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 - seehttps://electorama.com/em  for list info

Thankyou Forest Simmons. It is appreciated. The link is: https://www.smashwords.com/books/view/997528 Richard Lung. On 19/01/2020 22:30, Forest Simmons wrote: > Fascinating! We need people like you to knock us out of complacency > ... out of the comfortable ruts that we inhabit. > > I look forward to following the link you gave me! > > On Thu, Jan 16, 2020 at 10:25 AM Richard Lung <voting@ukscientists.com > <mailto:voting@ukscientists.com>> wrote: > > 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 - seehttps://electorama.com/em for list info > >