FS
Forest Simmons
Sun, Oct 23, 2022 2:55 AM
Richard Lung has been patiently teaching and reminding us that the
information from ballot last choices is just as valuable as the top choice
information ... if only we incorporate it wisely ... as suggested by
Richard and other proponents of Binomial STV, for eexample.
For decades we have seen an echo of this wisdom in the form of ballots that
allow one vote for, and one vote against.
Critics have always maintained that this idea shows a lack of awareness of
clone dependence. But that judgment assumes that just because there is a
bad way of using those ballots, there can be no good way.
Just as "vote one" plurality ballots are perfectly adequate for the
benchmark lottery, the vote "one against" ballot is perfectly adequate for
the anti-favorite lottery.
We have seen already that these two lotteries have equally important roles
in de-cloning the Kendall-tau metric for making a clone free version of
Kemeny-Young.
Here's another application of this idea whose time has come:
Gauge pairwise defeat strength of Y by X as the product f(X)*f'(Y), where
f and f' give the benchmark and anti-benchmark lottery probabilities,
respectively.
Condorcet with this defeat strength gauge is the method we should be
testing for dishonest strategy resistance, and for Voter Satisfaction
Efficiency!
It could be the best all around single winner deterministic Universal
Domain method ever!
Thanks to Richard for your patience in keeping us on the right track!
And thanks to Kevin and Kristofer for keeping us honest by experimental
testing of our ideas ... two versatile scientists with both analytical and
experimental creativity and insight.
And Richard ... a well read renaissance man of wide ranging historical
social and hard science intellectual interest ... with amazing intuition!
-Forest
Richard Lung has been patiently teaching and reminding us that the
information from ballot last choices is just as valuable as the top choice
information ... if only we incorporate it wisely ... as suggested by
Richard and other proponents of Binomial STV, for eexample.
For decades we have seen an echo of this wisdom in the form of ballots that
allow one vote for, and one vote against.
Critics have always maintained that this idea shows a lack of awareness of
clone dependence. But that judgment assumes that just because there is a
bad way of using those ballots, there can be no good way.
Just as "vote one" plurality ballots are perfectly adequate for the
benchmark lottery, the vote "one against" ballot is perfectly adequate for
the anti-favorite lottery.
We have seen already that these two lotteries have equally important roles
in de-cloning the Kendall-tau metric for making a clone free version of
Kemeny-Young.
Here's another application of this idea whose time has come:
Gauge pairwise defeat strength of Y by X as the product f(X)*f'(Y), where
f and f' give the benchmark and anti-benchmark lottery probabilities,
respectively.
Condorcet with this defeat strength gauge is the method we should be
testing for dishonest strategy resistance, and for Voter Satisfaction
Efficiency!
It could be the best all around single winner deterministic Universal
Domain method ever!
Thanks to Richard for your patience in keeping us on the right track!
And thanks to Kevin and Kristofer for keeping us honest by experimental
testing of our ideas ... two versatile scientists with both analytical and
experimental creativity and insight.
And Richard ... a well read renaissance man of wide ranging historical
social and hard science intellectual interest ... with amazing intuition!
-Forest
FS
Forest Simmons
Mon, Oct 24, 2022 7:03 AM
Jobst pointed out clone dependence of a related method I see the need to
fix this one, too.
Let Good(A) be the "goodness" of A, (judging from the superficial first
place lottery probabilities) defined as ...
Sum {fp(X)|A is not defeated by X},
where fo(X) is the percentage of first place ballot positions occupied by X.
Likewise, let Bad(B) be the superficial "badness" of B, defined as ..
Sum {bot(Z)|Z is not defeated by B},
where bot(Z) is the percentage of bottom ballot positions occupied by Z.
The pairwise defeat A>B is what you would expect when B is bad and A is
good. The worse B, and the better A, the bigger numerically both Bad(B) and
Good(A). So their sum Bad(B)+Good(A) is a natural measure of defeat
strength that gives equal importance to top and bottom ballot positions.
Presently (meaning soon) we'll test it on a few examples to see if it lives
up to expectations!
Forest
On Sat, Oct 22, 2022, 7:55 PM Forest Simmons forest.simmons21@gmail.com
wrote:
Richard Lung has been patiently teaching and reminding us that the
information from ballot last choices is just as valuable as the top choice
information ... if only we incorporate it wisely ... as suggested by
Richard and other proponents of Binomial STV, for eexample.
For decades we have seen an echo of this wisdom in the form of ballots
that allow one vote for, and one vote against.
Critics have always maintained that this idea shows a lack of awareness of
clone dependence. But that judgment assumes that just because there is a
bad way of using those ballots, there can be no good way.
Just as "vote one" plurality ballots are perfectly adequate for the
benchmark lottery, the vote "one against" ballot is perfectly adequate for
the anti-favorite lottery.
We have seen already that these two lotteries have equally important roles
in de-cloning the Kendall-tau metric for making a clone free version of
Kemeny-Young.
Here's another application of this idea whose time has come:
Gauge pairwise defeat strength of Y by X as the product f(X)*f'(Y), where
f and f' give the benchmark and anti-benchmark lottery probabilities,
respectively.
Condorcet with this defeat strength gauge is the method we should be
testing for dishonest strategy resistance, and for Voter Satisfaction
Efficiency!
It could be the best all around single winner deterministic Universal
Domain method ever!
Thanks to Richard for your patience in keeping us on the right track!
And thanks to Kevin and Kristofer for keeping us honest by experimental
testing of our ideas ... two versatile scientists with both analytical and
experimental creativity and insight.
And Richard ... a well read renaissance man of wide ranging historical
social and hard science intellectual interest ... with amazing intuition!
-Forest
Jobst pointed out clone dependence of a related method I see the need to
fix this one, too.
Let Good(A) be the "goodness" of A, (judging from the superficial first
place lottery probabilities) defined as ...
Sum {fp(X)|A is not defeated by X},
where fo(X) is the percentage of first place ballot positions occupied by X.
Likewise, let Bad(B) be the superficial "badness" of B, defined as ..
Sum {bot(Z)|Z is not defeated by B},
where bot(Z) is the percentage of bottom ballot positions occupied by Z.
The pairwise defeat A>B is what you would expect when B is bad and A is
good. The worse B, and the better A, the bigger numerically both Bad(B) and
Good(A). So their sum Bad(B)+Good(A) is a natural measure of defeat
strength that gives equal importance to top and bottom ballot positions.
Presently (meaning soon) we'll test it on a few examples to see if it lives
up to expectations!
Forest
On Sat, Oct 22, 2022, 7:55 PM Forest Simmons <forest.simmons21@gmail.com>
wrote:
> Richard Lung has been patiently teaching and reminding us that the
> information from ballot last choices is just as valuable as the top choice
> information ... if only we incorporate it wisely ... as suggested by
> Richard and other proponents of Binomial STV, for eexample.
>
> For decades we have seen an echo of this wisdom in the form of ballots
> that allow one vote for, and one vote against.
>
> Critics have always maintained that this idea shows a lack of awareness of
> clone dependence. But that judgment assumes that just because there is a
> bad way of using those ballots, there can be no good way.
>
> Just as "vote one" plurality ballots are perfectly adequate for the
> benchmark lottery, the vote "one against" ballot is perfectly adequate for
> the anti-favorite lottery.
>
> We have seen already that these two lotteries have equally important roles
> in de-cloning the Kendall-tau metric for making a clone free version of
> Kemeny-Young.
>
> Here's another application of this idea whose time has come:
>
> Gauge pairwise defeat strength of Y by X as the product f(X)*f'(Y), where
> f and f' give the benchmark and anti-benchmark lottery probabilities,
> respectively.
>
> Condorcet with this defeat strength gauge is the method we should be
> testing for dishonest strategy resistance, and for Voter Satisfaction
> Efficiency!
>
> It could be the best all around single winner deterministic Universal
> Domain method ever!
>
> Thanks to Richard for your patience in keeping us on the right track!
>
> And thanks to Kevin and Kristofer for keeping us honest by experimental
> testing of our ideas ... two versatile scientists with both analytical and
> experimental creativity and insight.
>
> And Richard ... a well read renaissance man of wide ranging historical
> social and hard science intellectual interest ... with amazing intuition!
>
> -Forest
>
KM
Kristofer Munsterhjelm
Mon, Oct 24, 2022 9:43 AM
On 10/23/22 04:55, Forest Simmons wrote:
Critics have always maintained that this idea shows a lack of awareness
of clone dependence. But that judgment assumes that just because there
is a bad way of using those ballots, there can be no good way.
Here's a thought that occurred to me, that would explain why the
(seemingly out of nowhere) implication that we can't have both reversal
symmetry and DMTCBR.
First preferences are unaffected by burial, and last preferences are
unaffected by compromising. Suppose we had a method that were DMTCBR and
reversal symmetric. Then we could freely translate between a method
that's very strong against burial and very strong against compromise by
just reversing the ballots, since the reversed ballots' first
preferences would be last preferences.
Thus a method that passes both DMTCBR and rev. sym. would be extremely
resistant to both burial and to compromise. But since the favorite
betrayal criterion is so hard to pass, we have reason to believe that
this is impossible. So no such method can be rev. sym -- which is what
we at least see with Condorcet methods!
It's thus quite that the implication is stronger: that we can't have all
of DMTBR, majority, and reversal symmetry. But the proof is probably a
lot harder to find, too.
So all of the above implies that when creating a resistant ranked
method, we can't both have extreme resistance to burial and compromising
- we have to pick one. Fortunately (as James Green-Armytage originally
showed), we already get a great deal of compromising resistance from the
Condorcet criterion itself (since, for instance, it does the right thing
under center squeeze). Thus it's more sensible to choose further burial
resistance over further compromise resistance if we can only have one.
(Unless we consider maximum compromise resistance absolutely
non-negotiable, e.g. Mike O's insistence on the FBC.)
...
Finally, it might be useful to see just what the analog of the DMTCBR is
for a reversed DMTCBR-compliant method. It's something like...
Suppose that more than 1/3 of the ranks some Condorcet loser last. Then
nobody who prefers this loser to the current winner can make the loser
win by upranking him.
-km
On 10/23/22 04:55, Forest Simmons wrote:
> Critics have always maintained that this idea shows a lack of awareness
> of clone dependence. But that judgment assumes that just because there
> is a bad way of using those ballots, there can be no good way.
Here's a thought that occurred to me, that would explain why the
(seemingly out of nowhere) implication that we can't have both reversal
symmetry and DMTCBR.
First preferences are unaffected by burial, and last preferences are
unaffected by compromising. Suppose we had a method that were DMTCBR and
reversal symmetric. Then we could freely translate between a method
that's very strong against burial and very strong against compromise by
just reversing the ballots, since the reversed ballots' first
preferences would be last preferences.
Thus a method that passes both DMTCBR and rev. sym. would be extremely
resistant to both burial and to compromise. But since the favorite
betrayal criterion is so hard to pass, we have reason to believe that
this is impossible. So no such method can be rev. sym -- which is what
we at least see with Condorcet methods!
It's thus quite that the implication is stronger: that we can't have all
of DMTBR, majority, and reversal symmetry. But the proof is probably a
lot harder to find, too.
So all of the above implies that when creating a resistant ranked
method, we can't both have extreme resistance to burial and compromising
- we have to pick one. Fortunately (as James Green-Armytage originally
showed), we already get a great deal of compromising resistance from the
Condorcet criterion itself (since, for instance, it does the right thing
under center squeeze). Thus it's more sensible to choose further burial
resistance over further compromise resistance if we can only have one.
(Unless we consider maximum compromise resistance absolutely
non-negotiable, e.g. Mike O's insistence on the FBC.)
...
Finally, it might be useful to see just what the analog of the DMTCBR is
for a reversed DMTCBR-compliant method. It's something like...
Suppose that more than 1/3 of the ranks some Condorcet loser last. Then
nobody who prefers this loser to the current winner can make the loser
win by upranking him.
-km
FS
Forest Simmons
Mon, Oct 24, 2022 6:29 PM
That is a great insight!
My most recent message in this thread adds a term to the defeat strength
that achieves reverse symmetry, but it comes at the cost of increasing
burial incentive.
The term is Bad(B) defined as ...
Sum bottom(Z) | B does not defeat Z
in the context of defeat strength, where B is the pairwise loser of the
defeat in question. Bottom(Z) is the percentage of bottom ballot positions
occupied by Z.
So if B is the Condorcet Loser, then Bad(B) is 100%.
Obviously if this term is given equal weight with its reverse symmetry
counterpart, it will contribute an appreciable burial incentive.
The reverse symmetry counterpart is Good(A) defined by
Sum Top(X) | X does not defeat A
in the context of defeat strength of a defeat where A is the pairwise
winner.
Top(X) is the percentage of Too ballot positions occupied by X.
So if A is the CW, then Good(A) is 100percent.
So jt's probably not a good idea to use Bad(B) to create reverse symmetry.
However, perhaps it could be given non-symmetrical, infinitesimal weight
for tie breaking purposes only.
Also, perhaps their is a milder version of Good(A), whose reverse symmetry
counterpart Bad(B), would have a tolerable burial incentive.
-Forest
On Mon, Oct 24, 2022, 2:43 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 10/23/22 04:55, Forest Simmons wrote:
Critics have always maintained that this idea shows a lack of awareness
of clone dependence. But that judgment assumes that just because there
is a bad way of using those ballots, there can be no good way.
Here's a thought that occurred to me, that would explain why the
(seemingly out of nowhere) implication that we can't have both reversal
symmetry and DMTCBR.
First preferences are unaffected by burial, and last preferences are
unaffected by compromising. Suppose we had a method that were DMTCBR and
reversal symmetric. Then we could freely translate between a method
that's very strong against burial and very strong against compromise by
just reversing the ballots, since the reversed ballots' first
preferences would be last preferences.
Thus a method that passes both DMTCBR and rev. sym. would be extremely
resistant to both burial and to compromise. But since the favorite
betrayal criterion is so hard to pass, we have reason to believe that
this is impossible. So no such method can be rev. sym -- which is what
we at least see with Condorcet methods!
It's thus quite that the implication is stronger: that we can't have all
of DMTBR, majority, and reversal symmetry. But the proof is probably a
lot harder to find, too.
So all of the above implies that when creating a resistant ranked
method, we can't both have extreme resistance to burial and compromising
- we have to pick one. Fortunately (as James Green-Armytage originally
showed), we already get a great deal of compromising resistance from the
Condorcet criterion itself (since, for instance, it does the right thing
under center squeeze). Thus it's more sensible to choose further burial
resistance over further compromise resistance if we can only have one.
(Unless we consider maximum compromise resistance absolutely
non-negotiable, e.g. Mike O's insistence on the FBC.)
...
Finally, it might be useful to see just what the analog of the DMTCBR is
for a reversed DMTCBR-compliant method. It's something like...
Suppose that more than 1/3 of the ranks some Condorcet loser last. Then
nobody who prefers this loser to the current winner can make the loser
win by upranking him.
-km
That is a great insight!
My most recent message in this thread adds a term to the defeat strength
that achieves reverse symmetry, but it comes at the cost of increasing
burial incentive.
The term is Bad(B) defined as ...
Sum bottom(Z) | B does not defeat Z
in the context of defeat strength, where B is the pairwise loser of the
defeat in question. Bottom(Z) is the percentage of bottom ballot positions
occupied by Z.
So if B is the Condorcet Loser, then Bad(B) is 100%.
Obviously if this term is given equal weight with its reverse symmetry
counterpart, it will contribute an appreciable burial incentive.
The reverse symmetry counterpart is Good(A) defined by
Sum Top(X) | X does not defeat A
in the context of defeat strength of a defeat where A is the pairwise
winner.
Top(X) is the percentage of Too ballot positions occupied by X.
So if A is the CW, then Good(A) is 100percent.
So jt's probably not a good idea to use Bad(B) to create reverse symmetry.
However, perhaps it could be given non-symmetrical, infinitesimal weight
for tie breaking purposes only.
Also, perhaps their is a milder version of Good(A), whose reverse symmetry
counterpart Bad(B), would have a tolerable burial incentive.
-Forest
On Mon, Oct 24, 2022, 2:43 AM Kristofer Munsterhjelm <km_elmet@t-online.de>
wrote:
> On 10/23/22 04:55, Forest Simmons wrote:
>
> > Critics have always maintained that this idea shows a lack of awareness
> > of clone dependence. But that judgment assumes that just because there
> > is a bad way of using those ballots, there can be no good way.
>
> Here's a thought that occurred to me, that would explain why the
> (seemingly out of nowhere) implication that we can't have both reversal
> symmetry and DMTCBR.
>
> First preferences are unaffected by burial, and last preferences are
> unaffected by compromising. Suppose we had a method that were DMTCBR and
> reversal symmetric. Then we could freely translate between a method
> that's very strong against burial and very strong against compromise by
> just reversing the ballots, since the reversed ballots' first
> preferences would be last preferences.
>
> Thus a method that passes both DMTCBR and rev. sym. would be extremely
> resistant to both burial and to compromise. But since the favorite
> betrayal criterion is so hard to pass, we have reason to believe that
> this is impossible. So no such method can be rev. sym -- which is what
> we at least see with Condorcet methods!
>
> It's thus quite that the implication is stronger: that we can't have all
> of DMTBR, majority, and reversal symmetry. But the proof is probably a
> lot harder to find, too.
>
> So all of the above implies that when creating a resistant ranked
> method, we can't both have extreme resistance to burial and compromising
> - we have to pick one. Fortunately (as James Green-Armytage originally
> showed), we already get a great deal of compromising resistance from the
> Condorcet criterion itself (since, for instance, it does the right thing
> under center squeeze). Thus it's more sensible to choose further burial
> resistance over further compromise resistance if we can only have one.
>
> (Unless we consider maximum compromise resistance absolutely
> non-negotiable, e.g. Mike O's insistence on the FBC.)
>
> ...
>
> Finally, it might be useful to see just what the analog of the DMTCBR is
> for a reversed DMTCBR-compliant method. It's something like...
>
> Suppose that more than 1/3 of the ranks some Condorcet loser last. Then
> nobody who prefers this loser to the current winner can make the loser
> win by upranking him.
>
> -km
>
FS
Forest Simmons
Mon, Oct 24, 2022 7:24 PM
Suppose we start with Defeat Strength DS(A>B) defined by ...
Sum Top(X) | X does not defeat A
Minus
Sum Top(Y) | B defeats Y,
and add a difference that will confer reverse symmetry onto the resulting
defeat strength ... something like this ...
Sum Bottom(Z) | B is not defeated by Z
Minus
Sum Bottom(K) | K defeats A
If we put these differences together, and combine the subtrahends to
minimize subtractions, we get a defeat strength expression with reverse
symmetry for the A>B defeat:
Sum Top(X) | X does not defeat A
Plus
Sum Bottom(Z) | B is not defeated by Z
Minus
[Sum Bottom(K) | K defeats A+Sum Top(Y) | B defeats Y]
If A is the CW and B is the CL, this strength is 200 percent, so perhaps we
should divide the whole thing by two.
With all the bottom and top percentage terms involved in one way or
another, this expression should be very decisive.
But in the rare case of a tie or ties, a complete ranking created by random
ballot draws should be an acceptable traditional way of resolving any
ambiguities in the Ranked Pairs finish order.
-Forest
On Mon, Oct 24, 2022, 11:29 AM Forest Simmons forest.simmons21@gmail.com
wrote:
That is a great insight!
My most recent message in this thread adds a term to the defeat strength
that achieves reverse symmetry, but it comes at the cost of increasing
burial incentive.
The term is Bad(B) defined as ...
Sum bottom(Z) | B does not defeat Z
in the context of defeat strength, where B is the pairwise loser of the
defeat in question. Bottom(Z) is the percentage of bottom ballot positions
occupied by Z.
So if B is the Condorcet Loser, then Bad(B) is 100%.
Obviously if this term is given equal weight with its reverse symmetry
counterpart, it will contribute an appreciable burial incentive.
The reverse symmetry counterpart is Good(A) defined by
Sum Top(X) | X does not defeat A
in the context of defeat strength of a defeat where A is the pairwise
winner.
Top(X) is the percentage of Too ballot positions occupied by X.
So if A is the CW, then Good(A) is 100percent.
So jt's probably not a good idea to use Bad(B) to create reverse symmetry.
However, perhaps it could be given non-symmetrical, infinitesimal weight
for tie breaking purposes only.
Also, perhaps their is a milder version of Good(A), whose reverse symmetry
counterpart Bad(B), would have a tolerable burial incentive.
-Forest
On Mon, Oct 24, 2022, 2:43 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 10/23/22 04:55, Forest Simmons wrote:
Critics have always maintained that this idea shows a lack of awareness
of clone dependence. But that judgment assumes that just because there
is a bad way of using those ballots, there can be no good way.
Here's a thought that occurred to me, that would explain why the
(seemingly out of nowhere) implication that we can't have both reversal
symmetry and DMTCBR.
First preferences are unaffected by burial, and last preferences are
unaffected by compromising. Suppose we had a method that were DMTCBR and
reversal symmetric. Then we could freely translate between a method
that's very strong against burial and very strong against compromise by
just reversing the ballots, since the reversed ballots' first
preferences would be last preferences.
Thus a method that passes both DMTCBR and rev. sym. would be extremely
resistant to both burial and to compromise. But since the favorite
betrayal criterion is so hard to pass, we have reason to believe that
this is impossible. So no such method can be rev. sym -- which is what
we at least see with Condorcet methods!
It's thus quite that the implication is stronger: that we can't have all
of DMTBR, majority, and reversal symmetry. But the proof is probably a
lot harder to find, too.
So all of the above implies that when creating a resistant ranked
method, we can't both have extreme resistance to burial and compromising
- we have to pick one. Fortunately (as James Green-Armytage originally
showed), we already get a great deal of compromising resistance from the
Condorcet criterion itself (since, for instance, it does the right thing
under center squeeze). Thus it's more sensible to choose further burial
resistance over further compromise resistance if we can only have one.
(Unless we consider maximum compromise resistance absolutely
non-negotiable, e.g. Mike O's insistence on the FBC.)
...
Finally, it might be useful to see just what the analog of the DMTCBR is
for a reversed DMTCBR-compliant method. It's something like...
Suppose that more than 1/3 of the ranks some Condorcet loser last. Then
nobody who prefers this loser to the current winner can make the loser
win by upranking him.
-km
Suppose we start with Defeat Strength DS(A>B) defined by ...
Sum Top(X) | X does not defeat A
Minus
Sum Top(Y) | B defeats Y,
and add a difference that will confer reverse symmetry onto the resulting
defeat strength ... something like this ...
Sum Bottom(Z) | B is not defeated by Z
Minus
Sum Bottom(K) | K defeats A
If we put these differences together, and combine the subtrahends to
minimize subtractions, we get a defeat strength expression with reverse
symmetry for the A>B defeat:
Sum Top(X) | X does not defeat A
Plus
Sum Bottom(Z) | B is not defeated by Z
Minus
[Sum Bottom(K) | K defeats A+Sum Top(Y) | B defeats Y]
If A is the CW and B is the CL, this strength is 200 percent, so perhaps we
should divide the whole thing by two.
With all the bottom and top percentage terms involved in one way or
another, this expression should be very decisive.
But in the rare case of a tie or ties, a complete ranking created by random
ballot draws should be an acceptable traditional way of resolving any
ambiguities in the Ranked Pairs finish order.
-Forest
On Mon, Oct 24, 2022, 11:29 AM Forest Simmons <forest.simmons21@gmail.com>
wrote:
> That is a great insight!
>
> My most recent message in this thread adds a term to the defeat strength
> that achieves reverse symmetry, but it comes at the cost of increasing
> burial incentive.
>
> The term is Bad(B) defined as ...
>
> Sum bottom(Z) | B does not defeat Z
>
> in the context of defeat strength, where B is the pairwise loser of the
> defeat in question. Bottom(Z) is the percentage of bottom ballot positions
> occupied by Z.
>
> So if B is the Condorcet Loser, then Bad(B) is 100%.
>
> Obviously if this term is given equal weight with its reverse symmetry
> counterpart, it will contribute an appreciable burial incentive.
>
> The reverse symmetry counterpart is Good(A) defined by
>
> Sum Top(X) | X does not defeat A
>
> in the context of defeat strength of a defeat where A is the pairwise
> winner.
> Top(X) is the percentage of Too ballot positions occupied by X.
>
> So if A is the CW, then Good(A) is 100percent.
>
> So jt's probably not a good idea to use Bad(B) to create reverse symmetry.
> However, perhaps it could be given non-symmetrical, infinitesimal weight
> for tie breaking purposes only.
>
> Also, perhaps their is a milder version of Good(A), whose reverse symmetry
> counterpart Bad(B), would have a tolerable burial incentive.
>
> -Forest
>
> On Mon, Oct 24, 2022, 2:43 AM Kristofer Munsterhjelm <km_elmet@t-online.de>
> wrote:
>
>> On 10/23/22 04:55, Forest Simmons wrote:
>>
>> > Critics have always maintained that this idea shows a lack of awareness
>> > of clone dependence. But that judgment assumes that just because there
>> > is a bad way of using those ballots, there can be no good way.
>>
>> Here's a thought that occurred to me, that would explain why the
>> (seemingly out of nowhere) implication that we can't have both reversal
>> symmetry and DMTCBR.
>>
>> First preferences are unaffected by burial, and last preferences are
>> unaffected by compromising. Suppose we had a method that were DMTCBR and
>> reversal symmetric. Then we could freely translate between a method
>> that's very strong against burial and very strong against compromise by
>> just reversing the ballots, since the reversed ballots' first
>> preferences would be last preferences.
>>
>> Thus a method that passes both DMTCBR and rev. sym. would be extremely
>> resistant to both burial and to compromise. But since the favorite
>> betrayal criterion is so hard to pass, we have reason to believe that
>> this is impossible. So no such method can be rev. sym -- which is what
>> we at least see with Condorcet methods!
>>
>> It's thus quite that the implication is stronger: that we can't have all
>> of DMTBR, majority, and reversal symmetry. But the proof is probably a
>> lot harder to find, too.
>>
>> So all of the above implies that when creating a resistant ranked
>> method, we can't both have extreme resistance to burial and compromising
>> - we have to pick one. Fortunately (as James Green-Armytage originally
>> showed), we already get a great deal of compromising resistance from the
>> Condorcet criterion itself (since, for instance, it does the right thing
>> under center squeeze). Thus it's more sensible to choose further burial
>> resistance over further compromise resistance if we can only have one.
>>
>> (Unless we consider maximum compromise resistance absolutely
>> non-negotiable, e.g. Mike O's insistence on the FBC.)
>>
>> ...
>>
>> Finally, it might be useful to see just what the analog of the DMTCBR is
>> for a reversed DMTCBR-compliant method. It's something like...
>>
>> Suppose that more than 1/3 of the ranks some Condorcet loser last. Then
>> nobody who prefers this loser to the current winner can make the loser
>> win by upranking him.
>>
>> -km
>>
>
KV
Kevin Venzke
Tue, Oct 25, 2022 12:41 AM
Hi Kristofer,
Le lundi 24 octobre 2022 à 04:43:58 UTC−5, Kristofer Munsterhjelm km_elmet@t-online.de a écrit :
Thus a method that passes both DMTCBR and rev. sym. would be extremely
resistant to both burial and to compromise. But since the favorite
betrayal criterion is so hard to pass, we have reason to believe that
this is impossible. So no such method can be rev. sym -- which is what
we at least see with Condorcet methods!
It's thus quite that the implication is stronger: that we can't have all
of DMTBR, majority, and reversal symmetry. But the proof is probably a
lot harder to find, too.
So all of the above implies that when creating a resistant ranked
method, we can't both have extreme resistance to burial and compromising
- we have to pick one. Fortunately (as James Green-Armytage originally
showed), we already get a great deal of compromising resistance from the
Condorcet criterion itself (since, for instance, it does the right thing
under center squeeze). Thus it's more sensible to choose further burial
resistance over further compromise resistance if we can only have one.
(Unless we consider maximum compromise resistance absolutely
non-negotiable, e.g. Mike O's insistence on the FBC.)
Well, insisting on weak FBC would rule out Condorcet. Maybe a better example would
be my "Condorcet Compromise Extension":
votingmethods.net/cce
This proposes a (convoluted) way to make use of the fact that in all Condorcet
methods there are possible results under various scenarios that would necessarily
create compromise incentive. So we can simply directly try to avoid those.
As I've suggested before, I don't share the feeling that we should say that
Condorcet inherently ensures adequate compromise resistance, and from there try to
maximize burial resistance. I think the worst Condorcet methods wrt compromise
incentive are to be sure not worth advocating.
What I think instead is that voters will see burial under Condorcet as an
unattractive, excessively risky option provided that:
- voters have a natural inclination to truncate the options they like less than
the best frontrunner (as opposed to ranking them sincerely, or using burial). And
- truncation is an effective defensive strategy under the method.
#1 I believe is just true. #2 we can certainly foul up. (Without #2, offensive and
defensive strategy become indistinguishable: Burying the worse frontrunner may not
be an attempt to steal a win, but to thwart someone else trying to steal it.
Voters need to feel that truncation is a sufficient defense, so they don't do
this.)
I'm assuming generally that the way the burial strategy works is that A voters
falsely rank non-viable candidate C over rival frontrunner B, and expect that B
voters will prevent a disaster by reporting that A is better than C. But I wonder
in what scenarios that is realistic to expect? Some will say it's a shame if B
voters can't freely and safely vote B>A>C, as they really feel, but to me it is a
luxury, when A vs B is the only real question to be answered in the election.
Kevin
votingmethods.net
Hi Kristofer,
Le lundi 24 octobre 2022 à 04:43:58 UTC−5, Kristofer Munsterhjelm <km_elmet@t-online.de> a écrit :
> Thus a method that passes both DMTCBR and rev. sym. would be extremely
> resistant to both burial and to compromise. But since the favorite
> betrayal criterion is so hard to pass, we have reason to believe that
> this is impossible. So no such method can be rev. sym -- which is what
> we at least see with Condorcet methods!
>
> It's thus quite that the implication is stronger: that we can't have all
> of DMTBR, majority, and reversal symmetry. But the proof is probably a
> lot harder to find, too.
>
> So all of the above implies that when creating a resistant ranked
> method, we can't both have extreme resistance to burial and compromising
> - we have to pick one. Fortunately (as James Green-Armytage originally
> showed), we already get a great deal of compromising resistance from the
> Condorcet criterion itself (since, for instance, it does the right thing
> under center squeeze). Thus it's more sensible to choose further burial
> resistance over further compromise resistance if we can only have one.
>
> (Unless we consider maximum compromise resistance absolutely
> non-negotiable, e.g. Mike O's insistence on the FBC.)
Well, insisting on weak FBC would rule out Condorcet. Maybe a better example would
be my "Condorcet Compromise Extension":
votingmethods.net/cce
This proposes a (convoluted) way to make use of the fact that in all Condorcet
methods there are possible results under various scenarios that would necessarily
create compromise incentive. So we can simply directly try to avoid those.
As I've suggested before, I don't share the feeling that we should say that
Condorcet inherently ensures adequate compromise resistance, and from there try to
maximize burial resistance. I think the worst Condorcet methods wrt compromise
incentive are to be sure not worth advocating.
What I think instead is that voters will see burial under Condorcet as an
unattractive, excessively risky option provided that:
1. voters have a natural inclination to truncate the options they like less than
the best frontrunner (as opposed to ranking them sincerely, or using burial). And
2. truncation is an effective defensive strategy under the method.
#1 I believe is just true. #2 we can certainly foul up. (Without #2, offensive and
defensive strategy become indistinguishable: Burying the worse frontrunner may not
be an attempt to steal a win, but to thwart someone else trying to steal it.
Voters need to feel that truncation is a sufficient defense, so they don't do
this.)
I'm assuming generally that the way the burial strategy works is that A voters
falsely rank non-viable candidate C over rival frontrunner B, and expect that B
voters will prevent a disaster by reporting that A is better than C. But I wonder
in what scenarios that is realistic to expect? Some will say it's a shame if B
voters can't freely and safely vote B>A>C, as they really feel, but to me it is a
luxury, when A vs B is the only real question to be answered in the election.
Kevin
votingmethods.net
FS
Forest Simmons
Tue, Oct 25, 2022 1:53 AM
As I understand it, with RP, CSSD, and River, defensive truncation, eg
below the putative CW will likely work as long as defeat strength is gauged
with winning votes (wv), as opposed to margins.
Any comments on that?
And what if defeat strength is gauged by winning approval? ... especially
winning friendly-approval (wfa)?
-Forest
On Mon, Oct 24, 2022, 5:54 PM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Kristofer,
Le lundi 24 octobre 2022 à 04:43:58 UTC−5, Kristofer Munsterhjelm <
km_elmet@t-online.de> a écrit :
Thus a method that passes both DMTCBR and rev. sym. would be extremely
resistant to both burial and to compromise. But since the favorite
betrayal criterion is so hard to pass, we have reason to believe that
this is impossible. So no such method can be rev. sym -- which is what
we at least see with Condorcet methods!
It's thus quite that the implication is stronger: that we can't have all
of DMTBR, majority, and reversal symmetry. But the proof is probably a
lot harder to find, too.
So all of the above implies that when creating a resistant ranked
method, we can't both have extreme resistance to burial and compromising
- we have to pick one. Fortunately (as James Green-Armytage originally
showed), we already get a great deal of compromising resistance from the
Condorcet criterion itself (since, for instance, it does the right thing
under center squeeze). Thus it's more sensible to choose further burial
resistance over further compromise resistance if we can only have one.
(Unless we consider maximum compromise resistance absolutely
non-negotiable, e.g. Mike O's insistence on the FBC.)
Well, insisting on weak FBC would rule out Condorcet. Maybe a better
example would
be my "Condorcet Compromise Extension":
votingmethods.net/cce
This proposes a (convoluted) way to make use of the fact that in all
Condorcet
methods there are possible results under various scenarios that would
necessarily
create compromise incentive. So we can simply directly try to avoid those.
As I've suggested before, I don't share the feeling that we should say that
Condorcet inherently ensures adequate compromise resistance, and from
there try to
maximize burial resistance. I think the worst Condorcet methods wrt
compromise
incentive are to be sure not worth advocating.
What I think instead is that voters will see burial under Condorcet as an
unattractive, excessively risky option provided that:
- voters have a natural inclination to truncate the options they like
less than
the best frontrunner (as opposed to ranking them sincerely, or using
burial). And
- truncation is an effective defensive strategy under the method.
#1 I believe is just true. #2 we can certainly foul up. (Without #2,
offensive and
defensive strategy become indistinguishable: Burying the worse frontrunner
may not
be an attempt to steal a win, but to thwart someone else trying to steal
it.
Voters need to feel that truncation is a sufficient defense, so they don't
do
this.)
I'm assuming generally that the way the burial strategy works is that A
voters
falsely rank non-viable candidate C over rival frontrunner B, and expect
that B
voters will prevent a disaster by reporting that A is better than C. But I
wonder
in what scenarios that is realistic to expect? Some will say it's a shame
if B
voters can't freely and safely vote B>A>C, as they really feel, but to me
it is a
luxury, when A vs B is the only real question to be answered in the
election.
Kevin
votingmethods.net
As I understand it, with RP, CSSD, and River, defensive truncation, eg
below the putative CW will likely work as long as defeat strength is gauged
with winning votes (wv), as opposed to margins.
Any comments on that?
And what if defeat strength is gauged by winning approval? ... especially
winning friendly-approval (wfa)?
-Forest
On Mon, Oct 24, 2022, 5:54 PM Kevin Venzke <stepjak@yahoo.fr> wrote:
> Hi Kristofer,
>
> Le lundi 24 octobre 2022 à 04:43:58 UTC−5, Kristofer Munsterhjelm <
> km_elmet@t-online.de> a écrit :
> > Thus a method that passes both DMTCBR and rev. sym. would be extremely
> > resistant to both burial and to compromise. But since the favorite
> > betrayal criterion is so hard to pass, we have reason to believe that
> > this is impossible. So no such method can be rev. sym -- which is what
> > we at least see with Condorcet methods!
> >
> > It's thus quite that the implication is stronger: that we can't have all
> > of DMTBR, majority, and reversal symmetry. But the proof is probably a
> > lot harder to find, too.
> >
> > So all of the above implies that when creating a resistant ranked
> > method, we can't both have extreme resistance to burial and compromising
> > - we have to pick one. Fortunately (as James Green-Armytage originally
> > showed), we already get a great deal of compromising resistance from the
> > Condorcet criterion itself (since, for instance, it does the right thing
> > under center squeeze). Thus it's more sensible to choose further burial
> > resistance over further compromise resistance if we can only have one.
> >
> > (Unless we consider maximum compromise resistance absolutely
> > non-negotiable, e.g. Mike O's insistence on the FBC.)
>
> Well, insisting on weak FBC would rule out Condorcet. Maybe a better
> example would
> be my "Condorcet Compromise Extension":
> votingmethods.net/cce
>
> This proposes a (convoluted) way to make use of the fact that in all
> Condorcet
> methods there are possible results under various scenarios that would
> necessarily
> create compromise incentive. So we can simply directly try to avoid those.
>
> As I've suggested before, I don't share the feeling that we should say that
> Condorcet inherently ensures adequate compromise resistance, and from
> there try to
> maximize burial resistance. I think the worst Condorcet methods wrt
> compromise
> incentive are to be sure not worth advocating.
>
> What I think instead is that voters will see burial under Condorcet as an
> unattractive, excessively risky option provided that:
> 1. voters have a natural inclination to truncate the options they like
> less than
> the best frontrunner (as opposed to ranking them sincerely, or using
> burial). And
> 2. truncation is an effective defensive strategy under the method.
>
> #1 I believe is just true. #2 we can certainly foul up. (Without #2,
> offensive and
> defensive strategy become indistinguishable: Burying the worse frontrunner
> may not
> be an attempt to steal a win, but to thwart someone else trying to steal
> it.
> Voters need to feel that truncation is a sufficient defense, so they don't
> do
> this.)
>
> I'm assuming generally that the way the burial strategy works is that A
> voters
> falsely rank non-viable candidate C over rival frontrunner B, and expect
> that B
> voters will prevent a disaster by reporting that A is better than C. But I
> wonder
> in what scenarios that is realistic to expect? Some will say it's a shame
> if B
> voters can't freely and safely vote B>A>C, as they really feel, but to me
> it is a
> luxury, when A vs B is the only real question to be answered in the
> election.
>
> Kevin
> votingmethods.net
>
FS
Forest Simmons
Tue, Oct 25, 2022 2:02 AM
Btw, defeat strength (wfv-lfv) winning minus losing friendly votes/approval
is my current understanding of the natural destiny of the fpA-fpC odyssey.
Any additional thoughts on that?
-Forest
On Mon, Oct 24, 2022, 6:53 PM Forest Simmons forest.simmons21@gmail.com
wrote:
As I understand it, with RP, CSSD, and River, defensive truncation, eg
below the putative CW will likely work as long as defeat strength is gauged
with winning votes (wv), as opposed to margins.
Any comments on that?
And what if defeat strength is gauged by winning approval? ... especially
winning friendly-approval (wfa)?
-Forest
On Mon, Oct 24, 2022, 5:54 PM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Kristofer,
Le lundi 24 octobre 2022 à 04:43:58 UTC−5, Kristofer Munsterhjelm <
km_elmet@t-online.de> a écrit :
Thus a method that passes both DMTCBR and rev. sym. would be extremely
resistant to both burial and to compromise. But since the favorite
betrayal criterion is so hard to pass, we have reason to believe that
this is impossible. So no such method can be rev. sym -- which is what
we at least see with Condorcet methods!
It's thus quite that the implication is stronger: that we can't have all
of DMTBR, majority, and reversal symmetry. But the proof is probably a
lot harder to find, too.
So all of the above implies that when creating a resistant ranked
method, we can't both have extreme resistance to burial and compromising
- we have to pick one. Fortunately (as James Green-Armytage originally
showed), we already get a great deal of compromising resistance from the
Condorcet criterion itself (since, for instance, it does the right thing
under center squeeze). Thus it's more sensible to choose further burial
resistance over further compromise resistance if we can only have one.
(Unless we consider maximum compromise resistance absolutely
non-negotiable, e.g. Mike O's insistence on the FBC.)
Well, insisting on weak FBC would rule out Condorcet. Maybe a better
example would
be my "Condorcet Compromise Extension":
votingmethods.net/cce
This proposes a (convoluted) way to make use of the fact that in all
Condorcet
methods there are possible results under various scenarios that would
necessarily
create compromise incentive. So we can simply directly try to avoid those.
As I've suggested before, I don't share the feeling that we should say
that
Condorcet inherently ensures adequate compromise resistance, and from
there try to
maximize burial resistance. I think the worst Condorcet methods wrt
compromise
incentive are to be sure not worth advocating.
What I think instead is that voters will see burial under Condorcet as an
unattractive, excessively risky option provided that:
- voters have a natural inclination to truncate the options they like
less than
the best frontrunner (as opposed to ranking them sincerely, or using
burial). And
- truncation is an effective defensive strategy under the method.
#1 I believe is just true. #2 we can certainly foul up. (Without #2,
offensive and
defensive strategy become indistinguishable: Burying the worse
frontrunner may not
be an attempt to steal a win, but to thwart someone else trying to steal
it.
Voters need to feel that truncation is a sufficient defense, so they
don't do
this.)
I'm assuming generally that the way the burial strategy works is that A
voters
falsely rank non-viable candidate C over rival frontrunner B, and expect
that B
voters will prevent a disaster by reporting that A is better than C. But
I wonder
in what scenarios that is realistic to expect? Some will say it's a shame
if B
voters can't freely and safely vote B>A>C, as they really feel, but to me
it is a
luxury, when A vs B is the only real question to be answered in the
election.
Kevin
votingmethods.net
Btw, defeat strength (wfv-lfv) winning minus losing friendly votes/approval
is my current understanding of the natural destiny of the fpA-fpC odyssey.
Any additional thoughts on that?
-Forest
On Mon, Oct 24, 2022, 6:53 PM Forest Simmons <forest.simmons21@gmail.com>
wrote:
> As I understand it, with RP, CSSD, and River, defensive truncation, eg
> below the putative CW will likely work as long as defeat strength is gauged
> with winning votes (wv), as opposed to margins.
>
> Any comments on that?
>
> And what if defeat strength is gauged by winning approval? ... especially
> winning friendly-approval (wfa)?
>
> -Forest
>
> On Mon, Oct 24, 2022, 5:54 PM Kevin Venzke <stepjak@yahoo.fr> wrote:
>
>> Hi Kristofer,
>>
>> Le lundi 24 octobre 2022 à 04:43:58 UTC−5, Kristofer Munsterhjelm <
>> km_elmet@t-online.de> a écrit :
>> > Thus a method that passes both DMTCBR and rev. sym. would be extremely
>> > resistant to both burial and to compromise. But since the favorite
>> > betrayal criterion is so hard to pass, we have reason to believe that
>> > this is impossible. So no such method can be rev. sym -- which is what
>> > we at least see with Condorcet methods!
>> >
>> > It's thus quite that the implication is stronger: that we can't have all
>> > of DMTBR, majority, and reversal symmetry. But the proof is probably a
>> > lot harder to find, too.
>> >
>> > So all of the above implies that when creating a resistant ranked
>> > method, we can't both have extreme resistance to burial and compromising
>> > - we have to pick one. Fortunately (as James Green-Armytage originally
>> > showed), we already get a great deal of compromising resistance from the
>> > Condorcet criterion itself (since, for instance, it does the right thing
>> > under center squeeze). Thus it's more sensible to choose further burial
>> > resistance over further compromise resistance if we can only have one.
>> >
>> > (Unless we consider maximum compromise resistance absolutely
>> > non-negotiable, e.g. Mike O's insistence on the FBC.)
>>
>> Well, insisting on weak FBC would rule out Condorcet. Maybe a better
>> example would
>> be my "Condorcet Compromise Extension":
>> votingmethods.net/cce
>>
>> This proposes a (convoluted) way to make use of the fact that in all
>> Condorcet
>> methods there are possible results under various scenarios that would
>> necessarily
>> create compromise incentive. So we can simply directly try to avoid those.
>>
>> As I've suggested before, I don't share the feeling that we should say
>> that
>> Condorcet inherently ensures adequate compromise resistance, and from
>> there try to
>> maximize burial resistance. I think the worst Condorcet methods wrt
>> compromise
>> incentive are to be sure not worth advocating.
>>
>> What I think instead is that voters will see burial under Condorcet as an
>> unattractive, excessively risky option provided that:
>> 1. voters have a natural inclination to truncate the options they like
>> less than
>> the best frontrunner (as opposed to ranking them sincerely, or using
>> burial). And
>> 2. truncation is an effective defensive strategy under the method.
>>
>> #1 I believe is just true. #2 we can certainly foul up. (Without #2,
>> offensive and
>> defensive strategy become indistinguishable: Burying the worse
>> frontrunner may not
>> be an attempt to steal a win, but to thwart someone else trying to steal
>> it.
>> Voters need to feel that truncation is a sufficient defense, so they
>> don't do
>> this.)
>>
>> I'm assuming generally that the way the burial strategy works is that A
>> voters
>> falsely rank non-viable candidate C over rival frontrunner B, and expect
>> that B
>> voters will prevent a disaster by reporting that A is better than C. But
>> I wonder
>> in what scenarios that is realistic to expect? Some will say it's a shame
>> if B
>> voters can't freely and safely vote B>A>C, as they really feel, but to me
>> it is a
>> luxury, when A vs B is the only real question to be answered in the
>> election.
>>
>> Kevin
>> votingmethods.net
>>
>
