> Well. That kind of method is a stone's throw away from just being approval.
>>>
>>>> Furthermore, it appears that if defeat strength is gauged by margins, then the method is
>>>> Chicken resistant.
>>>
>>> If you mean "more" chicken-resistant then OK, but if you mean satisfying the CD criterion,
>>> there's no reason for that to be true. If you want to guarantee CD you need to deliberately
>>> reject some majorities (which is completely in its spirit), not simply be indifferent to
>>> them.
>>>
>>> More importantly, I would point out that from a CD criterion standpoint, the Alaska RCV
>>> outcome was probably completely correct.
>>>
>>> It seems to me the Alaska race demonstrates that the CD criterion can't deliver on its
>>> promise even under IRV, its most advantageous setting. It's not going to be better under a
>>> method that poses actual incentives to withhold lower preferences.
>>>
>>>> A fairly simple modification ... where the chain is built up from both ends ... always
>>>> giving priority to the end where the new defeat is stronger .... preserves all six of the
>>>> nice features in our list while adding a Strong Reverse Symmetry feature ... reversing all
>>>> of the ballot rankings precisely reverses the output chain .... swapping the head and tail
>>>> of the completed chain.
>>>
>>> I don't follow. Are you just saying there's a choice of whether you beat the head or the
>>> tail, but in either case the newly added candidate becomes the new head?
>>>
>>> Kevin
>>> votingmethods.net
>>>
>>
>
FS
Forest Simmons
Fri, Jan 13, 2023 6:43 AM
Kevin,
Thanks for your valuable tests and insights.
I wonder how this DSC-with-max-gradient-finisher would do:
Initialize X as the DSC winner. Then ...
While X is covered, replace X with the candidate X' with the strongest
defeat against X among those candidates that cover X.
Elect the last value of X... i.e. the first X that turns out to be
uncovered.
Does any of the DSC burial resistance flavor make it through this
afterburner?
Also how does DSC do with regard to Chicken Defense?
Thanks!
Forest
On Thu, Jan 12, 2023, 3:53 PM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Forest, I think it satisfies it. Assuming I coded it correctly I didn't
see any Mono-raise issues going up to 7 candidates.
It seems like it's broadly in the neighborhood of Condorcet//Approval,
with reduced truncation and compromise, but higher burial incentive. Not
shabby though probably not Kristofer's type of method.
Kevin
(end)
Le jeudi 12 janvier 2023 à 11:30:13 UTC−6, Forest Simmons <
forest.simmons21@gmail.com> a écrit :
It seems the way through is to make every step a covering step ... then
when the winner W gets a stronger step ... cutting in front of a bunch of
Y's that it followed before its strength increase ... it still covers all
of those Y's so no Z can be added just because it beats W and the previous
members of the chain.
I think we can get away with the very first step A>B not being a covering:
Make it the single strongest defeat possible so that the first chain head
A is the "Gross Defeat Strength Champ."
Then until the current chain head is uncovered ... at each stage the new
head is the candidate with the strongest possible defeat of the old head by
any candidate covering it (the old head).
Example:
35 A>B>C
25 B>C>A
40 C>A>B
The strongest defeat is A>B (75 to 25).
And since the head A is uncovered, the chain cannot be continued, since by
our new rule all defeats after the first must be coverings.
So A wins.
Now is this monotone?
Shall we call it Max Gradient Ascent MGA?
-Forest
On Mon, Jan 9, 2023, 10:51 AM Forest Simmons forest.simmons21@gmail.com
wrote:
Let's see where my proof goes wrong .... my mistaken proof of
monotonicity for the one sided chain where every addition to the chain
becomes the new head:
Suppose the final head (the winner) H increases pairwise relative to
some candidate X while all of the other pairwise relations are undisturbed.
Then before H is added the sequence of additions proceeds exactly as
before ... H has no influence.
If X is among those added before H, then the increase in H>X strength
has no relevance unless it allows H to immediately follow X instead of
waiting for Y1,Y2, etc ... where the Y1>X defeat was stronger than the H>X
defeat (but no longer is).
But now none of these Y's can be added because they are still defeated
How about some Z that defeats H but was kept out by one of those Y's?
Now that those Y's are gone, that Z gets admitted.
So H is no longer the final head of the chain.
Back to the drawing board!
On Mon, Jan 9, 2023, 12:17 AM Forest Simmons forest.simmons21@gmail.com
The candidate added to the tail would be the one defeated most strongly
by the current tail. Whether to lengthen the chain forward or backwards at
a given stage would depend on which new direct defeat was stronger.
Hi Forest, I may give it a look, but a couple of issues.
One thing, I feel a little unsure it will be monotone to pick a new
chain based on who the current head is. Normally these methods don't
ordering of candidates already in the chain.
It is well known that not all nice properties are compatible with
single winner voting method. However, we shall see by example that
features are mutually compatible in a simple RCV voting method (MGCB
Therefore, excluding any of them can only be justified by trading in
equally important ones in an equally simple method.
- The method should be clone independent like IRV ... therefore not
problem like First Past The Post Plurality or by "teaming" like the
Generous of you to imply that IRV is not plagued by a spoiler problem.
It was a comment of Kristofer that inspired this method. He mentioned
recent simulations electing the winner of the over-all strongest
surprisingly burial resistant stand-alone method. It seems to me
that the burial resistance
should carry over to this MGCB completion of his discovery.
Well. That kind of method is a stone's throw away from just being
Furthermore, it appears that if defeat strength is gauged by margins,
If you mean "more" chicken-resistant then OK, but if you mean
satisfying the CD criterion,
there's no reason for that to be true. If you want to guarantee CD you
reject some majorities (which is completely in its spirit), not simply
them.
More importantly, I would point out that from a CD criterion
standpoint, the Alaska RCV
outcome was probably completely correct.
It seems to me the Alaska race demonstrates that the CD criterion
promise even under IRV, its most advantageous setting. It's not going
method that poses actual incentives to withhold lower preferences.
A fairly simple modification ... where the chain is built up from
giving priority to the end where the new defeat is stronger ....
nice features in our list while adding a Strong Reverse Symmetry
feature ... reversing all
of the ballot rankings precisely reverses the output chain ....
swapping the head and tail
I don't follow. Are you just saying there's a choice of whether you
tail, but in either case the newly added candidate becomes the new
Kevin,
Thanks for your valuable tests and insights.
I wonder how this DSC-with-max-gradient-finisher would do:
Initialize X as the DSC winner. Then ...
While X is covered, replace X with the candidate X' with the strongest
defeat against X among those candidates that cover X.
Elect the last value of X... i.e. the first X that turns out to be
uncovered.
Does any of the DSC burial resistance flavor make it through this
afterburner?
Also how does DSC do with regard to Chicken Defense?
Thanks!
Forest
On Thu, Jan 12, 2023, 3:53 PM Kevin Venzke <stepjak@yahoo.fr> wrote:
> Hi Forest, I think it satisfies it. Assuming I coded it correctly I didn't
> see any Mono-raise issues going up to 7 candidates.
>
> It seems like it's broadly in the neighborhood of Condorcet//Approval,
> with reduced truncation and compromise, but higher burial incentive. Not
> shabby though probably not Kristofer's type of method.
>
> Kevin
>
> (end)
>
>
> Le jeudi 12 janvier 2023 à 11:30:13 UTC−6, Forest Simmons <
> forest.simmons21@gmail.com> a écrit :
> It seems the way through is to make every step a covering step ... then
> when the winner W gets a stronger step ... cutting in front of a bunch of
> Y's that it followed before its strength increase ... it still covers all
> of those Y's so no Z can be added just because it beats W and the previous
> members of the chain.
>
> I think we can get away with the very first step A>B not being a covering:
>
> Make it the single strongest defeat possible so that the first chain head
> A is the "Gross Defeat Strength Champ."
>
> Then until the current chain head is uncovered ... at each stage the new
> head is the candidate with the strongest possible defeat of the old head by
> any candidate covering it (the old head).
>
> Example:
>
> 35 A>B>C
> 25 B>C>A
> 40 C>A>B
>
> The strongest defeat is A>B (75 to 25).
>
> And since the head A is uncovered, the chain cannot be continued, since by
> our new rule all defeats after the first must be coverings.
>
> So A wins.
>
> Now is this monotone?
>
> Shall we call it Max Gradient Ascent MGA?
>
> -Forest
>
>
> On Mon, Jan 9, 2023, 10:51 AM Forest Simmons <forest.simmons21@gmail.com>
> wrote:
> > Let's see where my proof goes wrong .... my mistaken proof of
> monotonicity for the one sided chain where every addition to the chain
> becomes the new head:
> >
> > Suppose the final head (the winner) H increases pairwise relative to
> some candidate X while all of the other pairwise relations are undisturbed.
> >
> > Then before H is added the sequence of additions proceeds exactly as
> before ... H has no influence.
> >
> > If X is among those added before H, then the increase in H>X strength
> has no relevance unless it allows H to immediately follow X instead of
> waiting for Y1,Y2, etc ... where the Y1>X defeat was stronger than the H>X
> defeat (but no longer is).
> >
> > But now none of these Y's can be added because they are still defeated
> by H.
> >
> > How about some Z that defeats H but was kept out by one of those Y's?
> Now that those Y's are gone, that Z gets admitted.
> >
> > So H is no longer the final head of the chain.
> >
> > Back to the drawing board!
> >
> > On Mon, Jan 9, 2023, 12:17 AM Forest Simmons <forest.simmons21@gmail.com>
> wrote:
> >> The candidate added to the tail would be the one defeated most strongly
> by the current tail. Whether to lengthen the chain forward or backwards at
> a given stage would depend on which new direct defeat was stronger.
> >>
> >> On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke <stepjak@yahoo.fr> wrote:
> >>> Hi Forest, I may give it a look, but a couple of issues.
> >>>
> >>> One thing, I feel a little unsure it will be monotone to pick a new
> candidate to add to the
> >>> chain based on who the current head is. Normally these methods don't
> actually depend on the
> >>> ordering of candidates already in the chain.
> >>>
> >>>> It is well known that not all nice properties are compatible with
> each other in a common
> >>>> single winner voting method. However, we shall see by example that
> the following nice
> >>>> features are mutually compatible in a simple RCV voting method (MGCB
> defined below).
> >>>> Therefore, excluding any of them can only be justified by trading in
> the excluded ones for
> >>>> equally important ones in an equally simple method.
> >>>>
> >>>> 1. The method should be clone independent like IRV ... therefore not
> plagued by the spoiler
> >>>> problem like First Past The Post Plurality or by "teaming" like the
> Borda Count.
> >>>
> >>> Generous of you to imply that IRV is not plagued by a spoiler problem.
> >>>
> >>>> It was a comment of Kristofer that inspired this method. He mentioned
> that according to his
> >>>> recent simulations electing the winner of the over-all strongest
> defeat A>B is a
> >>>> surprisingly burial resistant stand-alone method. It seems to me
> that the burial resistance
> >>>> should carry over to this MGCB completion of his discovery.
> >>>
> >>> Well. That kind of method is a stone's throw away from just being
> approval.
> >>>
> >>>> Furthermore, it appears that if defeat strength is gauged by margins,
> then the method is
> >>>> Chicken resistant.
> >>>
> >>> If you mean "more" chicken-resistant then OK, but if you mean
> satisfying the CD criterion,
> >>> there's no reason for that to be true. If you want to guarantee CD you
> need to deliberately
> >>> reject some majorities (which is completely in its spirit), not simply
> be indifferent to
> >>> them.
> >>>
> >>> More importantly, I would point out that from a CD criterion
> standpoint, the Alaska RCV
> >>> outcome was probably completely correct.
> >>>
> >>> It seems to me the Alaska race demonstrates that the CD criterion
> can't deliver on its
> >>> promise even under IRV, its most advantageous setting. It's not going
> to be better under a
> >>> method that poses actual incentives to withhold lower preferences.
> >>>
> >>>> A fairly simple modification ... where the chain is built up from
> both ends ... always
> >>>> giving priority to the end where the new defeat is stronger ....
> preserves all six of the
> >>>> nice features in our list while adding a Strong Reverse Symmetry
> feature ... reversing all
> >>>> of the ballot rankings precisely reverses the output chain ....
> swapping the head and tail
> >>>> of the completed chain.
> >>>
> >>> I don't follow. Are you just saying there's a choice of whether you
> beat the head or the
> >>> tail, but in either case the newly added candidate becomes the new
> head?
> >>>
> >>> Kevin
> >>> votingmethods.net
> >>>
> >>
> >
>
>
KV
Kevin Venzke
Fri, Jan 13, 2023 1:37 PM
Hi Forest,
Let's tackle this question first:
Also how does DSC do with regard to Chicken Defense?
I'm glad you asked. DSC is a ""great"" CD method, maybe the only one.
I have complained before that the CD criterion allows the larger faction in a fragmented
majority to truncate without issue. That seems like a problem both philosophically (i.e.,
what is the significance of faction size in a chicken game?) and also practically (i.e. a
faction might truncate out of an erroneous belief that their faction is the large one).
Consider this election:
40 A
35 B
25 C>B
IRV and Condorcet methods go soft and let B win. Maybe B was driving a truck and C was
driving a car. But with DSC justice is blind. It stands its ground and elects A, handing
the fragmented majority a well-earned punishment!
And it goes much further:
100 A>B
99 B
98 C>B
97 D>B
... etc
50 Z>B
DSC will still elect A.
I wonder how this DSC-with-max-gradient-finisher would do:
Initialize X as the DSC winner. Then ...
I tried this with a few methods (DSC, DAC, FPP, approval) as I felt unsure you really meant
to pick DSC for this. However, I seem to find that generally, no matter the seed method,
this approach is violating monotonicity. Maybe this is creating ways to rig the initial
chain head.
While X is covered, replace X with the candidate X' with the strongest defeat against X
among those candidates that cover X.
Elect the last value of X... i.e. the first X that turns out to be uncovered.
Does any of the DSC burial resistance flavor make it through this afterburner?
DSC isn't particularly burial-resistant. Its significance is in lacking truncation
incentive. But since it likes to agree with FPP, that might moderate the burial issue.
As far as simulations:
Seeding with FPP or DSC made it a lot worse with minimal defense, so I can't say I like
those ones.
Some best-to-worst rankings for each seed type, and also C//A, with four candidates:
Compromise:
DAC > Approval > C//A > Gross score > DSC > FPP
Truncation:
FPP > DSC > DAC > Gross score > Approval > C//A
Burial:
C//A > FPP > Approval > DAC > DSC > Gross score
For burial, FPP is the best seed probably because you can't manipulate the initial chain
head through adjusting your lower preferences.
In general it seems like the covering rule will introduce burial, because it gives voters
some levers to indirectly attack a potential chain head.
Kevin
votingmethods.net
Hi Forest,
Let's tackle this question first:
> Also how does DSC do with regard to Chicken Defense?
I'm glad you asked. DSC is a ""great"" CD method, maybe the only one.
I have complained before that the CD criterion allows the larger faction in a fragmented
majority to truncate without issue. That seems like a problem both philosophically (i.e.,
what is the significance of faction size in a chicken game?) and also practically (i.e. a
faction might truncate out of an erroneous belief that their faction is the large one).
Consider this election:
40 A
35 B
25 C>B
IRV and Condorcet methods go soft and let B win. Maybe B was driving a truck and C was
driving a car. But with DSC justice is blind. It stands its ground and elects A, handing
the fragmented majority a well-earned punishment!
And it goes much further:
100 A>B
99 B
98 C>B
97 D>B
... etc
50 Z>B
DSC will still elect A.
> I wonder how this DSC-with-max-gradient-finisher would do:
>
> Initialize X as the DSC winner. Then ...
I tried this with a few methods (DSC, DAC, FPP, approval) as I felt unsure you really meant
to pick DSC for this. However, I seem to find that generally, no matter the seed method,
this approach is violating monotonicity. Maybe this is creating ways to rig the initial
chain head.
> While X is covered, replace X with the candidate X' with the strongest defeat against X
> among those candidates that cover X.
>
> Elect the last value of X... i.e. the first X that turns out to be uncovered.
>
> Does any of the DSC burial resistance flavor make it through this afterburner?
DSC isn't particularly burial-resistant. Its significance is in lacking truncation
incentive. But since it likes to agree with FPP, that might moderate the burial issue.
As far as simulations:
Seeding with FPP or DSC made it a lot worse with minimal defense, so I can't say I like
those ones.
Some best-to-worst rankings for each seed type, and also C//A, with four candidates:
Compromise:
DAC > Approval > C//A > Gross score > DSC > FPP
Truncation:
FPP > DSC > DAC > Gross score > Approval > C//A
Burial:
C//A > FPP > Approval > DAC > DSC > Gross score
For burial, FPP is the best seed probably because you can't manipulate the initial chain
head through adjusting your lower preferences.
In general it seems like the covering rule will introduce burial, because it gives voters
some levers to indirectly attack a potential chain head.
Kevin
votingmethods.net
FS
Forest Simmons
Sat, Jan 14, 2023 8:53 AM
Very Good!
I have another more elaborate application of max gradient in mind, but I
was hoping that some choice of seed would be good enough for a simple
stand-alone max gradient.
Too bad Brenham's Gross Loser Elimination is not monotone.
On Fri, Jan 13, 2023, 5:39 AM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Forest,
Let's tackle this question first:
Also how does DSC do with regard to Chicken Defense?
I'm glad you asked. DSC is a ""great"" CD method, maybe the only one.
I have complained before that the CD criterion allows the larger faction
in a fragmented
majority to truncate without issue. That seems like a problem both
philosophically (i.e.,
what is the significance of faction size in a chicken game?) and also
practically (i.e. a
faction might truncate out of an erroneous belief that their faction is
the large one).
Consider this election:
40 A
35 B
25 C>B
IRV and Condorcet methods go soft and let B win. Maybe B was driving a
truck and C was
driving a car. But with DSC justice is blind. It stands its ground and
elects A, handing
the fragmented majority a well-earned punishment!
And it goes much further:
100 A>B
99 B
98 C>B
97 D>B
... etc
50 Z>B
DSC will still elect A.
I wonder how this DSC-with-max-gradient-finisher would do:
Initialize X as the DSC winner. Then ...
I tried this with a few methods (DSC, DAC, FPP, approval) as I felt unsure
you really meant
to pick DSC for this. However, I seem to find that generally, no matter
the seed method,
this approach is violating monotonicity. Maybe this is creating ways to
rig the initial
chain head.
While X is covered, replace X with the candidate X' with the strongest
among those candidates that cover X.
Elect the last value of X... i.e. the first X that turns out to be
Does any of the DSC burial resistance flavor make it through this
afterburner?
DSC isn't particularly burial-resistant. Its significance is in lacking
truncation
incentive. But since it likes to agree with FPP, that might moderate the
burial issue.
As far as simulations:
Seeding with FPP or DSC made it a lot worse with minimal defense, so I
can't say I like
those ones.
Some best-to-worst rankings for each seed type, and also C//A, with four
candidates:
Compromise:
DAC > Approval > C//A > Gross score > DSC > FPP
Truncation:
FPP > DSC > DAC > Gross score > Approval > C//A
Burial:
C//A > FPP > Approval > DAC > DSC > Gross score
For burial, FPP is the best seed probably because you can't manipulate the
initial chain
head through adjusting your lower preferences.
In general it seems like the covering rule will introduce burial, because
it gives voters
some levers to indirectly attack a potential chain head.
Kevin
votingmethods.net
Very Good!
I have another more elaborate application of max gradient in mind, but I
was hoping that some choice of seed would be good enough for a simple
stand-alone max gradient.
Too bad Brenham's Gross Loser Elimination is not monotone.
On Fri, Jan 13, 2023, 5:39 AM Kevin Venzke <stepjak@yahoo.fr> wrote:
> Hi Forest,
>
> Let's tackle this question first:
>
> > Also how does DSC do with regard to Chicken Defense?
>
> I'm glad you asked. DSC is a ""great"" CD method, maybe the only one.
>
> I have complained before that the CD criterion allows the larger faction
> in a fragmented
> majority to truncate without issue. That seems like a problem both
> philosophically (i.e.,
> what is the significance of faction size in a chicken game?) and also
> practically (i.e. a
> faction might truncate out of an erroneous belief that their faction is
> the large one).
>
> Consider this election:
>
> 40 A
> 35 B
> 25 C>B
>
> IRV and Condorcet methods go soft and let B win. Maybe B was driving a
> truck and C was
> driving a car. But with DSC justice is blind. It stands its ground and
> elects A, handing
> the fragmented majority a well-earned punishment!
>
> And it goes much further:
>
> 100 A>B
> 99 B
> 98 C>B
> 97 D>B
> ... etc
> 50 Z>B
>
> DSC will still elect A.
>
> > I wonder how this DSC-with-max-gradient-finisher would do:
> >
> > Initialize X as the DSC winner. Then ...
>
> I tried this with a few methods (DSC, DAC, FPP, approval) as I felt unsure
> you really meant
> to pick DSC for this. However, I seem to find that generally, no matter
> the seed method,
> this approach is violating monotonicity. Maybe this is creating ways to
> rig the initial
> chain head.
>
> > While X is covered, replace X with the candidate X' with the strongest
> defeat against X
> > among those candidates that cover X.
> >
> > Elect the last value of X... i.e. the first X that turns out to be
> uncovered.
> >
> > Does any of the DSC burial resistance flavor make it through this
> afterburner?
>
> DSC isn't particularly burial-resistant. Its significance is in lacking
> truncation
> incentive. But since it likes to agree with FPP, that might moderate the
> burial issue.
>
> As far as simulations:
>
> Seeding with FPP or DSC made it a lot worse with minimal defense, so I
> can't say I like
> those ones.
>
> Some best-to-worst rankings for each seed type, and also C//A, with four
> candidates:
>
> Compromise:
> DAC > Approval > C//A > Gross score > DSC > FPP
>
> Truncation:
> FPP > DSC > DAC > Gross score > Approval > C//A
>
> Burial:
> C//A > FPP > Approval > DAC > DSC > Gross score
>
> For burial, FPP is the best seed probably because you can't manipulate the
> initial chain
> head through adjusting your lower preferences.
>
> In general it seems like the covering rule will introduce burial, because
> it gives voters
> some levers to indirectly attack a potential chain head.
>
> Kevin
> votingmethods.net
>
FS
Forest Simmons
Sat, Jan 14, 2023 9:54 PM
Perhaps we need to use the entire finish order of the seed method to get an
appropriate uncovered winner:
Unc(Finish Order)
Initialize the variable X as the candidate highest in Finish Order.
Then ...
While X is covered, replace it with the highest Finish Order candidate that
covers it. EndWhile.
Elect the updated X.
I would like to suggest as the seed method the following version of
MaxMinPairwise Support:
Let M be the matrix whose entry in column k of row j is the number of
ballots on which candidate j is ranked ahead of or equal to candidate k
(but not truncated).
In particular, the i_th diagonal entry M(i,i) is the number of ballots on
which candidate i is ranked.
Sort the entries in each row in non-decreasing order from left to right.
Note that this sort moves the diagonal entries of M to the extreme right
of each row.
While keeping track of the correspondence between rows and candidates, sort
the rows lexicographically so that row R is above row R' iff R(i)>R'(i),
where i is the first place where the two rows disagree.
The order of the rows induces the modified finish order of the respective
candidates.
If I'm not mistaken, the following variant of the FBC is satisfied by this
version of MaxMinPairwise Support (before the uncovering modification):
If the winner W of this method is ranked top on ballot B, and the winner
changes when F is moved to equal top with W on ballot B, then the new
winner must be F.
Example:
48 C
28 A>B
24 B
The MaxMinPS finish order is C>A>B, and C is already uncovered.
Comments?
-Forest
On Sat, Jan 14, 2023, 12:53 AM Forest Simmons forest.simmons21@gmail.com
wrote:
Very Good!
I have another more elaborate application of max gradient in mind, but I
was hoping that some choice of seed would be good enough for a simple
stand-alone max gradient.
Too bad Brenham's Gross Loser Elimination is not monotone.
On Fri, Jan 13, 2023, 5:39 AM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Forest,
Let's tackle this question first:
Also how does DSC do with regard to Chicken Defense?
I'm glad you asked. DSC is a ""great"" CD method, maybe the only one.
I have complained before that the CD criterion allows the larger faction
in a fragmented
majority to truncate without issue. That seems like a problem both
philosophically (i.e.,
what is the significance of faction size in a chicken game?) and also
practically (i.e. a
faction might truncate out of an erroneous belief that their faction is
the large one).
Consider this election:
40 A
35 B
25 C>B
IRV and Condorcet methods go soft and let B win. Maybe B was driving a
truck and C was
driving a car. But with DSC justice is blind. It stands its ground and
elects A, handing
the fragmented majority a well-earned punishment!
And it goes much further:
100 A>B
99 B
98 C>B
97 D>B
... etc
50 Z>B
DSC will still elect A.
I wonder how this DSC-with-max-gradient-finisher would do:
Initialize X as the DSC winner. Then ...
I tried this with a few methods (DSC, DAC, FPP, approval) as I felt
unsure you really meant
to pick DSC for this. However, I seem to find that generally, no matter
the seed method,
this approach is violating monotonicity. Maybe this is creating ways to
rig the initial
chain head.
While X is covered, replace X with the candidate X' with the strongest
among those candidates that cover X.
Elect the last value of X... i.e. the first X that turns out to be
Does any of the DSC burial resistance flavor make it through this
afterburner?
DSC isn't particularly burial-resistant. Its significance is in lacking
truncation
incentive. But since it likes to agree with FPP, that might moderate the
burial issue.
As far as simulations:
Seeding with FPP or DSC made it a lot worse with minimal defense, so I
can't say I like
those ones.
Some best-to-worst rankings for each seed type, and also C//A, with four
candidates:
Compromise:
DAC > Approval > C//A > Gross score > DSC > FPP
Truncation:
FPP > DSC > DAC > Gross score > Approval > C//A
Burial:
C//A > FPP > Approval > DAC > DSC > Gross score
For burial, FPP is the best seed probably because you can't manipulate
the initial chain
head through adjusting your lower preferences.
In general it seems like the covering rule will introduce burial, because
it gives voters
some levers to indirectly attack a potential chain head.
Kevin
votingmethods.net
Perhaps we need to use the entire finish order of the seed method to get an
appropriate uncovered winner:
Unc(Finish Order)
Initialize the variable X as the candidate highest in Finish Order.
Then ...
While X is covered, replace it with the highest Finish Order candidate that
covers it. EndWhile.
Elect the updated X.
I would like to suggest as the seed method the following version of
MaxMinPairwise Support:
Let M be the matrix whose entry in column k of row j is the number of
ballots on which candidate j is ranked ahead of or equal to candidate k
(but not truncated).
In particular, the i_th diagonal entry M(i,i) is the number of ballots on
which candidate i is ranked.
Sort the entries in each row in non-decreasing order from left to right.
Note that this sort moves the diagonal entries of M to the extreme right
of each row.
While keeping track of the correspondence between rows and candidates, sort
the rows lexicographically so that row R is above row R' iff R(i)>R'(i),
where i is the first place where the two rows disagree.
The order of the rows induces the modified finish order of the respective
candidates.
If I'm not mistaken, the following variant of the FBC is satisfied by this
version of MaxMinPairwise Support (before the uncovering modification):
If the winner W of this method is ranked top on ballot B, and the winner
changes when F is moved to equal top with W on ballot B, then the new
winner must be F.
Example:
48 C
28 A>B
24 B
The MaxMinPS finish order is C>A>B, and C is already uncovered.
Comments?
-Forest
On Sat, Jan 14, 2023, 12:53 AM Forest Simmons <forest.simmons21@gmail.com>
wrote:
> Very Good!
>
> I have another more elaborate application of max gradient in mind, but I
> was hoping that some choice of seed would be good enough for a simple
> stand-alone max gradient.
>
> Too bad Brenham's Gross Loser Elimination is not monotone.
>
>
>
>
>
>
> On Fri, Jan 13, 2023, 5:39 AM Kevin Venzke <stepjak@yahoo.fr> wrote:
>
>> Hi Forest,
>>
>> Let's tackle this question first:
>>
>> > Also how does DSC do with regard to Chicken Defense?
>>
>> I'm glad you asked. DSC is a ""great"" CD method, maybe the only one.
>>
>> I have complained before that the CD criterion allows the larger faction
>> in a fragmented
>> majority to truncate without issue. That seems like a problem both
>> philosophically (i.e.,
>> what is the significance of faction size in a chicken game?) and also
>> practically (i.e. a
>> faction might truncate out of an erroneous belief that their faction is
>> the large one).
>>
>> Consider this election:
>>
>> 40 A
>> 35 B
>> 25 C>B
>>
>> IRV and Condorcet methods go soft and let B win. Maybe B was driving a
>> truck and C was
>> driving a car. But with DSC justice is blind. It stands its ground and
>> elects A, handing
>> the fragmented majority a well-earned punishment!
>>
>> And it goes much further:
>>
>> 100 A>B
>> 99 B
>> 98 C>B
>> 97 D>B
>> ... etc
>> 50 Z>B
>>
>> DSC will still elect A.
>>
>> > I wonder how this DSC-with-max-gradient-finisher would do:
>> >
>> > Initialize X as the DSC winner. Then ...
>>
>> I tried this with a few methods (DSC, DAC, FPP, approval) as I felt
>> unsure you really meant
>> to pick DSC for this. However, I seem to find that generally, no matter
>> the seed method,
>> this approach is violating monotonicity. Maybe this is creating ways to
>> rig the initial
>> chain head.
>>
>> > While X is covered, replace X with the candidate X' with the strongest
>> defeat against X
>> > among those candidates that cover X.
>> >
>> > Elect the last value of X... i.e. the first X that turns out to be
>> uncovered.
>> >
>> > Does any of the DSC burial resistance flavor make it through this
>> afterburner?
>>
>> DSC isn't particularly burial-resistant. Its significance is in lacking
>> truncation
>> incentive. But since it likes to agree with FPP, that might moderate the
>> burial issue.
>>
>> As far as simulations:
>>
>> Seeding with FPP or DSC made it a lot worse with minimal defense, so I
>> can't say I like
>> those ones.
>>
>> Some best-to-worst rankings for each seed type, and also C//A, with four
>> candidates:
>>
>> Compromise:
>> DAC > Approval > C//A > Gross score > DSC > FPP
>>
>> Truncation:
>> FPP > DSC > DAC > Gross score > Approval > C//A
>>
>> Burial:
>> C//A > FPP > Approval > DAC > DSC > Gross score
>>
>> For burial, FPP is the best seed probably because you can't manipulate
>> the initial chain
>> head through adjusting your lower preferences.
>>
>> In general it seems like the covering rule will introduce burial, because
>> it gives voters
>> some levers to indirectly attack a potential chain head.
>>
>> Kevin
>> votingmethods.net
>>
>
