Fwd: Duncan Proposal Draft
Dear EM List Friends,
We need your feedback on this draft of a proposal before we submit a
version of it to the voting reform community at large.
---------- Forwarded message ---------
From: Forest Simmons forest.simmons21@gmail.com
Date: Thu, Oct 12, 2023, 5:35 PM
Subject: Duncan Proposal Draft
To: Michael Ossipoff email9648742@gmail.com
Michael Christened our new Q&D burial resistant method "Duncan" after
Duncan Black who popularized the idea of using Borda's Method as a
fallback "completion" when the ballots fail to unambiguously reveal the
sincere "Condorcet" pairbeats-all candidate.
Our Duncan method has the same form as Black's in that the official version
directly specifies electing the unambiguous Condorcet Candidate when there
is one, and falls back to another procedure that relies on Borda Scores,
otherwise.
It should be emphasized that in both cases the fall back Borda based
expedient is rarely needed. For that reason some misguided voting reform
advocates have cavalierly opined that any decisive completion/ fallback
method would be plenty adequate to supplement the Condorcet Criterion
requirement.
However, this casual attitude ignores the feedback aspects of voting
systems in that various voting methods vary in the degree that they
encourage or discourage the creation of artificial beat cycles that
subvert/ hide the Condorcet Candidate from view, bringing the completion
method into greater prominence in a potentially unstable cycle.
Unfortunately most of the extant methods fall into this "positive" feedback
category, including Borda itself. Some less sensitive methods like
Approval and IRV/RCV have a built in "friction" that dampens the feedback;
but as systems engineers know, the high performance components are the ones
that need the addition of some carefully engineered negative feedback
"circuit" to stabilize the system as a whole.
In our Condorcet Completion context, our use of the Borda Count scores is
carefully designed with that stabilizing influence in mind: adventurous
strategists who are aware of this feature, when acting rationally will be
deterred from creating these cycles that come back to bite them. Those not
aware will find out when their ploys backfire or otherwise disappoint them.
How do these pesky cycles arise so easily in Borda and other rank based
methods?
Suppose that your personal preference schedule for the alphabetized
candidates looks like ...
A>C>X>Y>Z, and that C is the Condorcet Candidate projected to win the
election if nobody acts nefariously.
You, and like minded friends, get the idea to insincerely move your second
choice to the bottom of your ballot (so it now reads A>X>Y>Z>C) ... not to
be "nefarious" so much as to just increase the winning chances of your
favorite A.
Could this work?
Yes, under Black's method if your friends follow your lead, this "nurial"
of C under the "busses" X, Y, and Z, could easily subvert one or more of
C's pairwise victories over X,Y, and Z, into defeats of C by them, thereby
hiding C's identity of sincere Universal "pairbeater" status to just one
more member of a "beatcycle" of the form A beats X beats Y beats Z beats C
beats A.
Note that the buried candidate C still beats the buriers' favorite, A ...
because lowering C does not decrease the number of ballots that support C
over A ... which is how easily and innocently beatcycles like this can be
created in Condorcet style elections ... at least in the absence of
negative feedback from the cycle resolution fallback method.
In traditional Black that fallback method is Borda. Does that fix the
problem? ... or does it exacerbate it.
Well ... the same burial that put C at disadvantage in the pairwise
contests with X thru Z, also lowered C's Borda score by 3 counts per
ballot, and raised
the Borda score of each of X thru Z to the tune of one count per ballot.
The likely outcome is that C will end up with the lowest score, and come in
last in the finish order.
By way of contrast, under our new Duncan method, the most likely winner is
X, and the least likely winner is A, the burier faction's favorite ... thus
disappointing the burier faction supporters ... teaching them that if they
try to outsmart new Duncan with insincere ballot rankings, they are apt to
end up helping elect their third (or later) choice instead of their first
choice or their second choice ... the one that they so cleverly buried
(however innocently or without malice).
Too many dabblers in voting method reform (as well as most professionals)
are unaware of these dynamics.
But now, with your new understanding, you, at least, can become part of the
solution.
Duncan Definition:
In the vast majority of the cases ... those in which the pairwise counts of
the ballots unambiguously identify the candidate that pairbeats each of the
others ... elect that candidate.
Otherwise, elect the highest score candidate that pairbeats every candidate
with lower score.
[Nominally "score" = Borda Count, though STAR Voting scores, for example,
could also serve]
How does this Duncan fallback procedure work to prevent A from getting
elected in our scenario regarding A thru Z?
Well, could A pairbeat every lower score candidate? In particular, could A
pairbeat C, which is now at the bottom of the Borda score pile ...
certainly lower than A ...?
Well, remember that "C beats A" was the last step in the beatcycle created
by A's friends.
So A does not pairbeat every lower score candidate, and therefore cannot
win.
New Duncan is burial resistant.
Next time ... more examples and insights ...
fws
Yes, I like Duncan because burying the CW in an attempt to help your
favorite won’t help hir when it causes hir disqualification, as it probably
will.
…& Duncan is remarkably briefly-defined, needing only a very slight
modification of Black’s method.
On Fri, Oct 13, 2023 at 10:11 Forest Simmons forest.simmons21@gmail.com
wrote:
Dear EM List Friends,
We need your feedback on this draft of a proposal before we submit a
version of it to the voting reform community at large.
---------- Forwarded message ---------
From: Forest Simmons forest.simmons21@gmail.com
Date: Thu, Oct 12, 2023, 5:35 PM
Subject: Duncan Proposal Draft
To: Michael Ossipoff email9648742@gmail.com
Michael Christened our new Q&D burial resistant method "Duncan" after
Duncan Black who popularized the idea of using Borda's Method as a
fallback "completion" when the ballots fail to unambiguously reveal the
sincere "Condorcet" pairbeats-all candidate.
Our Duncan method has the same form as Black's in that the official
version directly specifies electing the unambiguous Condorcet Candidate
when there is one, and falls back to another procedure that relies on Borda
Scores, otherwise.
It should be emphasized that in both cases the fall back Borda based
expedient is rarely needed. For that reason some misguided voting reform
advocates have cavalierly opined that any decisive completion/ fallback
method would be plenty adequate to supplement the Condorcet Criterion
requirement.
However, this casual attitude ignores the feedback aspects of voting
systems in that various voting methods vary in the degree that they
encourage or discourage the creation of artificial beat cycles that
subvert/ hide the Condorcet Candidate from view, bringing the completion
method into greater prominence in a potentially unstable cycle.
Unfortunately most of the extant methods fall into this "positive"
feedback category, including Borda itself. Some less sensitive methods
like Approval and IRV/RCV have a built in "friction" that dampens the
feedback; but as systems engineers know, the high performance components
are the ones that need the addition of some carefully engineered negative
feedback "circuit" to stabilize the system as a whole.
In our Condorcet Completion context, our use of the Borda Count scores is
carefully designed with that stabilizing influence in mind: adventurous
strategists who are aware of this feature, when acting rationally will be
deterred from creating these cycles that come back to bite them. Those not
aware will find out when their ploys backfire or otherwise disappoint them.
How do these pesky cycles arise so easily in Borda and other rank based
methods?
Suppose that your personal preference schedule for the alphabetized
candidates looks like ...
A>C>X>Y>Z, and that C is the Condorcet Candidate projected to win the
election if nobody acts nefariously.
You, and like minded friends, get the idea to insincerely move your second
choice to the bottom of your ballot (so it now reads A>X>Y>Z>C) ... not to
be "nefarious" so much as to just increase the winning chances of your
favorite A.
Could this work?
Yes, under Black's method if your friends follow your lead, this "nurial"
of C under the "busses" X, Y, and Z, could easily subvert one or more of
C's pairwise victories over X,Y, and Z, into defeats of C by them, thereby
hiding C's identity of sincere Universal "pairbeater" status to just one
more member of a "beatcycle" of the form A beats X beats Y beats Z beats C
beats A.
Note that the buried candidate C still beats the buriers' favorite, A ...
because lowering C does not decrease the number of ballots that support C
over A ... which is how easily and innocently beatcycles like this can be
created in Condorcet style elections ... at least in the absence of
negative feedback from the cycle resolution fallback method.
In traditional Black that fallback method is Borda. Does that fix the
problem? ... or does it exacerbate it.
Well ... the same burial that put C at disadvantage in the pairwise
contests with X thru Z, also lowered C's Borda score by 3 counts per
ballot, and raised
the Borda score of each of X thru Z to the tune of one count per ballot.
The likely outcome is that C will end up with the lowest score, and come
in last in the finish order.
By way of contrast, under our new Duncan method, the most likely winner is
X, and the least likely winner is A, the burier faction's favorite ... thus
disappointing the burier faction supporters ... teaching them that if they
try to outsmart new Duncan with insincere ballot rankings, they are apt to
end up helping elect their third (or later) choice instead of their first
choice or their second choice ... the one that they so cleverly buried
(however innocently or without malice).
Too many dabblers in voting method reform (as well as most professionals)
are unaware of these dynamics.
But now, with your new understanding, you, at least, can become part of
the solution.
Duncan Definition:
In the vast majority of the cases ... those in which the pairwise counts
of the ballots unambiguously identify the candidate that pairbeats each of
the others ... elect that candidate.
Otherwise, elect the highest score candidate that pairbeats every
candidate with lower score.
[Nominally "score" = Borda Count, though STAR Voting scores, for example,
could also serve]
How does this Duncan fallback procedure work to prevent A from getting
elected in our scenario regarding A thru Z?
Well, could A pairbeat every lower score candidate? In particular, could A
pairbeat C, which is now at the bottom of the Borda score pile ...
certainly lower than A ...?
Well, remember that "C beats A" was the last step in the beatcycle created
by A's friends.
So A does not pairbeat every lower score candidate, and therefore cannot
win.
New Duncan is burial resistant.
Next time ... more examples and insights ...
fws
"Cycles" (in the paper-scissors-rock sense) are a problem of the
(under-candidated) single member systems own making. They rapidly
disappear with a representative sample of candidates proportionally
elected to large constituencies. The problem is not the 'pesky' cycles,
it is the pesky single member system. Unless the politics in political
science is to dictate to the science, it is up to academics to point
out, as hundreds of American political scientists have, in conjunction
with The New York Times, I believe, this requirement of a
quota-preferential method.
Remedies to the single member system are cosmetic. They cannot possibly
please more than half the population, whatever you do -- and probably a
good deal less. UK monopolistic elections are a minorocracy not a
democracy, and that is probably a fair indication of the US state of
affairs.
Time to move on from the ancient Greek conception of democracy, as to
elect a tyrant, unconditionally -- making Britain what Hailsham called
an "elective dictatorship." Which shares some of the all too evident
failings of any dictatorship, elected or otherwise. This should be a
spur to avoid another Vietnam war or second Iraq war, which even W. may
deplore, in his heart.
Regards,
Richard Lung.
On 13/10/2023 18:11, Forest Simmons wrote:
Dear EM List Friends,
We need your feedback on this draft of a proposal before we submit a
version of it to the voting reform community at large.
---------- Forwarded message ---------
From: Forest Simmons forest.simmons21@gmail.com
Date: Thu, Oct 12, 2023, 5:35 PM
Subject: Duncan Proposal Draft
To: Michael Ossipoff email9648742@gmail.com
Michael Christened our new Q&D burial resistant method "Duncan" after
Duncan Black who popularized the idea of using Borda's Method as a
fallback "completion" when the ballots fail to unambiguously reveal
the sincere "Condorcet" pairbeats-all candidate.
Our Duncan method has the same form as Black's in that the official
version directly specifies electing the unambiguous Condorcet
Candidate when there is one, and falls back to another procedure that
relies on Borda Scores, otherwise.
It should be emphasized that in both cases the fall back Borda based
expedient is rarely needed. For that reason some misguided voting
reform advocates have cavalierly opined that any decisive completion/
fallback method would be plenty adequate to supplement the Condorcet
Criterion requirement.
However, this casual attitude ignores the feedback aspects of voting
systems in that various voting methods vary in the degree that they
encourage or discourage the creation of artificial beat cycles that
subvert/ hide the Condorcet Candidate from view, bringing the
completion method into greater prominence in a potentially unstable cycle.
Unfortunately most of the extant methods fall into this "positive"
feedback category, including Borda itself. Some less sensitive
methods like Approval and IRV/RCV have a built in "friction" that
dampens the feedback; but as systems engineers know, the high
performance components are the ones that need the addition of some
carefully engineered negative feedback "circuit" to stabilize the
system as a whole.
In our Condorcet Completion context, our use of the Borda Count scores
is carefully designed with that stabilizing influence in mind:
adventurous strategists who are aware of this feature, when acting
rationally will be deterred from creating these cycles that come back
to bite them. Those not aware will find out when their ploys backfire
or otherwise disappoint them.
How do these pesky cycles arise so easily in Borda and other rank
based methods?
Suppose that your personal preference schedule for the alphabetized
candidates looks like ...
A>C>X>Y>Z, and that C is the Condorcet Candidate projected to win the
election if nobody acts nefariously.
You, and like minded friends, get the idea to insincerely move your
second choice to the bottom of your ballot (so it now reads A>X>Y>Z>C)
... not to be "nefarious" so much as to just increase the winning
chances of your favorite A.
Could this work?
Yes, under Black's method if your friends follow your lead, this
"nurial" of C under the "busses" X, Y, and Z, could easily subvert one
or more of C's pairwise victories over X,Y, and Z, into defeats of C
by them, thereby hiding C's identity of sincere Universal "pairbeater"
status to just one more member of a "beatcycle" of the form A beats X
beats Y beats Z beats C beats A.
Note that the buried candidate C still beats the buriers' favorite, A
... because lowering C does not decrease the number of ballots that
support C over A ... which is how easily and innocently beatcycles
like this can be created in Condorcet style elections ... at least in
the absence of negative feedback from the cycle resolution fallback
method.
In traditional Black that fallback method is Borda. Does that fix the
problem? ... or does it exacerbate it.
Well ... the same burial that put C at disadvantage in the pairwise
contests with X thru Z, also lowered C's Borda score by 3 counts per
ballot, and raised
the Borda score of each of X thru Z to the tune of one count per ballot.
The likely outcome is that C will end up with the lowest score, and
come in last in the finish order.
By way of contrast, under our new Duncan method, the most likely
winner is X, and the least likely winner is A, the burier faction's
favorite ... thus disappointing the burier faction supporters ...
teaching them that if they try to outsmart new Duncan with insincere
ballot rankings, they are apt to end up helping elect their third (or
later) choice instead of their first choice or their second choice ...
the one that they so cleverly buried (however innocently or without
malice).
Too many dabblers in voting method reform (as well as most
professionals) are unaware of these dynamics.
But now, with your new understanding, you, at least, can become part
of the solution.
Duncan Definition:
In the vast majority of the cases ... those in which the pairwise
counts of the ballots unambiguously identify the candidate that
pairbeats each of the others ... elect that candidate.
Otherwise, elect the highest score candidate that pairbeats every
candidate with lower score.
[Nominally "score" = Borda Count, though STAR Voting scores, for
example, could also serve]
How does this Duncan fallback procedure work to prevent A from getting
elected in our scenario regarding A thru Z?
Well, could A pairbeat every lower score candidate? In particular,
could A pairbeat C, which is now at the bottom of the Borda score pile
... certainly lower than A ...?
Well, remember that "C beats A" was the last step in the beatcycle
created by A's friends.
So A does not pairbeat every lower score candidate, and therefore
cannot win.
New Duncan is burial resistant.
Next time ... more examples and insights ...
fws
Election-Methods mailing list - seehttps://electorama.com/em for list info
I also like proportional representation, but there are many different elections for many different things, and there will always be a need for single-winner methods. Because of that I'm not sure it's necessary to make the same point in every discussion about single-winner methods, especially specific discussions about solving specific problems (e.g. burial) rather than more general discussions.
Toby
On Friday, 13 October 2023 at 19:18:06 BST, Richard Lung voting@ukscientists.com wrote:
"Cycles" (in the paper-scissors-rock sense) are a problem of the (under-candidated) single member systems own making. They rapidly disappear with a representative sample of candidates proportionally elected to large constituencies. The problem is not the 'pesky' cycles, it is the pesky single member system. Unless the politics in political science is to dictate to the science, it is up to academics to point out, as hundreds of American political scientists have, in conjunction with The New York Times, I believe, this requirement of a quota-preferential method.
Remedies to the single member system are cosmetic. They cannot possibly please more than half the population, whatever you do -- and probably a good deal less. UK monopolistic elections are a minorocracy not a democracy, and that is probably a fair indication of the US state of affairs.
Time to move on from the ancient Greek conception of democracy, as to elect a tyrant, unconditionally -- making Britain what Hailsham called an "elective dictatorship." Which shares some of the all too evident failings of any dictatorship, elected or otherwise. This should be a spur to avoid another Vietnam war or second Iraq war, which even W. may deplore, in his heart.
Regards,
Richard Lung.
On 13/10/2023 18:11, Forest Simmons wrote:
Dear EM List Friends,
We need your feedback on this draft of a proposal before we submit a version of it to the voting reform community at large.
---------- Forwarded message ---------
From: Forest Simmons forest.simmons21@gmail.com
Date: Thu, Oct 12, 2023, 5:35 PM
Subject: Duncan Proposal Draft
To: Michael Ossipoff email9648742@gmail.com
Michael Christened our new Q&D burial resistant method "Duncan" after Duncan Black who popularized the idea of using Borda's Method as a fallback "completion" when the ballots fail to unambiguously reveal the sincere "Condorcet" pairbeats-all candidate.
Our Duncan method has the same form as Black's in that the official version directly specifies electing the unambiguous Condorcet Candidate when there is one, and falls back to another procedure that relies on Borda Scores, otherwise.
It should be emphasized that in both cases the fall back Borda based expedient is rarely needed. For that reason some misguided voting reform advocates have cavalierly opined that any decisive completion/ fallback method would be plenty adequate to supplement the Condorcet Criterion requirement.
However, this casual attitude ignores the feedback aspects of voting systems in that various voting methods vary in the degree that they encourage or discourage the creation of artificial beat cycles that subvert/ hide the Condorcet Candidate from view, bringing the completion method into greater prominence in a potentially unstable cycle.
Unfortunately most of the extant methods fall into this "positive" feedback category, including Borda itself. Some less sensitive methods like Approval and IRV/RCV have a built in "friction" that dampens the feedback; but as systems engineers know, the high performance components are the ones that need the addition of some carefully engineered negative feedback "circuit" to stabilize the system as a whole.
In our Condorcet Completion context, our use of the Borda Count scores is carefully designed with that stabilizing influence in mind: adventurous strategists who are aware of this feature, when acting rationally will be deterred from creating these cycles that come back to bite them. Those not aware will find out when their ploys backfire or otherwise disappoint them.
How do these pesky cycles arise so easily in Borda and other rank based methods?
Suppose that your personal preference schedule for the alphabetized candidates looks like ...
A>C>X>Y>Z, and that C is the Condorcet Candidate projected to win the election if nobody acts nefariously.
You, and like minded friends, get the idea to insincerely move your second choice to the bottom of your ballot (so it now reads A>X>Y>Z>C) ... not to be "nefarious" so much as to just increase the winning chances of your favorite A.
Could this work?
Yes, under Black's method if your friends follow your lead, this "nurial" of C under the "busses" X, Y, and Z, could easily subvert one or more of C's pairwise victories over X,Y, and Z, into defeats of C by them, thereby hiding C's identity of sincere Universal "pairbeater" status to just one more member of a "beatcycle" of the form A beats X beats Y beats Z beats C beats A.
Note that the buried candidate C still beats the buriers' favorite, A ... because lowering C does not decrease the number of ballots that support C over A ... which is how easily and innocently beatcycles like this can be created in Condorcet style elections ... at least in the absence of negative feedback from the cycle resolution fallback method.
In traditional Black that fallback method is Borda. Does that fix the problem? ... or does it exacerbate it.
Well ... the same burial that put C at disadvantage in the pairwise contests with X thru Z, also lowered C's Borda score by 3 counts per ballot, and raised the Borda score of each of X thru Z to the tune of one count per ballot.
The likely outcome is that C will end up with the lowest score, and come in last in the finish order.
By way of contrast, under our new Duncan method, the most likely winner is X, and the least likely winner is A, the burier faction's favorite ... thus disappointing the burier faction supporters ... teaching them that if they try to outsmart new Duncan with insincere ballot rankings, they are apt to end up helping elect their third (or later) choice instead of their first choice or their second choice ... the one that they so cleverly buried (however innocently or without malice).
Too many dabblers in voting method reform (as well as most professionals) are unaware of these dynamics.
But now, with your new understanding, you, at least, can become part of the solution.
Duncan Definition:
In the vast majority of the cases ... those in which the pairwise counts of the ballots unambiguously identify the candidate that pairbeats each of the others ... elect that candidate.
Otherwise, elect the highest score candidate that pairbeats every candidate with lower score.
[Nominally "score" = Borda Count, though STAR Voting scores, for example, could also serve]
How does this Duncan fallback procedure work to prevent A from getting elected in our scenario regarding A thru Z?
Well, could A pairbeat every lower score candidate? In particular, could A pairbeat C, which is now at the bottom of the Borda score pile ... certainly lower than A ...?
Well, remember that "C beats A" was the last step in the beatcycle created by A's friends.
So A does not pairbeat every lower score candidate, and therefore cannot win.
New Duncan is burial resistant.
Next time ... more examples and insights ...
fws
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
Richard—
No one is denying the desirability PR.
I don’t know where you reside, but, here in the U.S., PR for our national
legislature, Congress, is much less short-term feasible, due to
Constitutional structure.
The Constitution requires that every state gets a House representative,
regardless of how small it’s population is. If its population were 1, it
would nonetheless get a representative.
Additionally, the Constitution requires that every state must get the SAME
number of Senate-seats (two)…again, regardless of how small its population
is.
Those two Constitutional requirements would make nonsense of
proportionality.
Constitutional amendment is difficult & time-consuming. …&, for various
reasons we needn’t go into, a Constitutional convention now would be a
rather terrifying thing.
So, here, electoral-reform is single-winner reform.
BTW, I hasten to emphasize that I’m not against the small states. I don’t
want to deny them equal representation. “ Equal” is the operative word..
Equal representation could be achieved, but not without repairing the
Constitution’s built-in disproportionality. It was “The Great Compromise”,
which compromised-away any chance of equal representation. A very
regrettable compromise.
Here’s an example of equal representation…my favorite one:
A unicameral at large (no districts or gerrymandering) Parliament (yes, no
president), 150 seats, elected by open-list party-list PR, allocated by
Sainte Lague, or, preferably, Bias-Free.
Of the divisor-method allocation-rules that are or have been used, Sainte
Lague is the very nearly unbiased one.
SL is only very slightly biased favoring larger parties.
Bias-Free is entirely absolutely unbiased.
Divisor methods involve the rounding, up or down, to a whole number, of a
party’s number of “quotas” ( details are outside the scope of this
discussion).
Sainte Lague rounds to the nearest whole number.
i.e. the round-up point is the average of the two surrounding integers.
I.e. …
R = (a+b)/2.
For Bias-Free, determine R as follows:
Divide b^b by a^a. Then divide the result by e.
e is the base of the natural logarithms, equal to about 2.718
But I re-emphasize that, with proportionality now Constitutionally
impossible, national PR is unavailable.
Electoral reform means single-winner reform.
On Fri, Oct 13, 2023 at 11:18 Richard Lung voting@ukscientists.com wrote:
"Cycles" (in the paper-scissors-rock sense) are a problem of the
(under-candidated) single member systems own making. They rapidly disappear
with a representative sample of candidates proportionally elected to large
constituencies. The problem is not the 'pesky' cycles, it is the pesky
single member system. Unless the politics in political science is to
dictate to the science, it is up to academics to point out, as hundreds of
American political scientists have, in conjunction with The New York Times,
I believe, this requirement of a quota-preferential method.
Remedies to the single member system are cosmetic. They cannot possibly
please more than half the population, whatever you do -- and probably a
good deal less. UK monopolistic elections are a minorocracy not a
democracy, and that is probably a fair indication of the US state of
affairs.
Time to move on from the ancient Greek conception of democracy, as to
elect a tyrant, unconditionally -- making Britain what Hailsham called an
"elective dictatorship." Which shares some of the all too evident failings
of any dictatorship, elected or otherwise. This should be a spur to avoid
another Vietnam war or second Iraq war, which even W. may deplore, in his
heart.
Regards,
Richard Lung.
On 13/10/2023 18:11, Forest Simmons wrote:
Dear EM List Friends,
We need your feedback on this draft of a proposal before we submit a
version of it to the voting reform community at large.
---------- Forwarded message ---------
From: Forest Simmons forest.simmons21@gmail.com
Date: Thu, Oct 12, 2023, 5:35 PM
Subject: Duncan Proposal Draft
To: Michael Ossipoff email9648742@gmail.com
Michael Christened our new Q&D burial resistant method "Duncan" after
Duncan Black who popularized the idea of using Borda's Method as a
fallback "completion" when the ballots fail to unambiguously reveal the
sincere "Condorcet" pairbeats-all candidate.
Our Duncan method has the same form as Black's in that the official
version directly specifies electing the unambiguous Condorcet Candidate
when there is one, and falls back to another procedure that relies on Borda
Scores, otherwise.
It should be emphasized that in both cases the fall back Borda based
expedient is rarely needed. For that reason some misguided voting reform
advocates have cavalierly opined that any decisive completion/ fallback
method would be plenty adequate to supplement the Condorcet Criterion
requirement.
However, this casual attitude ignores the feedback aspects of voting
systems in that various voting methods vary in the degree that they
encourage or discourage the creation of artificial beat cycles that
subvert/ hide the Condorcet Candidate from view, bringing the completion
method into greater prominence in a potentially unstable cycle.
Unfortunately most of the extant methods fall into this "positive"
feedback category, including Borda itself. Some less sensitive methods
like Approval and IRV/RCV have a built in "friction" that dampens the
feedback; but as systems engineers know, the high performance components
are the ones that need the addition of some carefully engineered negative
feedback "circuit" to stabilize the system as a whole.
In our Condorcet Completion context, our use of the Borda Count scores is
carefully designed with that stabilizing influence in mind: adventurous
strategists who are aware of this feature, when acting rationally will be
deterred from creating these cycles that come back to bite them. Those not
aware will find out when their ploys backfire or otherwise disappoint them.
How do these pesky cycles arise so easily in Borda and other rank based
methods?
Suppose that your personal preference schedule for the alphabetized
candidates looks like ...
A>C>X>Y>Z, and that C is the Condorcet Candidate projected to win the
election if nobody acts nefariously.
You, and like minded friends, get the idea to insincerely move your second
choice to the bottom of your ballot (so it now reads A>X>Y>Z>C) ... not to
be "nefarious" so much as to just increase the winning chances of your
favorite A.
Could this work?
Yes, under Black's method if your friends follow your lead, this "nurial"
of C under the "busses" X, Y, and Z, could easily subvert one or more of
C's pairwise victories over X,Y, and Z, into defeats of C by them, thereby
hiding C's identity of sincere Universal "pairbeater" status to just one
more member of a "beatcycle" of the form A beats X beats Y beats Z beats C
beats A.
Note that the buried candidate C still beats the buriers' favorite, A ...
because lowering C does not decrease the number of ballots that support C
over A ... which is how easily and innocently beatcycles like this can be
created in Condorcet style elections ... at least in the absence of
negative feedback from the cycle resolution fallback method.
In traditional Black that fallback method is Borda. Does that fix the
problem? ... or does it exacerbate it.
Well ... the same burial that put C at disadvantage in the pairwise
contests with X thru Z, also lowered C's Borda score by 3 counts per
ballot, and raised
the Borda score of each of X thru Z to the tune of one count per ballot.
The likely outcome is that C will end up with the lowest score, and come
in last in the finish order.
By way of contrast, under our new Duncan method, the most likely winner is
X, and the least likely winner is A, the burier faction's favorite ... thus
disappointing the burier faction supporters ... teaching them that if they
try to outsmart new Duncan with insincere ballot rankings, they are apt to
end up helping elect their third (or later) choice instead of their first
choice or their second choice ... the one that they so cleverly buried
(however innocently or without malice).
Too many dabblers in voting method reform (as well as most professionals)
are unaware of these dynamics.
But now, with your new understanding, you, at least, can become part of
the solution.
Duncan Definition:
In the vast majority of the cases ... those in which the pairwise counts
of the ballots unambiguously identify the candidate that pairbeats each of
the others ... elect that candidate.
Otherwise, elect the highest score candidate that pairbeats every
candidate with lower score.
[Nominally "score" = Borda Count, though STAR Voting scores, for example,
could also serve]
How does this Duncan fallback procedure work to prevent A from getting
elected in our scenario regarding A thru Z?
Well, could A pairbeat every lower score candidate? In particular, could A
pairbeat C, which is now at the bottom of the Borda score pile ...
certainly lower than A ...?
Well, remember that "C beats A" was the last step in the beatcycle created
by A's friends.
So A does not pairbeat every lower score candidate, and therefore cannot
win.
New Duncan is burial resistant.
Next time ... more examples and insights ...
fws
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list
info
On 10/13/23 19:11, Forest Simmons wrote:
Dear EM List Friends,
We need your feedback on this draft of a proposal before we submit a
version of it to the voting reform community at large.
This is not feedback on the draft as such, but the results of my
strategy vulnerability tests with CTE-Borda (which I'm guessing this is).
My implementation uses bubble sort, which I understand is the same as
sink sort (see e.g. https://xlinux.nist.gov/dads/HTML/sinkSort.html). I
asked you if it's different, but I didn't got a response. If what you
mean by "sink sort" differs from bubble sort, my results may be off.
In any case, the method seems to have somewhat strange behavior under
impartial culture. With only a few voters (i.e. the election being far
from tied), there's still burial incentive. This burial incentive
disappears with increasing numbers of voters, but at a great cost of
general coalition strategy (which I imagine to be, but can't verify to
be, mostly pushover). The sum of burial and other strats push it to a
relatively high total susceptibility, although not quite as high as the
defeat-droppers.
Here are the stats:
Impartial culture, three candidates, 13 voters, 25k elections, 32k tests
per election:
CTE-Borda:
Burial, no compromise: 5381 0.21524
Compromise, no burial: 2050 0.082
Burial and compromise: 0 0
Two-sided: 5085 0.2034
Other coalition strats: 4120 0.1648
---=========
Manipulable elections: 16636 0.66544
For comparison, Schulze:
Burial, no compromise: 9988 0.426582
Compromise, no burial: 210 0.00896899
Burial and compromise: 282 0.0120441
Two-sided: 2206 0.0942171
Other coalition strats: 0 0
---=========
Manipulable elections: 12686 0.541813
Impartial culture, five candidates, 13 voters, 25k elections, 32k tests
per election:
CTE-Borda:
Burial, no compromise: 8654 0.34616
Compromise, no burial: 3864 0.15456
Burial and compromise: 2054 0.08216
Two-sided: 6673 0.26692
Other coalition strats: 2032 0.08128
---=========
Manipulable elections: 23277 0.93108
Schulze again:
Burial, no compromise: 11196 0.548985
Compromise, no burial: 495 0.0242718
Burial and compromise: 753 0.0369226
Two-sided: 3882 0.19035
Other coalition strats: 90 0.00441306
---=========
Manipulable elections: 16416 0.804943
and the higher number of voters, comparing to Smith//IRV:
Impartial culture, three candidtes, 97 voters, 50k elections, 32k tests
per election:
CTE-Borda:
Burial, no compromise: 737 0.01474
Compromise, no burial: 4346 0.08692
Burial and compromise: 0 0
Two-sided: 15674 0.31348
Other coalition strats: 29192 0.58384
---=========
Manipulable elections: 49949 0.99898
Smith//IRV:
Burial, no compromise: 1682 0.03364
Compromise, no burial: 4382 0.08764
Burial and compromise: 0 0
Two-sided: 0 0
Other coalition strats: 1866 0.03732
---=========
Manipulable elections: 7930 0.1586
fpA - fpC:
Burial, no compromise: 3404 0.06808
Compromise, no burial: 4392 0.08784
Burial and compromise: 0 0
Two-sided: 779 0.01558
Other coalition strats: 0 0
---=========
Manipulable elections: 8575 0.1715
Five candidates, 97 voters, 50k elections, 32k tests per election:
CTE-Borda:
Burial, no compromise: 838 0.01676
Compromise, no burial: 11720 0.2344
Burial and compromise: 522 0.01044
Two-sided: 9754 0.19508
Other coalition strats: 27166 0.54332
---=========
Manipulable elections: 50000 1
Smith//IRV:
Burial, no compromise: 3407 0.06814
Compromise, no burial: 10961 0.21922
Burial and compromise: 1490 0.0298
Two-sided: 2 4e-05
Other coalition strats: 7904 0.15808
---=========
Manipulable elections: 23764 0.47528
Here's a burial example with 13 voters:
2: A > B > C
4: A > C > B
1: B > A > C
4: C > A > B
2: C > B > A
A is the CW and wins. (The Borda order is A>C>B.) Then
2: A > B > C
4: A > C > B
1: B > A > C
4: C > B > A <-- was C > A > B
2: C > B > A
and C wins.
The Borda order is C>A>B and we have an ACBA cycle, the pairwise sort
step swaps C and A; B is the loser and is eliminated, taking down A with
it. So the problem seems to be that if either A or the candidate who
beats A pairwise is the Borda loser, or can be made into the Borda
loser, then burial pays.
-km
On 10/13/23 20:25, Toby Pereira wrote:
I also like proportional representation, but there are many different
elections for many different things, and there will always be a need for
single-winner methods. Because of that I'm not sure it's necessary to
make the same point in every discussion about single-winner methods,
especially specific discussions about solving specific problems (e.g.
burial) rather than more general discussions.
I imagine you could have cycles in PR too. Perhaps something like having
a party list case of a Condorcet paradox, with the number of seats not
being a multiple of the number of parties, e.g.
31: A1>...>An>B1>...>Bn>C1>...>Cn
30: B1>...>Bn>C1>...>Cn>A1>...>An
29: C1>...>Cn>A1>...>An>B1>...>Bn
with some prime number of seats to be filled.
That nobody has found an obvious extension of the concept of a Condorcet
winner to a multiwinner context doesn't need to imply that PR in itself
will make the problem disappear.
A better candidate for dissolving electoral problems entirely would be
asset -- or sortition.
By the way, although I've got Richard plonked,
Time to move on from the ancient Greek conception of democracy, as
to elect a tyrant, unconditionally
seems wrong. According to Wikipedia, the Greeks (the Athenians at least)
filled most of their offices by lot. Elections were limited to financial
officials and generals.
-km
Kristofer,
This is not feedback on the draft as such, but the results of my
strategy vulnerability tests with CTE-Borda (which I'm guessing this is).
My implementation uses bubble sort, which I understand is the same as
sink sort (see e.g. https://xlinux.nist.gov/dads/HTML/sinkSort.html).
I asked you if it's different, but I didn't got a response. If what
you mean by "sink sort" differs from bubble sort, my results may be off.
The definition of "sink sort" includes (from the link you gave):
*Definition:*Sort by comparing each adjacent pair of items in a/list/
https://xlinux.nist.gov/dads/HTML/list.htmlin turn, swapping the
items if necessary...
As I understand the items in the list are in order of whatever (in this
case Borda count) with the highest-ordered at the top of the list.
Sink sort starts at the top and "sinks" down it, while "bubble" sort
starts at the bottom and moves up (the same direction as bubbles in
water) it.
The choice of one over the other seems arbitrary to me.
The concise (i.e. minus the redundant preamble) definition given by
Forest of this "Duncan" method suggestion is
..elect the highest score candidate that pairbeats every candidate
with lower score.
I'm not sure of the exact definition of "CTE-Borda" but I don't think
Duncan is the same thing. Nor is it Sink-Sorted Borda or Bubble-Sorted
Borda
or Margins-Sorted Borda.
Believe it or not, it is simply "elect the Smith-set member with the
lowest Borda score".
(Someone please correct me if I have that wrong.)
Chris B.
On 14/10/2023 9:51 pm, Kristofer Munsterhjelm wrote:
On 10/13/23 19:11, Forest Simmons wrote:
Dear EM List Friends,
We need your feedback on this draft of a proposal before we submit a
version of it to the voting reform community at large.
This is not feedback on the draft as such, but the results of my
strategy vulnerability tests with CTE-Borda (which I'm guessing this is).
My implementation uses bubble sort, which I understand is the same as
sink sort (see e.g. https://xlinux.nist.gov/dads/HTML/sinkSort.html).
I asked you if it's different, but I didn't got a response. If what
you mean by "sink sort" differs from bubble sort, my results may be off.
In any case, the method seems to have somewhat strange behavior under
impartial culture. With only a few voters (i.e. the election being far
from tied), there's still burial incentive. This burial incentive
disappears with increasing numbers of voters, but at a great cost of
general coalition strategy (which I imagine to be, but can't verify to
be, mostly pushover). The sum of burial and other strats push it to a
relatively high total susceptibility, although not quite as high as
the defeat-droppers.
Here are the stats:
Impartial culture, three candidates, 13 voters, 25k elections, 32k
tests per election:
CTE-Borda:
Burial, no compromise: 5381 0.21524
Compromise, no burial: 2050 0.082
Burial and compromise: 0 0
Two-sided: 5085 0.2034
Other coalition strats: 4120 0.1648
---=========
Manipulable elections: 16636 0.66544
For comparison, Schulze:
Burial, no compromise: 9988 0.426582
Compromise, no burial: 210 0.00896899
Burial and compromise: 282 0.0120441
Two-sided: 2206 0.0942171
Other coalition strats: 0 0
---=========
Manipulable elections: 12686 0.541813
Impartial culture, five candidates, 13 voters, 25k elections, 32k
tests per election:
CTE-Borda:
Burial, no compromise: 8654 0.34616
Compromise, no burial: 3864 0.15456
Burial and compromise: 2054 0.08216
Two-sided: 6673 0.26692
Other coalition strats: 2032 0.08128
---=========
Manipulable elections: 23277 0.93108
Schulze again:
Burial, no compromise: 11196 0.548985
Compromise, no burial: 495 0.0242718
Burial and compromise: 753 0.0369226
Two-sided: 3882 0.19035
Other coalition strats: 90 0.00441306
---=========
Manipulable elections: 16416 0.804943
and the higher number of voters, comparing to Smith//IRV:
Impartial culture, three candidtes, 97 voters, 50k elections, 32k
tests per election:
CTE-Borda:
Burial, no compromise: 737 0.01474
Compromise, no burial: 4346 0.08692
Burial and compromise: 0 0
Two-sided: 15674 0.31348
Other coalition strats: 29192 0.58384
---=========
Manipulable elections: 49949 0.99898
Smith//IRV:
Burial, no compromise: 1682 0.03364
Compromise, no burial: 4382 0.08764
Burial and compromise: 0 0
Two-sided: 0 0
Other coalition strats: 1866 0.03732
---=========
Manipulable elections: 7930 0.1586
fpA - fpC:
Burial, no compromise: 3404 0.06808
Compromise, no burial: 4392 0.08784
Burial and compromise: 0 0
Two-sided: 779 0.01558
Other coalition strats: 0 0
---=========
Manipulable elections: 8575 0.1715
Five candidates, 97 voters, 50k elections, 32k tests per election:
CTE-Borda:
Burial, no compromise: 838 0.01676
Compromise, no burial: 11720 0.2344
Burial and compromise: 522 0.01044
Two-sided: 9754 0.19508
Other coalition strats: 27166 0.54332
---=========
Manipulable elections: 50000 1
Smith//IRV:
Burial, no compromise: 3407 0.06814
Compromise, no burial: 10961 0.21922
Burial and compromise: 1490 0.0298
Two-sided: 2 4e-05
Other coalition strats: 7904 0.15808
---=========
Manipulable elections: 23764 0.47528
Here's a burial example with 13 voters:
2: A > B > C
4: A > C > B
1: B > A > C
4: C > A > B
2: C > B > A
A is the CW and wins. (The Borda order is A>C>B.) Then
2: A > B > C
4: A > C > B
1: B > A > C
4: C > B > A <-- was C > A > B
2: C > B > A
and C wins.
The Borda order is C>A>B and we have an ACBA cycle, the pairwise sort
step swaps C and A; B is the loser and is eliminated, taking down A
with it. So the problem seems to be that if either A or the candidate
who beats A pairwise is the Borda loser, or can be made into the Borda
loser, then burial pays.
-km
I'm having some trouble sending mail directly to you - adam.com.au
bounces my mail. So I'm leaving your mail address off the To field; EM
should send it to you in turn.
On 2023-10-14 18:10, C.Benham wrote:
Kristofer,
This is not feedback on the draft as such, but the results of my
strategy vulnerability tests with CTE-Borda (which I'm guessing this is).
My implementation uses bubble sort, which I understand is the same as
sink sort (see e.g. https://xlinux.nist.gov/dads/HTML/sinkSort.html).
I asked you if it's different, but I didn't got a response. If what
you mean by "sink sort" differs from bubble sort, my results may be off.
The definition of "sink sort" includes (from the link you gave):
*Definition:*Sort by comparing each adjacent pair of items in a/list/
https://xlinux.nist.gov/dads/HTML/list.htmlin turn, swapping the
items if necessary...
As I understand the items in the list are in order of whatever (in this
case Borda count) with the highest-ordered at the top of the list.
Sink sort starts at the top and "sinks" down it, while "bubble" sort
starts at the bottom and moves up (the same direction as bubbles in
water) it.
In that case, I am indeed implementing sink sort. My code starts at the
top and swaps pairs that are out of order, repeating from the top, until
it finishes a whole pass without swapping anyone.
The choice of one over the other seems arbitrary to me.
The concise (i.e. minus the redundant preamble) definition given by
Forest of this "Duncan" method suggestion is
..elect the highest score candidate that pairbeats every candidate
with lower score.
I'm not sure of the exact definition of "CTE-Borda" but I don't think
Duncan is the same thing. Nor is it Sink-Sorted Borda or Bubble-Sorted
Borda or Margins-Sorted Borda.
Yeah, I was just going by Forest's previous discussion of the Condorcet
Takedown Elimination method. Looks like I jumped the gun.
Now that I think about it, mine is ever so slightly different from
theirs; perhaps it makes a difference. It shouldn't in a three candidate
case at least. Forest and Mike's is:
- Elect the undefeated candidate when there is one ... else ...
eliminate any candidate that defeats no other candidate ... and ... - List the remaining candidates in order of their Nominal Favorability
Score" NFS. - Update the list by Sink Sorting it pairwise.
- Let P (for Pivot) be the candidate that has sunk to the bottom of the
list. - Eliminate P along with any candidates defeated by P.
- While more than one candidate remains, repeat steps 2 through 5.
- Elect the uneliminated candidate.
And mine is:
- Elect the CW if there is one.
- Eliminate the Condorcet loser if there is one. (not every weak CL)
- List the remaining candidates in order of some base method ranking
(scores aren't needed for comparison-based sorting). - Sink sort this list pairwise.
- Eliminate the bottom-ranked candidate on the list along with
everybody he beats pairwise. - If more than one candidate remains, go to step 1 (not step 3!)
- Otherwise elect the sole remaining candidate.
Believe it or not, it is simply "elect the Smith-set member with the
lowest Borda score".
(Someone please correct me if I have that wrong.)
Suppose we have an A>B>C>A cycle and the Borda ranking is A>B>C. The
Smith set is {A, B, C}. But the highest ranking candidate who beats
everybody ranked below him would be B, not C, since B beats C pairwise.
So B would be elected. I think.
But I wouldn't imagine this is monotone? Suppose B wins here. Then let B
be upranked so that the Borda ranking becomes B>A>C (still an A>B>C>A
cycle). Then C wins because A doesn't beat C pairwise.
I'll have to check its burial performance with quadelect later.
-km
With regard to the Saint Lague divisor, this has been argued, for
instance by Carstairs, as the most equitable share-out. My findings
substantiate this system also called Webster apportionment after its
original discoverer.
The Droop quota is a minimum proportional representation, which largely
replaced the Hare quota for maximum representation in large
constituencies. (Because politicians wanted to safeguard their safe
seats from the greater electoral competition of being in large
constituencies.) But the average quota of the two, found by taking their
harmonic mean, is, on examination, a more optimally democratic
representation than maximum or minimum PR. The Harmonic Mean quota,
which I introduced, is V/(s+ ½). This is effectively equivalent to
Webster apportionment.
The democratic principle of voters lists (STV) compared to the
oligarchic principle of party lists, may use a no less proportional
principle (the Harmonic Mean quota) than some party lists use of the
Saint Lague divisor count
I briefly discussed this in my most recent e-book, Don't You Ever read
Anything But Serious Books?, in the review of Carstairs brief history of
West European voting methods.
The Harmonic Mean quota is one of te four averages I use in the higher
order counts of Binomial STV (STV^x]. Hence Four Averages Binomial STV
(FAB STV). The four averages are to make the count more representative,
not so much of candidate popularity, but for the representation of
information in general.
First order Binomial STV (STV^1) is probably sufficient for
representation of candidates. But it is still the first binomial count
and the first one-truth voting method, that uses the same count for both
election and exclusion of candidates - one persons election being
another persons exclusion, in principle.
Regards,
Richard Lung.
On 13/10/2023 20:22, Michael Ossipoff wrote:
Richard—
No one is denying the desirability PR.
I don’t know where you reside, but, here in the U.S., PR for our
national legislature, Congress, is much less short-term feasible, due
to Constitutional structure.
The Constitution requires that every state gets a House
representative, regardless of how small it’s population is. If its
population were 1, it would nonetheless get a representative.
Additionally, the Constitution requires that every state must get the
SAME number of Senate-seats (two)…again, regardless of how small its
population is.
Those two Constitutional requirements would make nonsense of
proportionality.
Constitutional amendment is difficult & time-consuming. …&, for
various reasons we needn’t go into, a Constitutional convention now
would be a rather terrifying thing.
So, here, electoral-reform is single-winner reform.
BTW, I hasten to emphasize that I’m not against the small states. I
don’t want to deny them equal representation. “ Equal” is the
operative word..
Equal representation could be achieved, but not without repairing the
Constitution’s built-in disproportionality. It was “The Great
Compromise”, which compromised-away any chance of equal
representation. A very regrettable compromise.
Here’s an example of equal representation…my favorite one:
A unicameral at large (no districts or gerrymandering) Parliament
(yes, no president), 150 seats, elected by open-list party-list PR,
allocated by Sainte Lague, or, preferably, Bias-Free.
Of the divisor-method allocation-rules that are or have been used,
Sainte Lague is the very nearly unbiased one.
SL is only very slightly biased favoring larger parties.
Bias-Free is entirely absolutely unbiased.
Divisor methods involve the rounding, up or down, to a whole number,
of a party’s number of “quotas” ( details are outside the scope of
this discussion).
Sainte Lague rounds to the nearest whole number.
i.e. the round-up point is the average of the two surrounding
integers. I.e. …
R = (a+b)/2.
For Bias-Free, determine R as follows:
Divide b^b by a^a. Then divide the result by e.
e is the base of the natural logarithms, equal to about 2.718
But I re-emphasize that, with proportionality now Constitutionally
impossible, national PR is unavailable.
Electoral reform means single-winner reform.
On Fri, Oct 13, 2023 at 11:18 Richard Lung voting@ukscientists.com
wrote:
"Cycles" (in the paper-scissors-rock sense) are a problem of the
(under-candidated) single member systems own making. They rapidly
disappear with a representative sample of candidates
proportionally elected to large constituencies. The problem is not
the 'pesky' cycles, it is the pesky single member system. Unless
the politics in political science is to dictate to the science, it
is up to academics to point out, as hundreds of American political
scientists have, in conjunction with The New York Times, I
believe, this requirement of a quota-preferential method.
Remedies to the single member system are cosmetic. They cannot
possibly please more than half the population, whatever you do --
and probably a good deal less. UK monopolistic elections are a
minorocracy not a democracy, and that is probably a fair
indication of the US state of affairs.
Time to move on from the ancient Greek conception of democracy, as
to elect a tyrant, unconditionally -- making Britain what Hailsham
called an "elective dictatorship." Which shares some of the all
too evident failings of any dictatorship, elected or otherwise.
This should be a spur to avoid another Vietnam war or second Iraq
war, which even W. may deplore, in his heart.
Regards,
Richard Lung.
On 13/10/2023 18:11, Forest Simmons wrote:
Dear EM List Friends,
We need your feedback on this draft of a proposal before we
submit a version of it to the voting reform community at large.
---------- Forwarded message ---------
From: *Forest Simmons* <forest.simmons21@gmail.com>
Date: Thu, Oct 12, 2023, 5:35 PM
Subject: Duncan Proposal Draft
To: Michael Ossipoff <email9648742@gmail.com>
Michael Christened our new Q&D burial resistant method "Duncan"
after Duncan Black who popularized the idea of using Borda's
Method as a fallback "completion" when the ballots fail to
unambiguously reveal the sincere "Condorcet" pairbeats-all
candidate.
Our Duncan method has the same form as Black's in that the
official version directly specifies electing the unambiguous
Condorcet Candidate when there is one, and falls back to another
procedure that relies on Borda Scores, otherwise.
It should be emphasized that in both cases the fall back Borda
based expedient is rarely needed. For that reason some misguided
voting reform advocates have cavalierly opined that any decisive
completion/ fallback method would be plenty adequate to
supplement the Condorcet Criterion requirement.
However, this casual attitude ignores the feedback aspects of
voting systems in that various voting methods vary in the degree
that they encourage or discourage the creation of artificial beat
cycles that subvert/ hide the Condorcet Candidate from view,
bringing the completion method into greater prominence in a
potentially unstable cycle.
Unfortunately most of the extant methods fall into this
"positive" feedback category, including Borda itself. Some less
sensitive methods like Approval and IRV/RCV have a built in
"friction" that dampens the feedback; but as systems engineers
know, the high performance components are the ones that need the
addition of some carefully engineered negative feedback "circuit"
to stabilize the system as a whole.
In our Condorcet Completion context, our use of the Borda Count
scores is carefully designed with that stabilizing influence in
mind: adventurous strategists who are aware of this feature, when
acting rationally will be deterred from creating these cycles
that come back to bite them. Those not aware will find out when
their ploys backfire or otherwise disappoint them.
How do these pesky cycles arise so easily in Borda and other rank
based methods?
Suppose that your personal preference schedule for the
alphabetized candidates looks like ...
A>C>X>Y>Z, and that C is the Condorcet Candidate projected to win
the election if nobody acts nefariously.
You, and like minded friends, get the idea to insincerely move
your second choice to the bottom of your ballot (so it now reads
A>X>Y>Z>C) ... not to be "nefarious" so much as to just increase
the winning chances of your favorite A.
Could this work?
Yes, under Black's method if your friends follow your lead, this
"nurial" of C under the "busses" X, Y, and Z, could easily
subvert one or more of C's pairwise victories over X,Y, and Z,
into defeats of C by them, thereby hiding C's identity of sincere
Universal "pairbeater" status to just one more member of a
"beatcycle" of the form A beats X beats Y beats Z beats C beats A.
Note that the buried candidate C still beats the buriers'
favorite, A ... because lowering C does not decrease the number
of ballots that support C over A ... which is how easily and
innocently beatcycles like this can be created in Condorcet style
elections ... at least in the absence of negative feedback from
the cycle resolution fallback method.
In traditional Black that fallback method is Borda. Does that fix
the problem? ... or does it exacerbate it.
Well ... the same burial that put C at disadvantage in the
pairwise contests with X thru Z, also lowered C's Borda score by
3 counts per ballot, and raised
the Borda score of each of X thru Z to the tune of one count per
ballot.
The likely outcome is that C will end up with the lowest score,
and come in last in the finish order.
By way of contrast, under our new Duncan method, the most likely
winner is X, and the least likely winner is A, the burier
faction's favorite ... thus disappointing the burier faction
supporters ... teaching them that if they try to outsmart new
Duncan with insincere ballot rankings, they are apt to end up
helping elect their third (or later) choice instead of their
first choice or their second choice ... the one that they so
cleverly buried (however innocently or without malice).
Too many dabblers in voting method reform (as well as most
professionals) are unaware of these dynamics.
But now, with your new understanding, you, at least, can become
part of the solution.
Duncan Definition:
In the vast majority of the cases ... those in which the pairwise
counts of the ballots unambiguously identify the candidate that
pairbeats each of the others ... elect that candidate.
Otherwise, elect the highest score candidate that pairbeats every
candidate with lower score.
[Nominally "score" = Borda Count, though STAR Voting scores, for
example, could also serve]
How does this Duncan fallback procedure work to prevent A from
getting elected in our scenario regarding A thru Z?
Well, could A pairbeat every lower score candidate? In
particular, could A pairbeat C, which is now at the bottom of the
Borda score pile ... certainly lower than A ...?
Well, remember that "C beats A" was the last step in the
beatcycle created by A's friends.
So A does not pairbeat every lower score candidate, and therefore
cannot win.
New Duncan is burial resistant.
Next time ... more examples and insights ...
fws
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