On 24.05.2022 21:05, Richard Lung wrote:

 have both,

 count.

 theorem, to

 order

 The criteria are method-agnostic: for any ranked voting method
 (in this
 case, that supports truncation), if someone gives you a failure
 example,
 you can verify if the method passes or fails the criterion without
 knowing anything about the internals of the method.

 Put differently, suppose that in a scenario perhaps reminiscent of
 Roadside Picnic, a mysterious device falls out of the sky. And it
 turns
 out that this mysterious device calls elections: you can input ranked
 ballots with a set of buttons and get the results shown as a
 series of
 lights on the other end.

 Then as long as it allows for ballots with truncation, it's
 possible to
 check if a particular ballot where A-first voters truncate can be
 used
 to induce a later-no-harm failure.

 Whether the strange technology that makes up the device implements
 rational election and exclusion counts doesn't matter. As long as
 it's a
 ranked voting method outputting winners and supporting
 truncation, the
 question "does this pass later-no-harm?" makes sense.

 The same goes for things like monotonicity, participation,
 consistency,
 Smith, Condorcet, etc. The criteria say something about the desired
 behavior of a method. Nothing about the inner workings makes the
 criteria inapplicable (apart from some exceptions like the polynomial
 runtime criterion).

 Without a mathematical description of the method, you couldn't be
 sure
 it actually passes later-no-harm or later-no-help, but as soon as you
 found a counterexample, that would settle the question in the
 negative.

 the bstv

 irrationalities to

 traditional

 system,

 As a ranked method, it must fail IIA, which means that strategy must
 sometimes be possible. And as it fails Condorcet, the obvious
 starting
 place to look is for an election where it doesn't pass Condorcet. For
 instance, this:

 549: A>B>C
 366: B>A>C
 366: B>C>A
 366: C>A>B

 A is the Condorcet winner. The first preferences are:
         A: 549, B: 732, C: 366
 and last preferences:
         A: 366, B: 366, C: 915

 so the ratios are:
         A: 366/549 = 0.67
         B: 366/732 = 0.5
         C: 915/366 = 2.5

 so B wins. Then the C>A>B voters have an incentive to vote A>C>B
 instead
 (compromising), after which the counts are:

         A: 366/915 = 0.29
         B: 366/732 = 0.5
         C: 915/0   = infinity

 and A wins. The C>A>B voters prefer A to B, so the strategy is to
 their
 benefit.

 It can be shown that, for methods where a majority can always
 force an
 outcome by coordinating how they vote, then modifying the method
 so that
 it elects the Condorcet winner if there is one never increases the
 proportion of elections where strategy is useful, and may indeed
 reduce it.

 be an

 their

 preference

 know that

 4 or

 thinking -- somewhat!

 value of  38957/58966.

 So by the keep values: A's first preference count is 58966 and last
 preference count is 38957, since the keep value is 38957/58966.

 You say that B's keep value is 38957/39366, i.e. first preference
 count
 of 39366 and last preference count of 38957. But that seems to be in
 reverse order. Indeed, your HTML page shows that it is 39366/38957.

 when
 counting last preferences. I was pretty sure that BSTV would fail
 later-no-harm because the standard way of counting truncations,
 as STV
 does, is to consider everybody not ranked to be equal-ranked for
 last;
 and if you had done that, then it would be possible to induce
 later-no-harm.

 The good news is that you avoid this particular problem if you count
 anything past truncation simply as abstentions. So I guessed wrong,
 which was then cleared up by the example, which shows how useful they
 are :-)

 However, instead it seems that you get later-no-*help* failure.
 Consider
 this modified election:

 18125: A
 20035: A>B>C
 18722: A>C>B
 34488: B>A>C
 38634: C>B>A

 By my count, the first preferences are: A: 56882, B: 34488, C: 38634
 and the last preferences are:           A: 38634, B: 18722, C: 54523
 and the last to first ratios are:       A: 0.68,  B: 0.54,  C: 1.41

 so B wins. But if now the A voters fill out their ballot by voting
 A>C>B, then B's last preference count changes to 36847 and A wins
 instead. This is a violation of later-no-help.

 Ordinary STV passes both.

 I should note that Condorcet methods, that I prefer, fail both.
 My point
 isn't as much that later-no-harm and later-no-help are intrinsically
 good, as that it's much easier to check a claim by concrete evidence
 than by references to personal terminology (which may be hard to
 understand for others or take a lot of time to get acquainted with).


 On a final note, I would say that always counting truncation as
 abstention could lead to an unknown candidate problem: suppose
 there's a
 candidate who nobody has heard of and thus nobody bothers to
 rank. But
 he has a dedicated following all of whom rank him first. If nobody
 obtains a majority, then this candidate could win, e.g. something
 like:

 3300: A>B>C
 3300: B>C>A
 3200: C>A>B
    2: D

 I'm also not entirely sure what's going on with the quota
 transfers. If,
 in the single-winner case, someone who exceeds the quota is
 automatically elected, then there's no need for any transfers.
 However,
 if passing the quota doesn't guarantee victory, then later-no-harm
 failure might actually be possible. Suppose A is just above the quota
 and B is just below it (with B closer to the majority line), then
 if the
 A voters only vote for A, A might win; but if they vote A>B, then the
 surplus might be transferred to B and make B win. Perhaps. As I said,
 I'm not sure how the logic works in that case.

 -km
 ----
 Election-Methods mailing list - see https://electorama.com/em for
 list info

On 02/06/2022 11:28, Richard Lung wrote: > > > Sometimes the keep value quotient, in binomial STV, does not help to > decide an election. It may even make the contest less decisive. Never > the less, the quotient is an extra source of rational information, to > that provided by the quota, as to the decision or indecision of the > public. > > The simple plurality method generally implies, representatively, that > it should not be in a single-member system, but at least in a two > member system, and often in a three or four member system. > > Likewise, I recommend a minimum of a 4 or 5 member system for binomial > STV, for sufficiently representative elections, to produce decisive > results. > > The draft Scottish constitution recommended a minimum of four member > STV constituencies. The Irish constitutional convention recommended a > minimum of five-member STV constituencies. > > The McAllister report on the Welsh Parliament cited an academic > consensus on four to seven member constituencies for sufficient > diversity of representation. > > Four Welsh reports have recommended the single transferable vote. > > Thus, a lack of decisiveness, in single-member binomial STV, is not > necessarily a problem of BSTV but it is a problem of single, double > and even triple member constituencies. The insistence on a decisive > election winner is a presumption of social choice theory. > > The incompleteness theorem of Kurt Gödel is not an insistence on the > “Impossibility” of deductive science. It took the theorem of Kenneth > Arrow to assert that for logical democracy. (The assertion, that no > election method is perfect, is not a scientific statement, and can be > disregarded as such.) > > A first principle of the philosophy of science is not to presume what > one is supposed to be trying to prove. The search for knowledge > requires that ones assumptions may be disproved. > > What elections demonstrate, from the irrational simple plurality > count, to the rationalistic binomial STV, is that popular opinion may > be indecisive. There may be no demonstrable winner. > > What first past the post does do is to provide an administratively > convenient decision, rather than a necessarily popular decision. > > Meek method also incorporates a help to the returning officer. Quota > reduction with exhausted preferences makes for less equitable > placements, but facilitates election to the final seat, in the > multi-member constituency. > > Thus, the impossibility theorem insistence on decisive results amounts > to an imperative for an administrative decision, and not necessarily > popular representation. But the United Statesis a republic, a thing of > the people, not a thing of Administration, or a “rebureau.” > > Regards, > > Richard Lung. > > > On 31/05/2022 01:29, Forest Simmons wrote: >> Kristofer noted in passing a very important and under-appreciated >> advantage of Condorcet methods: >> >> It can be shown that, for methods where a majority can always force >> an outcome by coordinating how they vote, then modifying the method >> so that it elects the Condorcet winner if there is one never >> increases the proportion of elections where strategy is useful, and >> may indeed reduce it. >> >> This is a good reason to routinely include in the description of >> every Universal Domain single winner method that satisfies the >> Majority Criterion, verbiage to the effect ... >> >> "Lacking a candidate that outranks any opponent on more ballots than >> not ..." >> >> -Forest >> >> El sáb., 28 de may. de 2022 9:43 a. m., Kristofer Munsterhjelm >> <km_elmet@t-online.de> escribió: >> >> On 24.05.2022 21:05, Richard Lung wrote: >> > >> > The snag is that these and other criteria were invented for what >> > amounts to uninomial elections, that is elections that don't >> have both, >> > or either, a rational election count and a rational exclusion >> count. >> > Together they make possible the application of the binomial >> theorem, to >> > higher order counts. My binomial STV hand count is just a first >> order >> > binomial count of one election count and one exclusion count. >> >> The criteria are method-agnostic: for any ranked voting method >> (in this >> case, that supports truncation), if someone gives you a failure >> example, >> you can verify if the method passes or fails the criterion without >> knowing anything about the internals of the method. >> >> Put differently, suppose that in a scenario perhaps reminiscent of >> Roadside Picnic, a mysterious device falls out of the sky. And it >> turns >> out that this mysterious device calls elections: you can input ranked >> ballots with a set of buttons and get the results shown as a >> series of >> lights on the other end. >> >> Then as long as it allows for ballots with truncation, it's >> possible to >> check if a particular ballot where A-first voters truncate can be >> used >> to induce a later-no-harm failure. >> >> Whether the strange technology that makes up the device implements >> rational election and exclusion counts doesn't matter. As long as >> it's a >> ranked voting method outputting winners and supporting >> truncation, the >> question "does this pass later-no-harm?" makes sense. >> >> The same goes for things like monotonicity, participation, >> consistency, >> Smith, Condorcet, etc. The criteria say something about the desired >> behavior of a method. Nothing about the inner workings makes the >> criteria inapplicable (apart from some exceptions like the polynomial >> runtime criterion). >> >> Without a mathematical description of the method, you couldn't be >> sure >> it actually passes later-no-harm or later-no-help, but as soon as you >> found a counterexample, that would settle the question in the >> negative. >> >> > I am not aware of any untoward effects of tactical voting on >> the bstv >> > system. I am aware of it doing away with residual >> irrationalities to >> > traditional stv, including Meek method. Tho I accept that >> traditional >> > stv (zero-order stv in relation to binomial stv) is a robust >> system, >> > in practise, as the Hare system of at-large stv/pr. >> >> As a ranked method, it must fail IIA, which means that strategy must >> sometimes be possible. And as it fails Condorcet, the obvious >> starting >> place to look is for an election where it doesn't pass Condorcet. For >> instance, this: >> >> 549: A>B>C >> 366: B>A>C >> 366: B>C>A >> 366: C>A>B >> >> A is the Condorcet winner. The first preferences are: >>         A: 549, B: 732, C: 366 >> and last preferences: >>         A: 366, B: 366, C: 915 >> >> so the ratios are: >>         A: 366/549 = 0.67 >>         B: 366/732 = 0.5 >>         C: 915/366 = 2.5 >> >> so B wins. Then the C>A>B voters have an incentive to vote A>C>B >> instead >> (compromising), after which the counts are: >> >>         A: 366/915 = 0.29 >>         B: 366/732 = 0.5 >>         C: 915/0   = infinity >> >> and A wins. The C>A>B voters prefer A to B, so the strategy is to >> their >> benefit. >> >> It can be shown that, for methods where a majority can always >> force an >> outcome by coordinating how they vote, then modifying the method >> so that >> it elects the Condorcet winner if there is one never increases the >> proportion of elections where strategy is useful, and may indeed >> reduce it. >> >> > BSTV counts require values for all preference positions, which are >> > equal to the number of candidates. Any preference position may >> be an >> > abstention. A citizen who never voted but made an exception of >> their >> > dislike for Donald or Hilary could abstain on their first >> preference >> > but vote for either on their second preference, effecting an >> > exclusion, because there is only one vacancy. >> >> > That is the theory of it. I don't know how well it would work in >> > practise, because there never has been a practise. But I do >> know that >> > democracy is minimised, and evidently works badly, based on single >> > vacancies, in the Anglo-American systems. >> >> > Fully fledged binomial stv, FAB STV, does not work on less than >> 4 or >> > 5 member constituencies, the minimum requirement for a democracy of >> > all the people being represented by their choices. >> >> > Thank you for your examples. They have helped clarify my >> thinking -- somewhat! >> > According to my (accident-prone) working, A wins on a keep >> value of  38957/58966. >> > B also has a less than unity keep value of 38957/39366. The >> > difference is that one can say A has been elected on a quota of >> > 48961.5, with 58966 first preferences. >> > But B has not reached the elective quota. Tho B has not reached the >> > exclusion quota, that only says B has not been excluded. >> >> So by the keep values: A's first preference count is 58966 and last >> preference count is 38957, since the keep value is 38957/58966. >> >> You say that B's keep value is 38957/39366, i.e. first preference >> count >> of 39366 and last preference count of 38957. But that seems to be in >> reverse order. Indeed, your HTML page shows that it is 39366/38957. >> >> >From the keep values, it seems that truncations are not included >> when >> counting last preferences. I was pretty sure that BSTV would fail >> later-no-harm because the standard way of counting truncations, >> as STV >> does, is to consider everybody not ranked to be equal-ranked for >> last; >> and if you had done that, then it would be possible to induce >> later-no-harm. >> >> The good news is that you avoid this particular problem if you count >> anything past truncation simply as abstentions. So I guessed wrong, >> which was then cleared up by the example, which shows how useful they >> are :-) >> >> However, instead it seems that you get later-no-*help* failure. >> Consider >> this modified election: >> >> 18125: A >> 20035: A>B>C >> 18722: A>C>B >> 34488: B>A>C >> 38634: C>B>A >> >> By my count, the first preferences are: A: 56882, B: 34488, C: 38634 >> and the last preferences are:           A: 38634, B: 18722, C: 54523 >> and the last to first ratios are:       A: 0.68,  B: 0.54,  C: 1.41 >> >> so B wins. But if now the A voters fill out their ballot by voting >> A>C>B, then B's last preference count changes to 36847 and A wins >> instead. This is a violation of later-no-help. >> >> Ordinary STV passes both. >> >> I should note that Condorcet methods, that I prefer, fail both. >> My point >> isn't as much that later-no-harm and later-no-help are intrinsically >> good, as that it's much easier to check a claim by concrete evidence >> than by references to personal terminology (which may be hard to >> understand for others or take a lot of time to get acquainted with). >> >> >> On a final note, I would say that always counting truncation as >> abstention could lead to an unknown candidate problem: suppose >> there's a >> candidate who nobody has heard of and thus nobody bothers to >> rank. But >> he has a dedicated following all of whom rank him first. If nobody >> obtains a majority, then this candidate could win, e.g. something >> like: >> >> 3300: A>B>C >> 3300: B>C>A >> 3200: C>A>B >>    2: D >> >> I'm also not entirely sure what's going on with the quota >> transfers. If, >> in the single-winner case, someone who exceeds the quota is >> automatically elected, then there's no need for any transfers. >> However, >> if passing the quota doesn't guarantee victory, then later-no-harm >> failure might actually be possible. Suppose A is just above the quota >> and B is just below it (with B closer to the majority line), then >> if the >> A voters only vote for A, A might win; but if they vote A>B, then the >> surplus might be transferred to B and make B win. Perhaps. As I said, >> I'm not sure how the logic works in that case. >> >> -km >> ---- >> Election-Methods mailing list - see https://electorama.com/em for >> list info >>

On 02.06.2022 19:10, Richard Lung wrote: > > On 02/06/2022 11:28, Richard Lung wrote: >> >> >> Sometimes the keep value quotient, in binomial STV, does not help to >> decide an election. It may even make the contest less decisive. Never >> the less, the quotient is an extra source of rational information, to >> that provided by the quota, as to the decision or indecision of the >> public. >> >> The simple plurality method generally implies, representatively, that >> it should not be in a single-member system, but at least in a two >> member system, and often in a three or four member system. >> >> Likewise, I recommend a minimum of a 4 or 5 member system for binomial >> STV, for sufficiently representative elections, to produce decisive >> results. >> >> The draft Scottish constitution recommended a minimum of four member >> STV constituencies. The Irish constitutional convention recommended a >> minimum of five-member STV constituencies. >> >> The McAllister report on the Welsh Parliament cited an academic >> consensus on four to seven member constituencies for sufficient >> diversity of representation. >> >> Four Welsh reports have recommended the single transferable vote. >> >>   >> >> Thus, a lack of decisiveness, in single-member binomial STV, is not >> necessarily a problem of BSTV but it is a problem of single, double >> and even triple member constituencies. The insistence on a decisive >> election winner is a presumption of social choice theory. I'm not sure what you're referring to, but the Duggan-Schwartz theorem states that for deterministic ranked multi-winner methods, unless the method always returns the set of every voter's first preferences as the outcome, there will exist elections where strategic voting pays off. So a multi-winner method has to be very tie-prone if it's to be unmanipulable. >> The incompleteness theorem of Kurt Gödel is not an insistence on the >> “Impossibility” of deductive science. It took the theorem of Kenneth >> Arrow to assert that for logical democracy. (The assertion, that no >> election method is perfect, is not a scientific statement, and can be >> disregarded as such.) Gödel's incompleteness theorem is a good example. It may not be a practical problem that the mathematical system can't prove every fact about itself. (Usually one gets around this by just creating a more powerful system to prove things with.) But it shows that some property that would really simplify things is unattainable. Similarly with voting methods: it may not be a practical problem that strategy is possible, but the lack of an unmanipulable deterministic method means we have to pick our poison about which kind of strategy to allow (that hopefully does the least harm). Or sidestep the question by looking at the greater context (analogous to creating a more powerful system) and use something like sortition instead of elections. >> Thus, the impossibility theorem insistence on decisive results amounts >> to an imperative for an administrative decision, and not necessarily >> popular representation. But the United Statesis a republic, a thing of >> the people, not a thing of Administration, or a “rebureau.” What's a rebureau? -km

El jue., 2 de jun. de 2022 11:33 a. m., Kristofer Munsterhjelm < km_elmet@t-online.de> escribió: > On 02.06.2022 19:10, Richard Lung wrote: > > > > On 02/06/2022 11:28, Richard Lung wrote: > >> > >> > >> Sometimes the keep value quotient, in binomial STV, does not help to > >> decide an election. It may even make the contest less decisive. Never > >> the less, the quotient is an extra source of rational information, to > >> that provided by the quota, as to the decision or indecision of the > >> public. > >> > >> The simple plurality method generally implies, representatively, that > >> it should not be in a single-member system, but at least in a two > >> member system, and often in a three or four member system. > >> > >> Likewise, I recommend a minimum of a 4 or 5 member system for binomial > >> STV, for sufficiently representative elections, to produce decisive > >> results. > >> > >> The draft Scottish constitution recommended a minimum of four member > >> STV constituencies. The Irish constitutional convention recommended a > >> minimum of five-member STV constituencies. > >> > >> The McAllister report on the Welsh Parliament cited an academic > >> consensus on four to seven member constituencies for sufficient > >> diversity of representation. > >> > >> Four Welsh reports have recommended the single transferable vote. > >> > >> > >> > >> Thus, a lack of decisiveness, in single-member binomial STV, is not > >> necessarily a problem of BSTV but it is a problem of single, double > >> and even triple member constituencies. The insistence on a decisive > >> election winner is a presumption of social choice theory. > > I'm not sure what you're referring to, but the Duggan-Schwartz theorem > states that for deterministic ranked multi-winner methods, unless the > method always returns the set of every voter's first preferences as the > outcome, there will exist elections where strategic voting pays off. > > So a multi-winner method has to be very tie-prone if it's to be > unmanipulable. > > >> The incompleteness theorem of Kurt Gödel is not an insistence on the > >> “Impossibility” of deductive science. It took the theorem of Kenneth > >> Arrow to assert that for logical democracy. (The assertion, that no > >> election method is perfect, is not a scientific statement, and can be > >> disregarded as such.) > > Gödel's incompleteness theorem is a good example. It may not be a > practical problem that the mathematical system can't prove every fact > about itself. (Usually one gets around this by just creating a more > powerful system to prove things with.) > > But it shows that some property that would really simplify things is > unattainable. Similarly with voting methods: it may not be a practical > problem that strategy is possible, but the lack of an unmanipulable > deterministic method means we have to pick our poison about which kind > of strategy to allow (that hopefully does the least harm). > > Or sidestep the question by looking at the greater context (analogous to > creating a more powerful system) and use something like sortition > instead of elections. > I compare this to the absolute limitations of thermodynamics on heat engine efficiency, but that doesn't mean that all internal combustion engines are equally bad, or that nuclear fusion (hence solar power) cannot surpass chemical combustion in efficiency. > > >> Thus, the impossibility theorem insistence on decisive results amounts > >> to an imperative for an administrative decision, and not necessarily > >> popular representation. But the United Statesis a republic, a thing of > >> the people, not a thing of Administration, or a “rebureau.” > > What's a rebureau? > > -km >