Re: [EM] Arrow's theorem and cardinal voting systems
Rob,
Thanks for starting this great thread!
The "no perfect car" analogy is good. More definite is the "no 100 percent
efficient internal combustion engine" analogy that follows from the second
law of thermodynamics. It applies to all kinds of engines, but that
doesn't mean that internal combustion is as good as it gets.
If Gibbard-Satterthwaite tells us that we cannot have all of the nice
properties we want in one election method, that doesn't mean that one
method is as good as the next.
It follows from Arrow that we cannot have the Majority Criterion and the
IIAC at the same time, but there are many decent methods (like River) that
do satisfy the MC, and a bunch of other nice properties, like Monotonicity,
Clone Independence, the Condorcet Criterion, and Independence from Pareto
Dominated Alternatives, as well as the basic Neutrality and Anonymity
fairness criteria.
The way to think of Arrow's "Dictator" theorem is that it is extremely hard
to get a rankings based method with even minimal decency conditions (like
non-dictatorship) without scuttling the IIAC.
In other words, no decent ordinal based method can satisfy the IIAC, which
is the same point of view that Toby and Eppley expressed. It comes down to
the mere existence of a Condorcet Cycle. Here's the subtle part that most
people don't understand. Condorcet Cycles can exist in the preference
schedules of an election even if the election method makes no mention of
Condorcet, for example even in IRV/Hare/STV/RCV elections:
45 A>B>C
20 B>C>A
35 C>A>B
There exists a majority preference cycle A>B>C>A even though it causes no
problem for IRV, since B is eliminated and then C is the majority winner
between the two remaining candidates.
Now let's check the IIAC. Suppose that A, one of the losers withdraws from
the race. Then the winner changes from C to B, since B beats C by a
majority. This shows that IRV does not satisfy the IIAC, because removing
a loser from the ballot changes the winner.
But this is not just a problem for IRV, it's a problem for any method that
respects the Majority Criterion; if the method makes A the winner, then
removing B changes the winner. If it makes B the winner, then removing C
changes the winner. If it makes C the winner, then (as we saw in the case
of IRV above) removing A changes the winner. to B.
So Arrow's "paradox" can be considered as forcing us to realize that the
IIAC is not a realistic possibility in the presence of ordinal ballots
because such ballots allow us to detect oairwise (head-to-head)
preferences, and when it comes down to a single pair of candidates the
Majority Criterion says the pairwise winner must be chosen,
However, as someone mentioned, Approval Voting avoids this "paradox" once
the ballots have been submitted, since the Approval winner A is always the
"ballot CW," and in two different ways:(1) For any other candidate X,
candidate A will be rated above X on more ballots than not, and (2) A's
approval score will be higher than the sore of any other candidate. From
either point of view, if we remove a loser Y from the ballots, then A will
still be the winner according to the same ballots with Y crossed out.
That's at the ballot level. But if Y withdrew before the ballots were
filled out, it could change the winner, because if Y were the only approved
candidate for a certain voter before the withdrawal, that voter might
decide to lower her personal approval cutoff before submitting her ballot.
Or she could raise the cutoff if Y had been the only disapproved candidate.
As others have mentioned in this discussion, Approval Voting externalizes
the problem of the IIAC from being a decision problem for the method itself
to a strategical decision problem for the voter. A voter might think of
that as an unfair burden.
One answer to this problem could be DSV (Designated Strategy Voting): You
submit your sincere ratings, and the DSV machine applies a strategy of your
choice or a default strategy to transform the ballots into approval style
ballots. Rob LeGrand explored some of the possibilities and limitations of
this approach in his master's thesis. He doesn't claim to have exhausted
the possibilities. (I also have some ideas in this vein that still need
exploring.)
What constitutes a "sincere rating." One approach to that has already been
mentioned in the ice-cream flavor context in this thread. Another is to use
as a rating for candidate X your subjective probability that on a typical
issue of any significance candidate X would support the same side you
support.
It's not just Approval that requires some hard thinking in conjunction with
filling out the ballots. Ranking many candidates (think about the number of
candidates in the election that propelled Schwarznegger into office) may be
just as burdensome as trying to decide exactly which candidates to mark as
approved. In Australia you can get around this difficulty by copying
"candidate cards" or by voting the party line. Presumably these experts are
reflecting state of the art strategy in their rankings ... the strategy
that is indispensable for optimum results according to
Gibbard-Satterthwaite. This is not just a problem of Approval, though it
may seem worse in Approval. In actuality, aoproval and score/range are the
only commonly used methods where optimal strategy never requires you to
"betray " your favorite.
To cut the Gordian knot of this complexity Charles Dodgson (aka Lewis
Carroll) suggested what we now call Asset Voting. Each Voter delegates her
vote to the candidate she trusts the most to rep[resent her in the decision
process. Since write-ins are allowed, she can write in herself if she
doesn't trust anybody else to be her proxy. These proxies get together
with their "assets" (delegated votes) and choose a winner by use of some
version of Robert's Rules of Order.
Which criteria are satisfied by this method? Does Gibbard Satthethwaite
have anything to say about it? How about Arrow? For that matter does first
past the post plurality satisfy the IIAC? (No more or less than Approval in
reality.)
Let's talk about Gibbard-Satterthwaite. Is there any incentive for a
person to delegate as proxy someone other than her favorite?
If we are talking representative democracy, then why would you want to
delegate your vote to candidate B when candidate A was the one you trusted
most to represent you in making important decisions once in office?
All of the "problems" with the method are essentially externalized to the
deliberations governed by"Robert's Rules of Order" in the smoke filled room.
Gibbard-Satterthwaite is taken to say that it is impossible to obtain
sincere preferences or sincere utilities from voters in the context of full
information (or disinformation) elections. Yet it turns out to be
relatively easy; you just need to separate the ballot into two parts. The
first part requires strategic voting to pick the two alternatives as
finalists. The second part is used solely to choose between these two
options. (In the case of cardinal ballots the finalists are lotteries.) A
version of the uncertainty principle obtains here: if you use the sincere
ballots for any other instrumental purpose than to choose between the two
finalists, then you almost certainly destroy their sincerity.
However there would be no problem comparing tthe sincere part with the
strategical part to get statistics about voters' willingness to vote
insincerely in choosing the finalists.
Another avenue that has been barely explored is the use of chance to
incentivize consensus when there is a potential for it.
For example, suppose that preferences are
60 A>C>>>>B
40 B>C>>>>A
Under approval voting the A faction has a strong incentive to downgrade C
and vote 60 A>>>>>C>B making A the (insincere) approval winner as
Gibbard-satterthwaite would predict.
However, if the rules said that in the absence of a full consensus approval
winner, the winner would be chosen by random ballot, then (assuming
rational voters voting in their own interest) C would be the sure outcome;
no rational voter in either faction would prefer random ballot expectations
over a sure deal on C.
Jobst Heitzig is the pioneer in this area.
In sum, Arrow, et.al. should not constitute a nail in the coffin of
creative progress in Election Methods. IMHO that is an important message
we need to send if we want to attract new talent.
Forest
Just a couple of additional thoughts:
Besides Arrow and Gibbard-Sattherwaite we have lots of criterion
incompatibility results from Woodall, and defensive strategy criteria from
Mike Ossipoff, Steve Eppley, et. al.. In particular we never worried about
Later No Help and later No Harm until Woodall came along. Venzke and Benham
picked up the torch and brought Woodall into the EM Listserv discussion.
Many EM contributors have clarified which combinations of various criteria
of more practical than academic stripe are compatible or not:
Participation, FBC, Precinct Summability, Chicken, etc.
In particular, we now know through the work of Ossipoff, Venzke, Benham,
and others that the Chicken Defense and Burial Defense (against CW burial)
are incompatible in the presence of Plurality and the the FBC, unless we
allow an explicit approval cutoff or some other strategic switch on the
ballots. Standard ordinal ballots are not adequate for this even when
truncation and equal rankings (including equal top) are allowed. A
non-standard ballot that allows us to get compatibility to all of these
except the CC is MDDA(sc) which is Majority Defeat Disqualification
Approval with symmetric completion below the approval cutoff. This method
also satisfies other basic criteria such as Participation, Clone
Independence, Mono-Raise, Mono-Add, and IDPA, for example.
In the context of the current discussion, the approval cutoff or some
equivalent strategic switch is essential for the compatibility of chicken
resistance and burial resistance.. No strategy, no compatibility. So
basically there is no decent method that is resistant to both Burial of the
CW and Chicken offensives. (IRV is chicken resistant and has a form of
burial resistance, but routinely buries the CW unless voters strategically
betray their favorite to save the CW. Furthermore, it fails mono-raise.)
Before collaborative efforts of EM List members there was no known clone
independent, monotonic method for electing from the uncovered set. The
closest thing was Copeland, which is clone dependent.
Again the main point is that Arrow, and Gibbard-Satterthwaite are not the
"end of history" for election methods, just like the collapse of the USSR
was not the end of history as Fukuyama once proclaimed or Thatcher's famous
TINA "there is no alternative" (to capitalism). Arrow and G-S give very
valuable insights and help us avoid cul-de-sacs, but they are not the last
word in election methods progress. The "end of history" and TINA slogans
are an excuse for giving up prematurely for lack of imagination. We cannot
allow Arrow and G-S to become excuses for lack of imagination in Election
Methods. What if Yee had given up before inventing the beautiful Yee
diagrams that constitute an Electo-Kaleidoscope for the study of election
methods analogous to the telesope and the electron microscope in astronomy
as instruments in other branches of knowledge?
On Mon, Jan 13, 2020 at 3:32 PM Forest Simmons fsimmons@pcc.edu wrote:
Rob,
Thanks for starting this great thread!
The "no perfect car" analogy is good. More definite is the "no 100
percent efficient internal combustion engine" analogy that follows from the
second law of thermodynamics. It applies to all kinds of engines, but that
doesn't mean that internal combustion is as good as it gets.
If Gibbard-Satterthwaite tells us that we cannot have all of the nice
properties we want in one election method, that doesn't mean that one
method is as good as the next.
It follows from Arrow that we cannot have the Majority Criterion and the
IIAC at the same time, but there are many decent methods (like River) that
do satisfy the MC, and a bunch of other nice properties, like Monotonicity,
Clone Independence, the Condorcet Criterion, and Independence from Pareto
Dominated Alternatives, as well as the basic Neutrality and Anonymity
fairness criteria.
The way to think of Arrow's "Dictator" theorem is that it is extremely
hard to get a rankings based method with even minimal decency conditions
(like non-dictatorship) without scuttling the IIAC.
In other words, no decent ordinal based method can satisfy the IIAC, which
is the same point of view that Toby and Eppley expressed. It comes down to
the mere existence of a Condorcet Cycle. Here's the subtle part that most
people don't understand. Condorcet Cycles can exist in the preference
schedules of an election even if the election method makes no mention of
Condorcet, for example even in IRV/Hare/STV/RCV elections:
45 A>B>C
20 B>C>A
35 C>A>B
There exists a majority preference cycle A>B>C>A even though it causes no
problem for IRV, since B is eliminated and then C is the majority winner
between the two remaining candidates.
Now let's check the IIAC. Suppose that A, one of the losers withdraws
from the race. Then the winner changes from C to B, since B beats C by a
majority. This shows that IRV does not satisfy the IIAC, because removing
a loser from the ballot changes the winner.
But this is not just a problem for IRV, it's a problem for any method that
respects the Majority Criterion; if the method makes A the winner, then
removing B changes the winner. If it makes B the winner, then removing C
changes the winner. If it makes C the winner, then (as we saw in the case
of IRV above) removing A changes the winner. to B.
So Arrow's "paradox" can be considered as forcing us to realize that the
IIAC is not a realistic possibility in the presence of ordinal ballots
because such ballots allow us to detect oairwise (head-to-head)
preferences, and when it comes down to a single pair of candidates the
Majority Criterion says the pairwise winner must be chosen,
However, as someone mentioned, Approval Voting avoids this "paradox" once
the ballots have been submitted, since the Approval winner A is always the
"ballot CW," and in two different ways:(1) For any other candidate X,
candidate A will be rated above X on more ballots than not, and (2) A's
approval score will be higher than the sore of any other candidate. From
either point of view, if we remove a loser Y from the ballots, then A will
still be the winner according to the same ballots with Y crossed out.
That's at the ballot level. But if Y withdrew before the ballots were
filled out, it could change the winner, because if Y were the only approved
candidate for a certain voter before the withdrawal, that voter might
decide to lower her personal approval cutoff before submitting her ballot.
Or she could raise the cutoff if Y had been the only disapproved candidate.
As others have mentioned in this discussion, Approval Voting externalizes
the problem of the IIAC from being a decision problem for the method itself
to a strategical decision problem for the voter. A voter might think of
that as an unfair burden.
One answer to this problem could be DSV (Designated Strategy Voting): You
submit your sincere ratings, and the DSV machine applies a strategy of your
choice or a default strategy to transform the ballots into approval style
ballots. Rob LeGrand explored some of the possibilities and limitations of
this approach in his master's thesis. He doesn't claim to have exhausted
the possibilities. (I also have some ideas in this vein that still need
exploring.)
What constitutes a "sincere rating." One approach to that has already
been mentioned in the ice-cream flavor context in this thread. Another is
to use as a rating for candidate X your subjective probability that on a
typical issue of any significance candidate X would support the same side
you support.
It's not just Approval that requires some hard thinking in conjunction
with filling out the ballots. Ranking many candidates (think about the
number of candidates in the election that propelled Schwarznegger into
office) may be just as burdensome as trying to decide exactly which
candidates to mark as approved. In Australia you can get around this
difficulty by copying "candidate cards" or by voting the party line.
Presumably these experts are reflecting state of the art strategy in their
rankings ... the strategy that is indispensable for optimum results
according to Gibbard-Satterthwaite. This is not just a problem of
Approval, though it may seem worse in Approval. In actuality, aoproval and
score/range are the only commonly used methods where optimal strategy never
requires you to "betray " your favorite.
To cut the Gordian knot of this complexity Charles Dodgson (aka Lewis
Carroll) suggested what we now call Asset Voting. Each Voter delegates her
vote to the candidate she trusts the most to rep[resent her in the decision
process. Since write-ins are allowed, she can write in herself if she
doesn't trust anybody else to be her proxy. These proxies get together
with their "assets" (delegated votes) and choose a winner by use of some
version of Robert's Rules of Order.
Which criteria are satisfied by this method? Does Gibbard Satthethwaite
have anything to say about it? How about Arrow? For that matter does first
past the post plurality satisfy the IIAC? (No more or less than Approval in
reality.)
Let's talk about Gibbard-Satterthwaite. Is there any incentive for a
person to delegate as proxy someone other than her favorite?
If we are talking representative democracy, then why would you want to
delegate your vote to candidate B when candidate A was the one you trusted
most to represent you in making important decisions once in office?
All of the "problems" with the method are essentially externalized to the
deliberations governed by"Robert's Rules of Order" in the smoke filled room.
Gibbard-Satterthwaite is taken to say that it is impossible to obtain
sincere preferences or sincere utilities from voters in the context of full
information (or disinformation) elections. Yet it turns out to be
relatively easy; you just need to separate the ballot into two parts. The
first part requires strategic voting to pick the two alternatives as
finalists. The second part is used solely to choose between these two
options. (In the case of cardinal ballots the finalists are lotteries.) A
version of the uncertainty principle obtains here: if you use the sincere
ballots for any other instrumental purpose than to choose between the two
finalists, then you almost certainly destroy their sincerity.
However there would be no problem comparing tthe sincere part with the
strategical part to get statistics about voters' willingness to vote
insincerely in choosing the finalists.
Another avenue that has been barely explored is the use of chance to
incentivize consensus when there is a potential for it.
For example, suppose that preferences are
60 A>C>>>>B
40 B>C>>>>A
Under approval voting the A faction has a strong incentive to downgrade C
and vote 60 A>>>>>C>B making A the (insincere) approval winner as
Gibbard-satterthwaite would predict.
However, if the rules said that in the absence of a full consensus
approval winner, the winner would be chosen by random ballot, then
(assuming rational voters voting in their own interest) C would be the sure
outcome; no rational voter in either faction would prefer random ballot
expectations over a sure deal on C.
Jobst Heitzig is the pioneer in this area.
In sum, Arrow, et.al. should not constitute a nail in the coffin of
creative progress in Election Methods. IMHO that is an important message
we need to send if we want to attract new talent.
Forest
This is obviously a very learned summary that would require considerable
study to do justice to, much more than my old head is capable of, quite
apart from severe personal distresses, that have been over-whelming our
lives.
Yet, just the other day, after a half century of amateur study, to my
surprise, my naive physicists mathematical text crawled across the
finishing line of publication. Only the last chapter is of direct
interest to electoral mathematicians. It contains an explanation of how
to conduct a two-dimensional election: FAB STV 2D.
The two dimensions are Representation and Arbitration. The latter graphs
at 90 degrees (neutrally) to the former, and the count is conducted
without disturbing the normal one-dimensional count that is FAB STV. But
taken together as a complex variable the count is according to the rules
of complex variables.
from
Richard Lung.
On 15/01/2020 20:57, Forest Simmons wrote:
Just a couple of additional thoughts:
Besides Arrow and Gibbard-Sattherwaite we have lots of criterion
incompatibility results from Woodall, and defensive strategy criteria
from Mike Ossipoff, Steve Eppley, et. al.. In particular we never
worried about Later No Help and later No Harm until Woodall came
along. Venzke and Benham picked up the torch and brought Woodall into
the EM Listserv discussion.
Many EM contributors have clarified which combinations of various
criteria of more practical than academic stripe are compatible or not:
Participation, FBC, Precinct Summability, Chicken, etc.
In particular, we now know through the work of Ossipoff, Venzke,
Benham, and others that the Chicken Defense and Burial Defense
(against CW burial) are incompatible in the presence of Plurality and
the the FBC, unless we allow an explicit approval cutoff or some other
strategic switch on the ballots. Standard ordinal ballots are not
adequate for this even when truncation and equal rankings (including
equal top) are allowed. A non-standard ballot that allows us to get
compatibility to all of these except the CC is MDDA(sc) which is
Majority Defeat Disqualification Approval with symmetric completion
below the approval cutoff. This method also satisfies other basic
criteria such as Participation, Clone Independence, Mono-Raise,
Mono-Add, and IDPA, for example.
In the context of the current discussion, the approval cutoff or some
equivalent strategic switch is essential for the compatibility of
chicken resistance and burial resistance.. No strategy, no
compatibility. So basically there is no decent method that is
resistant to both Burial of the CW and Chicken offensives. (IRV is
chicken resistant and has a form of burial resistance, but routinely
buries the CW unless voters strategically betray their favorite to
save the CW. Furthermore, it fails mono-raise.)
Before collaborative efforts of EM List members there was no known
clone independent, monotonic method for electing from the uncovered
set. The closest thing was Copeland, which is clone dependent.
Again the main point is that Arrow, and Gibbard-Satterthwaite are not
the "end of history" for election methods, just like the collapse of
the USSR was not the end of history as Fukuyama once proclaimed or
Thatcher's famous TINA "there is no alternative" (to capitalism).
Arrow and G-S give very valuable insights and help us avoid
cul-de-sacs, but they are not the last word in election methods
progress. The "end of history" and TINA slogans are an excuse for
giving up prematurely for lack of imagination. We cannot allow Arrow
and G-S to become excuses for lack of imagination in Election
Methods. What if Yee had given up before inventing the beautiful Yee
diagrams that constitute an Electo-Kaleidoscope for the study of
election methods analogous to the telesope and the electron microscope
in astronomy as instruments in other branches of knowledge?
On Mon, Jan 13, 2020 at 3:32 PM Forest Simmons <fsimmons@pcc.edu
mailto:fsimmons@pcc.edu> wrote:
Rob,
Thanks for starting this great thread!
The "no perfect car" analogy is good. More definite is the "no
100 percent efficient internal combustion engine" analogy that
follows from the second law of thermodynamics. It applies to all
kinds of engines, but that doesn't mean that internal combustion
is as good as it gets.
If Gibbard-Satterthwaite tells us that we cannot have all of the
nice properties we want in one election method, that doesn't mean
that one method is as good as the next.
It follows from Arrow that we cannot have the Majority Criterion
and the IIAC at the same time, but there are many decent methods
(like River) that do satisfy the MC, and a bunch of other nice
properties, like Monotonicity, Clone Independence, the Condorcet
Criterion, and Independence from Pareto Dominated Alternatives, as
well as the basic Neutrality and Anonymity fairness criteria.
The way to think of Arrow's "Dictator" theorem is that it is
extremely hard to get a rankings based method with even minimal
decency conditions (like non-dictatorship) without scuttling the IIAC.
In other words, no decent ordinal based method can satisfy the
IIAC, which is the same point of view that Toby and Eppley
expressed. It comes down to the mere existence of a Condorcet
Cycle. Here's the subtle part that most people don't understand.
Condorcet Cycles can exist in the preference schedules of an
election even if the election method makes no mention of
Condorcet, for example even in IRV/Hare/STV/RCV elections:
45 A>B>C
20 B>C>A
35 C>A>B
There exists a majority preference cycle A>B>C>A even though it
causes no problem for IRV, since B is eliminated and then C is the
majority winner between the two remaining candidates.
Now let's check the IIAC. Suppose that A, one of the losers
withdraws from the race. Then the winner changes from C to B,
since B beats C by a majority. This shows that IRV does not
satisfy the IIAC, because removing a loser from the ballot changes
the winner.
But this is not just a problem for IRV, it's a problem for any
method that respects the Majority Criterion; if the method makes A
the winner, then removing B changes the winner. If it makes B the
winner, then removing C changes the winner. If it makes C the
winner, then (as we saw in the case of IRV above) removing A
changes the winner. to B.
So Arrow's "paradox" can be considered as forcing us to realize
that the IIAC is not a realistic possibility in the presence of
ordinal ballots because such ballots allow us to detect oairwise
(head-to-head) preferences, and when it comes down to a single
pair of candidates the Majority Criterion says the pairwise winner
must be chosen,
However, as someone mentioned, Approval Voting avoids this
"paradox" once the ballots have been submitted, since the Approval
winner A is always the "ballot CW," and in two different ways:(1)
For any other candidate X, candidate A will be rated above X on
more ballots than not, and (2) A's approval score will be higher
than the sore of any other candidate. From either point of view,
if we remove a loser Y from the ballots, then A will still be the
winner according to the same ballots with Y crossed out.
That's at the ballot level. But if Y withdrew before the ballots
were filled out, it could change the winner, because if Y were the
only approved candidate for a certain voter before the withdrawal,
that voter might decide to lower her personal approval cutoff
before submitting her ballot. Or she could raise the cutoff if Y
had been the only disapproved candidate.
As others have mentioned in this discussion, Approval Voting
externalizes the problem of the IIAC from being a decision problem
for the method itself to a strategical decision problem for the
voter. A voter might think of that as an unfair burden.
One answer to this problem could be DSV (Designated Strategy
Voting): You submit your sincere ratings, and the DSV machine
applies a strategy of your choice or a default strategy to
transform the ballots into approval style ballots. Rob LeGrand
explored some of the possibilities and limitations of this
approach in his master's thesis. He doesn't claim to have
exhausted the possibilities. (I also have some ideas in this vein
that still need exploring.)
What constitutes a "sincere rating." One approach to that has
already been mentioned in the ice-cream flavor context in this
thread. Another is to use as a rating for candidate X your
subjective probability that on a typical issue of any significance
candidate X would support the same side you support.
It's not just Approval that requires some hard thinking in
conjunction with filling out the ballots. Ranking many candidates
(think about the number of candidates in the election that
propelled Schwarznegger into office) may be just as burdensome as
trying to decide exactly which candidates to mark as approved. In
Australia you can get around this difficulty by copying "candidate
cards" or by voting the party line. Presumably these experts are
reflecting state of the art strategy in their rankings ... the
strategy that is indispensable for optimum results according to
Gibbard-Satterthwaite. This is not just a problem of Approval,
though it may seem worse in Approval. In actuality, aoproval and
score/range are the only commonly used methods where optimal
strategy never requires you to "betray " your favorite.
To cut the Gordian knot of this complexity Charles Dodgson (aka
Lewis Carroll) suggested what we now call Asset Voting. Each Voter
delegates her vote to the candidate she trusts the most to
rep[resent her in the decision process. Since write-ins are
allowed, she can write in herself if she doesn't trust anybody
else to be her proxy. These proxies get together with their
"assets" (delegated votes) and choose a winner by use of some
version of Robert's Rules of Order.
Which criteria are satisfied by this method? Does Gibbard
Satthethwaite have anything to say about it? How about Arrow? For
that matter does first past the post plurality satisfy the IIAC?
(No more or less than Approval in reality.)
Let's talk about Gibbard-Satterthwaite. Is there any incentive
for a person to delegate as proxy someone other than her favorite?
If we are talking representative democracy, then why would you
want to delegate your vote to candidate B when candidate A was the
one you trusted most to represent you in making important
decisions once in office?
All of the "problems" with the method are essentially externalized
to the deliberations governed by"Robert's Rules of Order" in the
smoke filled room.
Gibbard-Satterthwaite is taken to say that it is impossible to
obtain sincere preferences or sincere utilities from voters in the
context of full information (or disinformation) elections. Yet it
turns out to be relatively easy; you just need to separate the
ballot into two parts. The first part requires strategic voting
to pick the two alternatives as finalists. The second part is
used solely to choose between these two options. (In the case of
cardinal ballots the finalists are lotteries.) A version of the
uncertainty principle obtains here: if you use the sincere ballots
for any other instrumental purpose than to choose between the two
finalists, then you almost certainly destroy their sincerity.
However there would be no problem comparing tthe sincere part with
the strategical part to get statistics about voters' willingness
to vote insincerely in choosing the finalists.
Another avenue that has been barely explored is the use of chance
to incentivize consensus when there is a potential for it.
For example, suppose that preferences are
60 A>C>>>>B
40 B>C>>>>A
Under approval voting the A faction has a strong incentive to
downgrade C and vote 60 A>>>>>C>B making A the (insincere)
approval winner as Gibbard-satterthwaite would predict.
However, if the rules said that in the absence of a full consensus
approval winner, the winner would be chosen by random ballot, then
(assuming rational voters voting in their own interest) C would be
the sure outcome; no rational voter in either faction would prefer
random ballot expectations over a sure deal on C.
Jobst Heitzig is the pioneer in this area.
In sum, Arrow, et.al <http://et.al>. should not constitute a nail
in the coffin of creative progress in Election Methods. IMHO that
is an important message we need to send if we want to attract new
talent.
Forest
Election-Methods mailing list - see https://electorama.com/em for list info
On 1/13/2020 6:32 PM, Forest Simmons wrote:
-snip-
It's not just Approval that requires some hard thinking in conjunction with filling out the ballots. Ranking many candidates (think about the number of candidates in the election that propelled Schwarznegger into office) may be just as burdensome as trying to decide exactly which candidates to mark as approved. In Australia you can get around this difficulty by copying "candidate cards" or by voting the party line.
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During the week or so before Schwarzenegger was elected Governor of California (ousting Governor Gray Davis in a recall election), likely voters were surveyed by a team of grad students led by economics & political science professor Rod Kiwiet of Caltech. The voters were asked the 6 pairwise preference questions regarding the 4 candidates judged by Kiwiet to be the top 4 (including Davis). The survey result was that Schwarzenegger defeated the other 3 candidates pairwise. A Condorcet winner. So I don't agree that Schwarzenegger was "propelled into office by the (large) number of candidates" but perhaps I'm unaware of better evidence.
Regarding Australia's solution for their tedious lengthy STV PR ballot, a similar way to make strategy simpler for voters is to use a voting method in the Vote for a Published Ranking (VPR) family of methods:
Before election day, each candidate publishes a ranking of
all the candidates (presumably with him/herself on top).
Any candidate who doesn't publish is disqualified.
(Alternatively, any candidate who doesn't publish is treated
as if s/he'd published the ranking that has him/herself on top
and all other candidates tied at the bottom.)
On election day, each voter votes by selecting one candidate.
Each vote is tallied as if it were the ranking published by the
voter's selected candidate (using society's favorite algorithm
for aggregating voters' rankings).
Some potential advantages of VPR:
(1) Good candidates wouldn't need as much money to win, since they can win by persuading some "popular" candidates to rank them over worse candidates. It might require only a few phone calls.
(2) After the candidates publish their rankings, journalists & pundits would presumably scrutinize the rankings looking for unusual preferences, a possible sign of corruption. Presumably many voters would learn about those oddities before election day, and reconsider who to vote for.
(3) It's relatively simple for the voters. My hunch is that strategically-optimal votes would typically be votes for one's favorite candidate, even when there are many candidates.
(4) It solves problems related to "too many candidates" and "low information voters" -- in particular that the best candidates might be left unranked by a lot of voters. It was this concern, expressed by Mike Alvarez of Caltech many years ago, which led me to propose VPR in an article published in 2007 in the Pasadena Weekly: https://pasadenaweekly.com/roberts-rules-for-voting/ (In 2007, Rudy Giuliani was considered a frontrunner for the 2008 Republican presidential nomination, so his name appears in an example in the article.)
Two variants of VPR:
- NGOs could publish rankings too, and be eligible for selection by voters on election day.
- Given adequate technology in the voting booth... The voter begins by selecting one candidate. The voting machine then displays that candidate's published ranking, and the voter may rearrange it. (A big time saver, yet the voter has maximal control over his/her ranking.)
Another way to simplify voter strategy is to allow candidates to withdraw from contention after election day, after the votes are published (in a summary format adequate to be tallied using the voting method). A spoiler could choose to withdraw to help a compromise defeat a "greater evil." The Candidate Withdrawal option would also make voting methods more compatible with the U.S. Electoral College, because candidates could withdraw to help a compromise candidate obtain a majority in the Electoral College. A variant of Candidate Withdrawal is to allow candidates to withdraw from particular pairings while remaining in the other pairings (assuming a pairwise voting method).
Subscribers to Election-Methods may already be familiar with VPR and Candidate Withdrawal since they were discussed here many years ago. I've read few messages in the last 10-ish years, so I have no clue about what current subscribers are familiar with.
--Steve
On 15/01/2020 21.57, Forest Simmons wrote:
Just a couple of additional thoughts:
Besides Arrow and Gibbard-Sattherwaite we have lots of criterion
incompatibility results from Woodall, and defensive strategy criteria
from Mike Ossipoff, Steve Eppley, et. al.. In particular we never
worried about Later No Help and later No Harm until Woodall came along.
Venzke and Benham picked up the torch and brought Woodall into the EM
Listserv discussion.
Many EM contributors have clarified which combinations of various
criteria of more practical than academic stripe are compatible or not:
Participation, FBC, Precinct Summability, Chicken, etc.
In particular, we now know through the work of Ossipoff, Venzke, Benham,
and others that the Chicken Defense and Burial Defense (against CW
burial) are incompatible in the presence of Plurality and the the FBC,
unless we allow an explicit approval cutoff or some other strategic
switch on the ballots. Standard ordinal ballots are not adequate for
this even when truncation and equal rankings (including equal top) are
allowed. A non-standard ballot that allows us to get compatibility to
all of these except the CC is MDDA(sc) which is Majority Defeat
Disqualification Approval with symmetric completion below the approval
cutoff. This method also satisfies other basic criteria such as
Participation, Clone Independence, Mono-Raise, Mono-Add, and IDPA, for
example.
In the context of the current discussion, the approval cutoff or some
equivalent strategic switch is essential for the compatibility of
chicken resistance and burial resistance.. No strategy, no
compatibility. So basically there is no decent method that is resistant
to both Burial of the CW and Chicken offensives. (IRV is chicken
resistant and has a form of burial resistance, but routinely buries the
CW unless voters strategically betray their favorite to save the CW.
Furthermore, it fails mono-raise.)
The various Condorcet-IRV hybrids do help there, e.g. Benham passes
DMTBR. But I see what you mean :-)
Before collaborative efforts of EM List members there was no known clone
independent, monotonic method for electing from the uncovered set. The
closest thing was Copeland, which is clone dependent.
Again the main point is that Arrow, and Gibbard-Satterthwaite are not
the "end of history" for election methods, just like the collapse of the
USSR was not the end of history as Fukuyama once proclaimed or
Thatcher's famous TINA "there is no alternative" (to capitalism). Arrow
and G-S give very valuable insights and help us avoid cul-de-sacs, but
they are not the last word in election methods progress. The "end of
history" and TINA slogans are an excuse for giving up prematurely for
lack of imagination.
If anything, it's the other way around. If there were a perfect method,
there would be no need for imagination: just find out what that perfect
method is and settle on it, done. That there is no perfect method is
what gives room for imagination.
Again the main point is that Arrow, and Gibbard-Satterthwaite are not
the "end of history" for election methods, just like the collapse of the
USSR was not the end of history as Fukuyama once proclaimed or
Thatcher's famous TINA "there is no alternative" (to capitalism). Arrow
and G-S give very valuable insights and help us avoid cul-de-sacs, but
they are not the last word in election methods progress. The "end of
history" and TINA slogans are an excuse for giving up prematurely for
lack of imagination.
If anything, it's the other way around. If there were a perfect method,
there would be no need for imagination: just find out what that perfect
method is and settle on it, done. That there is no perfect method is
what gives room for imagination.
Right on! In other words, if we had a perfect method we really would have
"the end of history," and there really would be "no alternative."
My simple explanation to myself is that group opinions may contain majority cycles (even if individual opinions do not). This is to me a natural explanation that covers most of these social ordering and voting related (seemingly paradoxical) problems. Majorities are meaningful also in cardinal voting systems since each majority can win the election if they agree to do so.
BR, Juho