Calisthenics tutorials make extensive use of "progressions", so that almost anybody with enough patience can progress by degrees over time from a leg assisted partial range "Australian Pullup" to a full range of motion standard form pullup. That's what we are trying to do with our "Pathways to Success" thread ... to make a gradual progression from relatively primitive to more solidly advanced methods. This progression is a progression of agenda based methods ... with Sequential Pairwise Elimination SPE right in the middle of it. Of all the single winner methods that have been used for centuries, SPE is the most solid, respectable, versatile, and unknown to the public at large ... though well known to organizations that convene Deliberative Assemblies goverened by Robert's Rules of Order. We have two things to consider... 1. How to set a good agenda ... and 2. How to process the agenda to extract a winner from it. The agenda plays the same role that seeding does in a tournament. It gives a nominal order that serves more as a tie breaking order than anything else. In the usual case (when rock paper Scissors ties are non existent), the agenda order has no effect on the outcome. The most important thing about the agenda is that it be based on some deterministic statistic correlated with democratic support and not easily distorted by proliferation of clones among the candidates. The agenda processing must be based on the majority rule principle, and must have built in safeguards against strategical manipulation by unscrupulous influencers ... the kinds of manipulations that create the rare, but not rare enough, cycles that can make the outcome depend on the agenda order. We will touch on these aspects in our examples. These concerns are not limited to agenda based methods ... but good agenda based methods (like the ones in our progression) deal with them more transparently and effectively than any other deterministic, single winner methods that we know of ... and we have carefully compared the methods in our progression with the realistic extant alternatives ... as well as many others. To be continued ...

On Thu, Mar 23, 2023, 10:07 PM Forest Simmons <forest.simmons21@gmail.com> wrote: > Calisthenics tutorials make extensive use of "progressions", so that > almost anybody with enough patience can progress by degrees over time from > a leg assisted partial range "Australian Pullup" to a full range of motion > standard form pullup. > > That's what we are trying to do with our "Pathways to Success" thread ... > to make a gradual progression from relatively primitive to more solidly > advanced methods. > > This progression is a progression of agenda based methods ... with > Sequential Pairwise Elimination SPE right in the middle of it. > > Of all the single winner methods that have been used for centuries, SPE is > the most solid, respectable, versatile, and unknown to the public at large > ... though well known to organizations that convene Deliberative Assemblies > goverened by Robert's Rules of Order. > > We have two things to consider... 1. How to set a good agenda ... and 2. > How to process the agenda to extract a winner from it. > > The agenda plays the same role that seeding does in a tournament. It gives > a nominal order that serves more as a tie breaking order than anything > else. In the usual case (when rock paper Scissors ties are non existent), > the agenda order has no effect on the outcome. The most important thing > about the agenda is that it be based on some deterministic statistic > correlated with democratic support and not easily distorted by > proliferation of clones among the candidates. > > The agenda processing must be based on the majority rule principle, and > must have built in safeguards against strategical manipulation by > unscrupulous influencers ... the kinds of manipulations that create the > rare, but not rare enough, cycles that can make the outcome depend on the > agenda order. > > We will touch on these aspects in our examples. > > These concerns are not limited to agenda based methods ... but good agenda > based methods (like the ones in our progression) deal with them more > transparently and effectively than any other deterministic, single winner > I should have included Universal Domain in this qualification ... comparing non UD methods like Majority Judgment or Approval Sorted Margins with the methods in our progression is like comparing Steriod Jacked Body Builders with Natties. methods that we know of ... and we have carefully compared the methods in > our progression with the realistic extant alternatives ... as well as many > others. > > To be continued ... > > > > > > >

Continuing onward... let's talk about agenda setting first. An agenda is a complete ranking of the candidates ... so a good agenda is a good complete ranking of the candidates. But if we already have a good complete ranking of the candidates, then we're done ... just use that ranking as our finish order ... right? Well kinda! In traditional use of SPE in Deliberative Assemblies the agenda order is set by wrangling,horse trading, and other highly political, exterior, non Universal Domain methods. The best of these is in the context of alternatives to a status quo. For example, the participants are asked which of the alternatives they prefer to the status quo. The more participants that prefer any particular alternative, the more favorable position it gets to occupy on the agenda. In other words, the agenda is set by an Approval vote. Or if each participant rates the alternatives on a scale of one to ten, then those scores determine the agenda order. So ideally, SPE ballots should allow complete preference information along with additional information like grades, scores, or approval cutoffs: so the preference information can be used in the elimination final stage ... after the agenda has been established by use of the approval, score, or judgment information. But our challenge is to stay strictly within the "Universal Domain" meaning ordinal input only ... that is, pure unadorned RCV style ballots. So somehow we have to get a decent nominal order from the ordinal ballots without any input exterior to the Universal Domain. Why not just use first place votes? The problem is vote splitting ... the same spoiler problem that is the raison de etre of voting reform in the first place ... the reason approval voting is used in traditional agenda setting ... the reason that brainstorming sessions suspend judgment until a later stage ... first the bulking before the cutting ... the processing stage is a refinement of the first approximation ballpark stage that is based on the more reliable direct majorrity comparison information.governing each elimination. Why not use Borda Counts? The vote splitting would away, but at the expense of a more subtle distortion ... an unfair advantage to the candidate with the most clones ... just as votes splitting methods like Plurality disadvantage candidates with too many clones ... Borda is hard on candidates that have too few clones to prop up their Borda count. So these considerations suggest something between Borda and Plurality ... something called Implicit Approval. A candidate's implicit approval is the number of ballots on which the candidate is ranked above bottom (i.e. ranked ahead of at least one candidate), which is a kind of minimal standard of approval ... nut plenty good for agenda setting which is not supposed to be the final order ... but just a nominal "seed" order to keep the agenda deterministic and correlated with the questions of favorabie vs unfavorable, promising or not, strong or weak, etc. As we pointed out before, the agenda order makes no difference in the usual case ... whenever there is one candidate that is preferred in every head-head contest ... that candidate will never be eliminated, because agenda based eliminations are always done by majority vote of the participating voters ... unlike in the case of IRV, for example. Still, it is important in public elections that the agendas be non random, decisive, etc and have as high a degree of correlation with the public will as possible without amounting to a full blown elaborate stand alone election method in its own right ... otherwise we could just use Ranked Pairs as an agenda setter. We need something simple like Approval ... and the closest thing to Approval in the Universal Domain is Implicit Approval. The first place votes idea that we rejected for setting the agenda is perfectly adequate for breaking ties when two candidates have the same implicit Approval, especially if equal first rankings are allowed. There is a mild tension against both equal Top and equal Bottom usage in the UD domain because it creates a tradeoff between the need for unequal preference expression for use in the agenda processing (on the one hand) and the need to use equal whole Top/ Bottom approval/ disapproval counts for clone free agenda setting (on the other hand). That tension is much weaker ... practically non existant really, at the Bottom ... which is why we reserve the equal Top count for tipping the balance in the relatively rare cases where candidates' Bottom counts might be identical (resulting in implicit approval ties). The only other UD agenda setting method that we have found to be both simple and adequate is through the Max Pairwise Support scores. The support score for one candidate relative to another is information that is essential anyway for the majority eliminations that are central to the agenda processing ... so why not take advantage of that information in the agenda setting stage? The pairwise support score of candidate X relative to candidate Y is the number of ballots on which candidate X is ranked ahead of candidate Y. So X's agenda score is the highest of these scores against any opponent Y. X's position on the agenda is determined by her best support relative to or in comparison with the candidate that "let her win" the most votes, so to speak. You could say that the candidate whose Max Pairwise Support is minimal is kind of similar to the candidate with the smallest Implicit Approval ... and it turns out that they are indeed the same candidate in our crucial examples ... where they are the first candidate to be eliminated. Example 1 48 C 28 A>B 24 B (sincere is B>A) The Implicit Approvals of A, B, and C are respectively 28, 52, and 48 ... so A has the smallest IA. The respective MaxPS values are also 28, 52, and 48. So the elimination agenda order (from least to most favorable) is A C B. All of our agenda processing methods eliminate A first because C is preferred over A on 48 ballots while A is preferred over C on only 28 ballots. Our (new) methods stop there because (in the advanced versions) no candidate is preferred over both A and C ... and (in the simplest version) only the candidate with the strongest victory over the first eliminated candidate is kept. The old SPE method goes on to eliminate C leaving B as winner ... which is unfortunate, because in this example, this rewards B for an insincere truncation ... having thrown the sincere CW (namely A) under the bus. It's not just old SPE that fails here ... all of the classical Condorcet methods like Ranked Pairs, CSSD. MjnMax, etc fail .. because they have no way of knowing when to stop going around the artificial cycle created by the insincere truncation of A by the B faction! That's enough for today ... To be continued ... On Fri, Mar 24, 2023, 10:38 AM Forest Simmons <forest.simmons21@gmail.com> wrote: > > > On Thu, Mar 23, 2023, 10:07 PM Forest Simmons <forest.simmons21@gmail.com> > wrote: > >> Calisthenics tutorials make extensive use of "progressions", so that >> almost anybody with enough patience can progress by degrees over time from >> a leg assisted partial range "Australian Pullup" to a full range of motion >> standard form pullup. >> >> That's what we are trying to do with our "Pathways to Success" thread ... >> to make a gradual progression from relatively primitive to more solidly >> advanced methods. >> >> This progression is a progression of agenda based methods ... with >> Sequential Pairwise Elimination SPE right in the middle of it. >> >> Of all the single winner methods that have been used for centuries, SPE >> is the most solid, respectable, versatile, and unknown to the public at >> large ... though well known to organizations that convene Deliberative >> Assemblies goverened by Robert's Rules of Order. >> >> We have two things to consider... 1. How to set a good agenda ... and 2. >> How to process the agenda to extract a winner from it. >> >> The agenda plays the same role that seeding does in a tournament. It >> gives a nominal order that serves more as a tie breaking order than >> anything else. In the usual case (when rock paper Scissors ties are non >> existent), the agenda order has no effect on the outcome. The most >> important thing about the agenda is that it be based on some deterministic >> statistic correlated with democratic support and not easily distorted by >> proliferation of clones among the candidates. >> >> The agenda processing must be based on the majority rule principle, and >> must have built in safeguards against strategical manipulation by >> unscrupulous influencers ... the kinds of manipulations that create the >> rare, but not rare enough, cycles that can make the outcome depend on the >> agenda order. >> >> We will touch on these aspects in our examples. >> >> These concerns are not limited to agenda based methods ... but good >> agenda based methods (like the ones in our progression) deal with them more >> transparently and effectively than any other deterministic, single winner >> > > I should have included Universal Domain in this qualification ... > comparing non UD methods like Majority Judgment or Approval Sorted Margins > with the methods in our progression is like comparing Steriod Jacked Body > Builders with Natties. > > methods that we know of ... and we have carefully compared the methods in >> our progression with the realistic extant alternatives ... as well as many >> others. >> >> To be continued ... >> >> >> >> >> >> >>

Another Example... Assume the C faction to be smallest ... with any two factions constituting a majority: a A>B(sincere A>C) b B>C c C (sincere C>A) Candidate C, the sincere CW has truncated A as a defensive precaution. A buried C to create a cycle that would benefit it under RP, CSSD, River, MinMax, etc. [The sincere CW is squeezed out under IRV, ... but in practice the B faction voters would compromise to save C, which they prefer over A. IRV does this under full information conditions with rational strategic voters ... but it's not a ringing endorsement of IRV.] Our agenda order, whether based on implicit approval or max pairwise support is (from least favorable to most promising) A C B. Under traditional SPE, candidateC survives the A C comparison but keeps going (because like Mister Magoo it has no clue) and gives away its rightful victory to B. At least it did not reward the burying faction A. The classical Condorcet methods all break the cycle at the weakest defeat A>B ... so they too elect B. How about our new agenda based methods? The simplest one elects the strongest victor C over the "bottom" agenda item A ... rescuing the sincere CW. The more advanced version eliminates the nominally worst candidate A and the candidate (B) that it beats, leaving only C, the sincere CW. I hope you can see the superiority of the new agenda methods over the old in this context ... the context of insincere burial (this example) as well as insincere truncation defection in the previous example where traditional Condorcet rewarded the B faction for throwing its coalition buddy A under the bus. One might say ... "But these cases are relatively rare ... most of the time nobody thinks to subvert the sincere CW by insincere reversals and truncations." It doesn't matter if our fire extinguisher works very well, because fires are rare! But those rare cases are the only cases where the Condorcet completion method matters... and if the completion method rewards the unscrupulous manipulators, those cases will gradually become less rare through positive feedback ... the kind of unstable dynamic that all good policies (worthy of the name) guard against. If our manipulation resistant methods were more expensive than RP or CSSD or traditional SPE or IRV, that would be one thing ... but the new methods are actually cheaper than the old ... because, instead of wandering around in the desert, they immediately stop after simply and quickly discerning the winner. Compare the following "first baby step method" to CSSD or traditional SPE: Lacking an undefeated candidate, elect the candidate with the strongest defeat over the candidate at the "bottom" of the agenda. This is simpler, cheaper, and more effective than any EM proposal heretofore publicly tendered. It is monotonic, clone free, efficiently summable, manipulation resistant, and transparently easy to explain in both concept and operation. It is the first simple step to the following Banks efficient elimination method that even now stands by in the wings ready to replace it ... should any other proposal start to catch up to it in the future: 1. Update the agenda by sink sorting it pairwise. 2. Update it again by eliminating from it every candidate that does not defeat its "bottom" candidate Z (including Z itself). 3. While more than one candidate remains, repeat steps 1&2. That's it! This is a Cadillac generalization of the first, baby-step agenda method that we just talked about ... which is already uniformly more suitable for public proposal compared to any extant voing method in the deterministic, single winner RCV category ... which excludes MaxParC, Majority Judgment, Score Sorted Margins, Asset Voting, Chiastic Approval, Dyadic Approval, Ranked Ranks, etc. I hope that puts into current perspective the things we've been writing about over the last 22 years. Thanks! -Forest On Fri, Mar 24, 2023, 5:46 PM Forest Simmons <forest.simmons21@gmail.com> wrote: > Continuing onward... let's talk about agenda setting first. > > An agenda is a complete ranking of the candidates ... so a good agenda is > a good complete ranking of the candidates. > > But if we already have a good complete ranking of the candidates, then > we're done ... just use that ranking as our finish order ... right? > > Well kinda! > > In traditional use of SPE in Deliberative Assemblies the agenda order is > set by wrangling,horse trading, and other highly political, exterior, non > Universal Domain methods. > > The best of these is in the context of alternatives to a status quo. For > example, the participants are asked which of the alternatives they prefer > to the status quo. The more participants that prefer any particular > alternative, the more favorable position it gets to occupy on the agenda. > > In other words, the agenda is set by an Approval vote. Or if each > participant rates the alternatives on a scale of one to ten, then those > scores determine the agenda order. > > So ideally, SPE ballots should allow complete preference information along > with additional information like grades, scores, or approval cutoffs: so > the preference information can be used in the elimination final stage ... > after the agenda has been established by use of the approval, score, or > judgment information. > > But our challenge is to stay strictly within the "Universal Domain" > meaning ordinal input only ... that is, pure unadorned RCV style ballots. > > So somehow we have to get a decent nominal order from the ordinal ballots > without any input exterior to the Universal Domain. > > Why not just use first place votes? > > The problem is vote splitting ... the same spoiler problem that is the > raison de etre of voting reform in the first place ... the reason approval > voting is used in traditional agenda setting ... the reason that > brainstorming sessions suspend judgment until a later stage ... first the > bulking before the cutting ... the processing stage is a refinement of the > first approximation ballpark stage that is based on the more reliable > direct majorrity comparison information.governing each elimination. > > Why not use Borda Counts? > > The vote splitting would away, but at the expense of a more subtle > distortion ... an unfair advantage to the candidate with the most clones > ... just as votes splitting methods like Plurality disadvantage candidates > with too many clones ... Borda is hard on candidates that have too few > clones to prop up their Borda count. > > So these considerations suggest something between Borda and Plurality ... > something called Implicit Approval. > > A candidate's implicit approval is the number of ballots on which the > candidate is ranked above bottom (i.e. ranked ahead of at least one > candidate), which is a kind of minimal standard of approval ... nut plenty > good for agenda setting which is not supposed to be the final order ... but > just a nominal "seed" order to keep the agenda deterministic and correlated > with the questions of favorabie vs unfavorable, promising or not, strong or > weak, etc. > > As we pointed out before, the agenda order makes no difference in the > usual case ... whenever there is one candidate that is preferred in every > head-head contest ... that candidate will never be eliminated, because > agenda based eliminations are always done by majority vote of the > participating voters ... unlike in the case of IRV, for example. > > Still, it is important in public elections that the agendas be non random, > decisive, etc and have as high a degree of correlation with the public will > as possible without amounting to a full blown elaborate stand alone > election method in its own right ... otherwise we could just use Ranked > Pairs as an agenda setter. > > We need something simple like Approval ... and the closest thing to > Approval in the Universal Domain is Implicit Approval. > > The first place votes idea that we rejected for setting the agenda is > perfectly adequate for breaking ties when two candidates have the same > implicit Approval, especially if equal first rankings are allowed. > > There is a mild tension against both equal Top and equal Bottom usage in > the UD domain because it creates a tradeoff between the need for unequal > preference expression for use in the agenda processing (on the one hand) > and the need to use equal whole Top/ Bottom approval/ disapproval counts > for clone free agenda setting (on the other hand). > > That tension is much weaker ... practically non existant really, at the > Bottom ... which is why we reserve the equal Top count for tipping the > balance in the relatively rare cases where candidates' Bottom counts might > be identical (resulting in implicit approval ties). > > The only other UD agenda setting method that we have found to be both > simple and adequate is through the Max Pairwise Support scores. > > The support score for one candidate relative to another is information > that is essential anyway for the majority eliminations that are central to > the agenda processing ... so why not take advantage of that information in > the agenda setting stage? > > The pairwise support score of candidate X relative to candidate Y is the > number of ballots on which candidate X is ranked ahead of candidate Y. So > X's agenda score is the highest of these scores against any opponent Y. > X's position on the agenda is determined by her best support relative to > or in comparison with the candidate that "let her win" the most votes, so > to speak. > > You could say that the candidate whose Max Pairwise Support is minimal is > kind of similar to the candidate with the smallest Implicit Approval ... > and it turns out that they are indeed the same candidate in our crucial > examples ... where they are the first candidate to be eliminated. > > Example 1 > > 48 C > 28 A>B > 24 B (sincere is B>A) > > The Implicit Approvals of A, B, and C are respectively 28, 52, and 48 ... > so A has the smallest IA. > > The respective MaxPS values are also 28, 52, and 48. > > So the elimination agenda order (from least to most favorable) is A C B. > > All of our agenda processing methods eliminate A first because C is > preferred over A on 48 ballots while A is preferred over C on only 28 > ballots. > > Our (new) methods stop there because (in the advanced versions) no > candidate is preferred over both A and C ... and (in the simplest version) > only the candidate with the strongest victory over the first eliminated > candidate is kept. > > The old SPE method goes on to eliminate C leaving B as winner ... which is > unfortunate, because in this example, this rewards B for an insincere > truncation ... having thrown the sincere CW (namely A) under the bus. > > It's not just old SPE that fails here ... all of the classical Condorcet > methods like Ranked Pairs, CSSD. MjnMax, etc fail .. > because they have no way of knowing when to stop going around the > artificial cycle created by the insincere truncation of A by the B faction! > > That's enough for today ... > > To be continued ... > > > > > > On Fri, Mar 24, 2023, 10:38 AM Forest Simmons <forest.simmons21@gmail.com> > wrote: > >> >> >> On Thu, Mar 23, 2023, 10:07 PM Forest Simmons <forest.simmons21@gmail.com> >> wrote: >> >>> Calisthenics tutorials make extensive use of "progressions", so that >>> almost anybody with enough patience can progress by degrees over time from >>> a leg assisted partial range "Australian Pullup" to a full range of motion >>> standard form pullup. >>> >>> That's what we are trying to do with our "Pathways to Success" thread >>> ... to make a gradual progression from relatively primitive to more solidly >>> advanced methods. >>> >>> This progression is a progression of agenda based methods ... with >>> Sequential Pairwise Elimination SPE right in the middle of it. >>> >>> Of all the single winner methods that have been used for centuries, SPE >>> is the most solid, respectable, versatile, and unknown to the public at >>> large ... though well known to organizations that convene Deliberative >>> Assemblies goverened by Robert's Rules of Order. >>> >>> We have two things to consider... 1. How to set a good agenda ... and 2. >>> How to process the agenda to extract a winner from it. >>> >>> The agenda plays the same role that seeding does in a tournament. It >>> gives a nominal order that serves more as a tie breaking order than >>> anything else. In the usual case (when rock paper Scissors ties are non >>> existent), the agenda order has no effect on the outcome. The most >>> important thing about the agenda is that it be based on some deterministic >>> statistic correlated with democratic support and not easily distorted by >>> proliferation of clones among the candidates. >>> >>> The agenda processing must be based on the majority rule principle, and >>> must have built in safeguards against strategical manipulation by >>> unscrupulous influencers ... the kinds of manipulations that create the >>> rare, but not rare enough, cycles that can make the outcome depend on the >>> agenda order. >>> >>> We will touch on these aspects in our examples. >>> >>> These concerns are not limited to agenda based methods ... but good >>> agenda based methods (like the ones in our progression) deal with them more >>> transparently and effectively than any other deterministic, single winner >>> >> >> I should have included Universal Domain in this qualification ... >> comparing non UD methods like Majority Judgment or Approval Sorted Margins >> with the methods in our progression is like comparing Steriod Jacked Body >> Builders with Natties. >> >> methods that we know of ... and we have carefully compared the methods in >>> our progression with the realistic extant alternatives ... as well as many >>> others. >>> >>> To be continued ... >>> >>> >>> >>> >>> >>> >>>