Matchup win and loss counts:

 Ava: 4 wins (against ...) and 2 losses (to ...)

 Bianca: 4 wins (against ...) and 2 losses (to ...)

 Cedric: 3 wins (against ...) and 3 losses (to ...)

 Deegan: 3 wins (against ...) and 3 losses (to ...)

 Eli: 2 wins (against ...) and 4 losses (to ...)

 Fabio: 0 wins and 6 losses


 The result is a tie between Ava and Bianca because they each have

 Ava: 213

 Bianca: 123

 So Ava wins!

On 3/30/2022 11:51 PM, Colin Champion wrote: > ... is the candidate with the highest support count not the > candidate with the highest Borda score? Have you not reinvented > Dasgupta-Maskin? Borda count is a positional voting method: https://en.wikipedia.org/wiki/Positional_voting As a tie breaker, only the candidates who are tied are considered in this count. When the tie is between just two candidates, the Borda count would still use the (positional) numbers assigned by the voters. In contrast, I'm recommending a counting method that disregards which position contains the mark being counted. So a two-candidate tie becomes simple plurality counting. To repeat, I'm suggesting breaking a tie by using pairwise support counts. On one ballot the pairwise support count is the number of candidates who are ranked lower than the candidate getting the support count. Those counts are added across all the ballots to yield that candidate's pairwise support count. A big advantage is that it can be counted directly from the ballots, without first creating a pairwise matrix. Although software would use the pairwise matrix approach, voters and the legal description and the tabulated results would not mention the pairwise matrix. Richard Fobes The VoteFair guy On 3/30/2022 11:51 PM, Colin Champion wrote: > Richard – is the candidate with the highest support count not the > candidate with the highest Borda score? Have you not reinvented > Dasgupta-Maskin? > Colin > > > On 31/03/2022 05:58, Richard, the VoteFair guy wrote: >> Here I'm suggesting a way to improve the recently (fall 2021) created >> "Ranked Robin" method, which is described at Electowiki at this link: >> >> https://electowiki.org/wiki/Ranked_Robin >> >> The improvement is to replace the first-level tie breaker -- which >> looks at margins calculated from the pairwise matrix -- with "pairwise >> support counts" -- which are easily described without using any >> numbers from the pairwise matrix. >> >> Starting from the beginning ... >> >> Currently the Ranked Robin method is described this way: >> >> "Elect the candidate who pairwise beats the greatest number of >> candidates." >> >> That's the method described by Ramon Llull (in 1299). >> >> According to Electowiki that's been improved to become the Copeland >> method, which elects "the candidate with the most (pairwise victories >> minus pairwise defeats)." >> >> According to Wikipedia the Copeland method doesn't do the subtraction >> and instead adds "half the number of candidates with whom he or she >> has a preference tie." >> >> All of these Copeland method variations produce lots of ties. >> >> So of course the Ranked Robin method needs tie breakers. Here's the >> first-level tie breaker as it's currently specified: >> >> "For each finalist, subtract the number of votes preferring each other >> finalist from the number of votes preferring them over each other >> finalist. The finalist with the greatest total difference is elected." >> >> A big disadvantage of this Ranked Robin tie breaker is that it uses >> numbers from the pairwise matrix. Yet one of the stated goals of the >> Ranked Robin method is to avoid confusing voters with the pairwise >> matrix. >> >> Therefore I suggest replacing this tie-breaker method with the use of >> "pairwise support counts." These counts are part of the "Instant >> Pairwise Elimination" (IPE) method, which is described at Electowiki >> at this link: >> >> https://electowiki.org/wiki/Instant_Pairwise_Elimination >> >> It says: >> >> "If an elimination round has no pairwise-losing candidate, then the >> method eliminates the candidate with the largest pairwise opposition >> count, which is determined by counting on each ballot the number of >> not-yet-eliminated candidates who are ranked above that candidate, and >> adding those numbers across all the ballots. If there is a tie for the >> largest pairwise opposition count, the method eliminates the candidate >> with the smallest pairwise support count, which similarly counts >> support rather than opposition. ..." >> >> Of course the second-level tie-breaker would be to use pairwise >> opposition counts. (The pairwise support counts and pairwise >> opposition counts are not always symmetrical.) >> >> Notice that the numbers in the pairwise matrix do not need to be >> mentioned. >> >> Yes, the software will calculate the pairwise support counts from the >> numbers in the pairwise matrix. But that fact doesn't need to be >> mentioned -- to the voters, or in the legal description. >> >> The resulting improved Ranked Robin method can be described as follows: >> >> "The [improved] Ranked Robin method elects the candidate who has the >> most number of one-on-one wins against every other candidate plus half >> the number of one-on-one ties. [*] If more than one candidate has the >> same largest number, the method elects from those tied candidates the >> candidate with the highest pairwise support count. The pairwise >> support count for each of the tied candidates is the sum, across all >> the ballots, of the number of tied [**] candidates who are ranked >> lower than the candidate whose pairwise support count is being counted." >> >> [*] The wording can be adjusted depending on which Copeland variation >> is desired. Adding the words "minus the number of one-on-one losses" >> would specify the other variation. >> >> [**] Importantly, the ballot marks for the non-tied candidates must be >> ignored when resolving the tie. >> >> When the election results are displayed, they might look something >> like this, where the names are from the Ranked Robin article, and the >> numbers don't apply to any particular case: >> >> >> Matchup win and loss counts: >> >> Ava: 4 wins (against ...) and 2 losses (to ...) >> >> Bianca: 4 wins (against ...) and 2 losses (to ...) >> >> Cedric: 3 wins (against ...) and 3 losses (to ...) >> >> Deegan: 3 wins (against ...) and 3 losses (to ...) >> >> Eli: 2 wins (against ...) and 4 losses (to ...) >> >> Fabio: 0 wins and 6 losses >> >> >> The result is a tie between Ava and Bianca because they each have >> 4 wins, and that's more than any other candidate. Considering just >> these tied candidates, their pairwise support counts are: >> >> Ava: 213 >> >> Bianca: 123 >> >> So Ava wins! >> >> >> Notice there's no need to show a pairwise matrix! >> >> To prevent a potential source of confusion, the Wikipedia article >> about the Borda count begins with the words "The Borda count is a >> family of positional voting rules which gives each candidate, for each >> ballot, a number of points corresponding to the number of candidates >> ranked lower." The last portion of this sentence describes pairwise >> support counts, but it has nothing to do with the Borda count. The >> Wikipedia article for "positional voting" correctly says: "Positional >> voting is a ranked voting electoral system in which the options or >> candidates receive points based on their rank position on each ballot >> and the one with the most points overall wins." The remainder of >> Wikipedia's Borda count article correctly specifies positional voting >> in the descriptions and examples. The Borda count article at >> Electowiki does not include this first-sentence mistake. I'm going to >> let someone else figure out how the first sentence in Wikipedia should >> be worded. (I'd rather fight other battles.) >> >> I'm calling attention to this difference between pairwise support >> counts and the Borda count because this issue has previously caused >> confusion in this forum. >> >> Getting back to the Ranked Robin method, this improved version is not >> likely to significantly increase the failure rates of the most >> important failure criteria, and it's likely to reduce some failure rates. >> >> Currently the Ranked Robin article claims that the method passes some >> fairness criteria that it actually doesn't pass. When the Ranked >> Robin article is improved to include a concise description of the >> method (which should be near the beginning), some experts here can >> identify which of the listed "pass" criteria need to be moved to the >> listed "fail" criteria. >> >> Interestingly, the Ranked Robin method and its name were created by >> people who have previously promoted only STAR voting. I'm pleased >> that they are finally recognizing that STAR ballots are not going to >> replace ranked choice ballots throughout the US. And that they >> recognize the need to promote a method that takes advantage of the >> Forward Party's recommendation of "ranked choice voting." >> >> Looking at the broader perspective ... >> >> The current version of Ranked Robin already has these advantages: >> >> * Uses pairwise vote counting, which looks deeper into the ballot >> preferences compared to instant-runoff voting. >> >> * Is precinct summable. >> >> * Allows voters to mark more than one candidate at the same ranking >> level. >> >> I suggest making it even easier to understand by using pairwise >> support counts. This improvement will eliminate the need to educate >> voters about the pairwise matrix. And I believe this change will >> still provide a similar level of fairness. >> >> Certainly, in multiple ways, it's much better than instant-runoff voting. >> >> Richard Fobes >> The VoteFair guy >> ---- >> Election-Methods mailing list - see https://electorama.com/em for list >> info >

Richard – there are two ways of using a Borda tiebreak, sometimes written "Llull//Borda" and "Llull,Borda". It sounds like you understood me to be attributing "Llull,Borda" to you while you were actually advocating "Llull//Borda". (I have no idea which of these was Dasgupta and Maskin’s preference – I don’t think they were clear.) Certainly Llull//Borda reduces to a plurality choice between two tied candidates.    Other tiebreaks (eg. minimax) can be used in the same two ways, which is why a fairly general notation exists. I can't say I like it as a notation, since it's far from self-explanatory.       Colin On 31/03/2022 18:10, Richard, the VoteFair guy wrote: > On 3/30/2022 11:51 PM, Colin Champion wrote: > > ... is the candidate with the highest support count not the > > candidate with the highest Borda score? Have you not reinvented > > Dasgupta-Maskin? > > Borda count is a positional voting method: > > https://en.wikipedia.org/wiki/Positional_voting > > As a tie breaker, only the candidates who are tied are considered in > this count. > > When the tie is between just two candidates, the Borda count would > still use the (positional) numbers assigned by the voters. > > In contrast, I'm recommending a counting method that disregards which > position contains the mark being counted.  So a two-candidate tie > becomes simple plurality counting. > > To repeat, I'm suggesting breaking a tie by using pairwise support > counts.  On one ballot the pairwise support count is the number of > candidates who are ranked lower than the candidate getting the support > count.  Those counts are added across all the ballots to yield that > candidate's pairwise support count. > > A big advantage is that it can be counted directly from the ballots, > without first creating a pairwise matrix.  Although software would use > the pairwise matrix approach, voters and the legal description and the > tabulated results would not mention the pairwise matrix. > > Richard Fobes > The VoteFair guy > > > On 3/30/2022 11:51 PM, Colin Champion wrote: >> Richard – is the candidate with the highest support count not the >> candidate with the highest Borda score? Have you not reinvented >> Dasgupta-Maskin? >>    Colin >> >> >> On 31/03/2022 05:58, Richard, the VoteFair guy wrote: >>> Here I'm suggesting a way to improve the recently (fall 2021) created >>> "Ranked Robin" method, which is described at Electowiki at this link: >>> >>>   https://electowiki.org/wiki/Ranked_Robin >>> >>> The improvement is to replace the first-level tie breaker -- which >>> looks at margins calculated from the pairwise matrix -- with "pairwise >>> support counts" -- which are easily described without using any >>> numbers from the pairwise matrix. >>> >>> Starting from the beginning ... >>> >>> Currently the Ranked Robin method is described this way: >>> >>> "Elect the candidate who pairwise beats the greatest number of >>> candidates." >>> >>> That's the method described by Ramon Llull (in 1299). >>> >>> According to Electowiki that's been improved to become the Copeland >>> method, which elects "the candidate with the most (pairwise victories >>> minus pairwise defeats)." >>> >>> According to Wikipedia the Copeland method doesn't do the subtraction >>> and instead adds "half the number of candidates with whom he or she >>> has a preference tie." >>> >>> All of these Copeland method variations produce lots of ties. >>> >>> So of course the Ranked Robin method needs tie breakers. Here's the >>> first-level tie breaker as it's currently specified: >>> >>> "For each finalist, subtract the number of votes preferring each other >>> finalist from the number of votes preferring them over each other >>> finalist. The finalist with the greatest total difference is elected." >>> >>> A big disadvantage of this Ranked Robin tie breaker is that it uses >>> numbers from the pairwise matrix.  Yet one of the stated goals of the >>> Ranked Robin method is to avoid confusing voters with the pairwise >>> matrix. >>> >>> Therefore I suggest replacing this tie-breaker method with the use of >>> "pairwise support counts."  These counts are part of the "Instant >>> Pairwise Elimination" (IPE) method, which is described at Electowiki >>> at this link: >>> >>>   https://electowiki.org/wiki/Instant_Pairwise_Elimination >>> >>> It says: >>> >>> "If an elimination round has no pairwise-losing candidate, then the >>> method eliminates the candidate with the largest pairwise opposition >>> count, which is determined by counting on each ballot the number of >>> not-yet-eliminated candidates who are ranked above that candidate, and >>> adding those numbers across all the ballots. If there is a tie for the >>> largest pairwise opposition count, the method eliminates the candidate >>> with the smallest pairwise support count, which similarly counts >>> support rather than opposition. ..." >>> >>> Of course the second-level tie-breaker would be to use pairwise >>> opposition counts.  (The pairwise support counts and pairwise >>> opposition counts are not always symmetrical.) >>> >>> Notice that the numbers in the pairwise matrix do not need to be >>> mentioned. >>> >>> Yes, the software will calculate the pairwise support counts from the >>> numbers in the pairwise matrix.  But that fact doesn't need to be >>> mentioned -- to the voters, or in the legal description. >>> >>> The resulting improved Ranked Robin method can be described as follows: >>> >>> "The [improved] Ranked Robin method elects the candidate who has the >>> most number of one-on-one wins against every other candidate plus half >>> the number of one-on-one ties. [*]  If more than one candidate has the >>> same largest number, the method elects from those tied candidates the >>> candidate with the highest pairwise support count.  The pairwise >>> support count for each of the tied candidates is the sum, across all >>> the ballots, of the number of tied [**] candidates who are ranked >>> lower than the candidate whose pairwise support count is being >>> counted." >>> >>> [*] The wording can be adjusted depending on which Copeland variation >>> is desired.  Adding the words "minus the number of one-on-one losses" >>> would specify the other variation. >>> >>> [**] Importantly, the ballot marks for the non-tied candidates must be >>> ignored when resolving the tie. >>> >>> When the election results are displayed, they might look something >>> like this, where the names are from the Ranked Robin article, and the >>> numbers don't apply to any particular case: >>> >>> >>>     Matchup win and loss counts: >>> >>>     Ava: 4 wins (against ...) and 2 losses (to ...) >>> >>>     Bianca: 4 wins (against ...) and 2 losses (to ...) >>> >>>     Cedric: 3 wins (against ...) and 3 losses (to ...) >>> >>>     Deegan: 3 wins (against ...) and 3 losses (to ...) >>> >>>     Eli: 2 wins (against ...) and 4 losses (to ...) >>> >>>     Fabio: 0 wins and 6 losses >>> >>> >>>     The result is a tie between Ava and Bianca because they each have >>> 4 wins, and that's more than any other candidate.  Considering just >>> these tied candidates, their pairwise support counts are: >>> >>>     Ava: 213 >>> >>>     Bianca: 123 >>> >>>     So Ava wins! >>> >>> >>> Notice there's no need to show a pairwise matrix! >>> >>> To prevent a potential source of confusion, the Wikipedia article >>> about the Borda count begins with the words "The Borda count is a >>> family of positional voting rules which gives each candidate, for each >>> ballot, a number of points corresponding to the number of candidates >>> ranked lower."  The last portion of this sentence describes pairwise >>> support counts, but it has nothing to do with the Borda count.  The >>> Wikipedia article for "positional voting" correctly says: "Positional >>> voting is a ranked voting electoral system in which the options or >>> candidates receive points based on their rank position on each ballot >>> and the one with the most points overall wins."  The remainder of >>> Wikipedia's Borda count article correctly specifies positional voting >>> in the descriptions and examples.  The Borda count article at >>> Electowiki does not include this first-sentence mistake.  I'm going to >>> let someone else figure out how the first sentence in Wikipedia should >>> be worded.  (I'd rather fight other battles.) >>> >>> I'm calling attention to this difference between pairwise support >>> counts and the Borda count because this issue has previously caused >>> confusion in this forum. >>> >>> Getting back to the Ranked Robin method, this improved version is not >>> likely to significantly increase the failure rates of the most >>> important failure criteria, and it's likely to reduce some failure >>> rates. >>> >>> Currently the Ranked Robin article claims that the method passes some >>> fairness criteria that it actually doesn't pass.  When the Ranked >>> Robin article is improved to include a concise description of the >>> method (which should be near the beginning), some experts here can >>> identify which of the listed "pass" criteria need to be moved to the >>> listed "fail" criteria. >>> >>> Interestingly, the Ranked Robin method and its name were created by >>> people who have previously promoted only STAR voting.  I'm pleased >>> that they are finally recognizing that STAR ballots are not going to >>> replace ranked choice ballots throughout the US.  And that they >>> recognize the need to promote a method that takes advantage of the >>> Forward Party's recommendation of "ranked choice voting." >>> >>> Looking at the broader perspective ... >>> >>> The current version of Ranked Robin already has these advantages: >>> >>> * Uses pairwise vote counting, which looks deeper into the ballot >>> preferences compared to instant-runoff voting. >>> >>> * Is precinct summable. >>> >>> * Allows voters to mark more than one candidate at the same ranking >>> level. >>> >>> I suggest making it even easier to understand by using pairwise >>> support counts.  This improvement will eliminate the need to educate >>> voters about the pairwise matrix.  And I believe this change will >>> still provide a similar level of fairness. >>> >>> Certainly, in multiple ways, it's much better than instant-runoff >>> voting. >>> >>> Richard Fobes >>> The VoteFair guy >>> ---- >>> Election-Methods mailing list - see https://electorama.com/em for list >>> info >>

 Matchup win and loss counts:

 Ava: 4 wins (against ...) and 2 losses (to ...)

 Bianca: 4 wins (against ...) and 2 losses (to ...)

 Cedric: 3 wins (against ...) and 3 losses (to ...)

 Deegan: 3 wins (against ...) and 3 losses (to ...)

 Eli: 2 wins (against ...) and 4 losses (to ...)

 Fabio: 0 wins and 6 losses


 The result is a tie between Ava and Bianca because they each have

 Ava: 213

 Bianca: 123

 So Ava wins!

Besides being prone to ties, Copeland also suffers from Clone Dependence, which makes it inferior to IRV in that regard. Here are two versions of decloned Copeland that are not prone to ties: 1.Elect the candidate that, on the greatest number of ballots, pairwise defeats the candidate designated "worst." That is the burial resistant version of decloned Copeland. The other version, that may be more appealing to some people, is this: 2. Elect the candidate that, on the fewest number of ballots, is pairwise defeated by the candidate designated "best." Both of these methods are monotonic, clone free, and "Round Robin Efficient." It is practically impossible for either method to yield a tied result in an actual political election involving hundreds of ballots. Because of that fact, the obligatory tie breaker does not need the special scrutiny that is so important for ordinary clone dependent Copeland. Random Favorite would be the simplest ... and perfectly adequate tie breaker. At the other end of the spectrum, method one could serve as the tie breaker for method two, and vice-versa. Between those possibilities there are many others that are also perfectly adequate. -Forest El jue., 31 de mar. de 2022 12:04 p. m., Colin Champion < colin.champion@routemaster.app> escribió: > Richard – there are two ways of using a Borda tiebreak, sometimes written > "Llull//Borda" and "Llull,Borda". It sounds like you understood me to be > attributing "Llull,Borda" to you while you were actually advocating > "Llull//Borda". (I have no idea which of these was Dasgupta and Maskin’s > preference – I don’t think they were clear.) Certainly Llull//Borda reduces > to a plurality choice between two tied candidates. > Other tiebreaks (eg. minimax) can be used in the same two ways, which > is why a fairly general notation exists. I can't say I like it as a > notation, since it's far from self-explanatory. > Colin > > On 31/03/2022 18:10, Richard, the VoteFair guy wrote: > > On 3/30/2022 11:51 PM, Colin Champion wrote: > > ... is the candidate with the highest support count not the > > candidate with the highest Borda score? Have you not reinvented > > Dasgupta-Maskin? > > Borda count is a positional voting method: > > https://en.wikipedia.org/wiki/Positional_voting > > As a tie breaker, only the candidates who are tied are considered in this > count. > > When the tie is between just two candidates, the Borda count would still > use the (positional) numbers assigned by the voters. > > In contrast, I'm recommending a counting method that disregards which > position contains the mark being counted. So a two-candidate tie becomes > simple plurality counting. > > To repeat, I'm suggesting breaking a tie by using pairwise support > counts. On one ballot the pairwise support count is the number of > candidates who are ranked lower than the candidate getting the support > count. Those counts are added across all the ballots to yield that > candidate's pairwise support count. > > A big advantage is that it can be counted directly from the ballots, > without first creating a pairwise matrix. Although software would use the > pairwise matrix approach, voters and the legal description and the > tabulated results would not mention the pairwise matrix. > > Richard Fobes > The VoteFair guy > > > On 3/30/2022 11:51 PM, Colin Champion wrote: > > Richard – is the candidate with the highest support count not the > candidate with the highest Borda score? Have you not reinvented > Dasgupta-Maskin? > Colin > > > On 31/03/2022 05:58, Richard, the VoteFair guy wrote: > > Here I'm suggesting a way to improve the recently (fall 2021) created > "Ranked Robin" method, which is described at Electowiki at this link: > > https://electowiki.org/wiki/Ranked_Robin > > The improvement is to replace the first-level tie breaker -- which > looks at margins calculated from the pairwise matrix -- with "pairwise > support counts" -- which are easily described without using any > numbers from the pairwise matrix. > > Starting from the beginning ... > > Currently the Ranked Robin method is described this way: > > "Elect the candidate who pairwise beats the greatest number of > candidates." > > That's the method described by Ramon Llull (in 1299). > > According to Electowiki that's been improved to become the Copeland > method, which elects "the candidate with the most (pairwise victories > minus pairwise defeats)." > > According to Wikipedia the Copeland method doesn't do the subtraction > and instead adds "half the number of candidates with whom he or she > has a preference tie." > > All of these Copeland method variations produce lots of ties. > > So of course the Ranked Robin method needs tie breakers. Here's the > first-level tie breaker as it's currently specified: > > "For each finalist, subtract the number of votes preferring each other > finalist from the number of votes preferring them over each other > finalist. The finalist with the greatest total difference is elected." > > A big disadvantage of this Ranked Robin tie breaker is that it uses > numbers from the pairwise matrix. Yet one of the stated goals of the > Ranked Robin method is to avoid confusing voters with the pairwise > matrix. > > Therefore I suggest replacing this tie-breaker method with the use of > "pairwise support counts." These counts are part of the "Instant > Pairwise Elimination" (IPE) method, which is described at Electowiki > at this link: > > https://electowiki.org/wiki/Instant_Pairwise_Elimination > > It says: > > "If an elimination round has no pairwise-losing candidate, then the > method eliminates the candidate with the largest pairwise opposition > count, which is determined by counting on each ballot the number of > not-yet-eliminated candidates who are ranked above that candidate, and > adding those numbers across all the ballots. If there is a tie for the > largest pairwise opposition count, the method eliminates the candidate > with the smallest pairwise support count, which similarly counts > support rather than opposition. ..." > > Of course the second-level tie-breaker would be to use pairwise > opposition counts. (The pairwise support counts and pairwise > opposition counts are not always symmetrical.) > > Notice that the numbers in the pairwise matrix do not need to be > mentioned. > > Yes, the software will calculate the pairwise support counts from the > numbers in the pairwise matrix. But that fact doesn't need to be > mentioned -- to the voters, or in the legal description. > > The resulting improved Ranked Robin method can be described as follows: > > "The [improved] Ranked Robin method elects the candidate who has the > most number of one-on-one wins against every other candidate plus half > the number of one-on-one ties. [*] If more than one candidate has the > same largest number, the method elects from those tied candidates the > candidate with the highest pairwise support count. The pairwise > support count for each of the tied candidates is the sum, across all > the ballots, of the number of tied [**] candidates who are ranked > lower than the candidate whose pairwise support count is being counted." > > [*] The wording can be adjusted depending on which Copeland variation > is desired. Adding the words "minus the number of one-on-one losses" > would specify the other variation. > > [**] Importantly, the ballot marks for the non-tied candidates must be > ignored when resolving the tie. > > When the election results are displayed, they might look something > like this, where the names are from the Ranked Robin article, and the > numbers don't apply to any particular case: > > > Matchup win and loss counts: > > Ava: 4 wins (against ...) and 2 losses (to ...) > > Bianca: 4 wins (against ...) and 2 losses (to ...) > > Cedric: 3 wins (against ...) and 3 losses (to ...) > > Deegan: 3 wins (against ...) and 3 losses (to ...) > > Eli: 2 wins (against ...) and 4 losses (to ...) > > Fabio: 0 wins and 6 losses > > > The result is a tie between Ava and Bianca because they each have > 4 wins, and that's more than any other candidate. Considering just > these tied candidates, their pairwise support counts are: > > Ava: 213 > > Bianca: 123 > > So Ava wins! > > > Notice there's no need to show a pairwise matrix! > > To prevent a potential source of confusion, the Wikipedia article > about the Borda count begins with the words "The Borda count is a > family of positional voting rules which gives each candidate, for each > ballot, a number of points corresponding to the number of candidates > ranked lower." The last portion of this sentence describes pairwise > support counts, but it has nothing to do with the Borda count. The > Wikipedia article for "positional voting" correctly says: "Positional > voting is a ranked voting electoral system in which the options or > candidates receive points based on their rank position on each ballot > and the one with the most points overall wins." The remainder of > Wikipedia's Borda count article correctly specifies positional voting > in the descriptions and examples. The Borda count article at > Electowiki does not include this first-sentence mistake. I'm going to > let someone else figure out how the first sentence in Wikipedia should > be worded. (I'd rather fight other battles.) > > I'm calling attention to this difference between pairwise support > counts and the Borda count because this issue has previously caused > confusion in this forum. > > Getting back to the Ranked Robin method, this improved version is not > likely to significantly increase the failure rates of the most > important failure criteria, and it's likely to reduce some failure rates. > > Currently the Ranked Robin article claims that the method passes some > fairness criteria that it actually doesn't pass. When the Ranked > Robin article is improved to include a concise description of the > method (which should be near the beginning), some experts here can > identify which of the listed "pass" criteria need to be moved to the > listed "fail" criteria. > > Interestingly, the Ranked Robin method and its name were created by > people who have previously promoted only STAR voting. I'm pleased > that they are finally recognizing that STAR ballots are not going to > replace ranked choice ballots throughout the US. And that they > recognize the need to promote a method that takes advantage of the > Forward Party's recommendation of "ranked choice voting." > > Looking at the broader perspective ... > > The current version of Ranked Robin already has these advantages: > > * Uses pairwise vote counting, which looks deeper into the ballot > preferences compared to instant-runoff voting. > > * Is precinct summable. > > * Allows voters to mark more than one candidate at the same ranking > level. > > I suggest making it even easier to understand by using pairwise > support counts. This improvement will eliminate the need to educate > voters about the pairwise matrix. And I believe this change will > still provide a similar level of fairness. > > Certainly, in multiple ways, it's much better than instant-runoff voting. > > Richard Fobes > The VoteFair guy > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info > > > > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >

Hi Forest, Le vendredi 1 avril 2022, 20:24:25 UTC−5, Forest Simmons <forest.simmons21@gmail.com> a écrit : > Here are two versions of decloned Copeland that are not prone to ties: >  > 1.Elect the candidate that, on the greatest number of ballots, pairwise defeats the candidate designated "worst." >  > That is the burial resistant version of decloned Copeland.  >  > The other version, that may be more appealing to some people, is this: >  > 2. Elect the candidate that, on the fewest number of ballots, is pairwise defeated by the candidate designated "best." >  > Both of these methods are monotonic, clone free, and "Round Robin Efficient." I think I prefer the second one because, if I understand you, the first one doesn't make sense with truncation. I'm not sure if I have it correct since I'm having a monotonicity issue. Could you solve these two elections: 0.333: C>A 0.243: B 0.202: A>B>C>D 0.140: D 0.079: A>C>D>B --> C>A>D>B It's an A>B>C>A cycle, and D loses to everyone. The .079 vote change doesn't affect any defeats. I think C wins and then B wins. What do you think? Kevin

On 02.04.2022 03:24, Forest Simmons wrote: > Besides being prone to ties, Copeland also suffers from Clone > Dependence, which makes it inferior to IRV in that regard. > > Here are two versions of decloned Copeland that are not prone to ties: > > 1.Elect the candidate that, on the greatest number of ballots, pairwise > defeats the candidate designated "worst." If I'm not mistaken, Stensholt's three-candidate method BPW can be phrased this way, and I don't think it's monotone. It elects the candidate who beats the Plurality winner when there's a cycle. -km

 Richard – there are two ways of using a Borda tiebreak, sometimes
 written "Llull//Borda" and "Llull,Borda". It sounds like you
 understood me to be attributing "Llull,Borda" to you while you were
 actually advocating "Llull//Borda". (I have no idea which of these
 was Dasgupta and Maskin’s preference – I don’t think they were
 clear.) Certainly Llull//Borda reduces to a plurality choice between
 two tied candidates.
    Other tiebreaks (eg. minimax) can be used in the same two ways,
 which is why a fairly general notation exists. I can't say I like it
 as a notation, since it's far from self-explanatory.
       Colin

 On 31/03/2022 18:10, Richard, the VoteFair guy wrote:

 On 3/30/2022 11:51 PM, Colin Champion wrote:

 Borda count is a positional voting method:

 https://en.wikipedia.org/wiki/Positional_voting

 As a tie breaker, only the candidates who are tied are considered
 in this count.

 When the tie is between just two candidates, the Borda count would
 still use the (positional) numbers assigned by the voters.

 In contrast, I'm recommending a counting method that disregards
 which position contains the mark being counted.  So a
 two-candidate tie becomes simple plurality counting.

 To repeat, I'm suggesting breaking a tie by using pairwise support
 counts.  On one ballot the pairwise support count is the number of
 candidates who are ranked lower than the candidate getting the
 support count.  Those counts are added across all the ballots to
 yield that candidate's pairwise support count.

 A big advantage is that it can be counted directly from the
 ballots, without first creating a pairwise matrix.  Although
 software would use the pairwise matrix approach, voters and the
 legal description and the tabulated results would not mention the
 pairwise matrix.

 Richard Fobes
 The VoteFair guy


 On 3/30/2022 11:51 PM, Colin Champion wrote:

 Richard – is the candidate with the highest support count not the
 candidate with the highest Borda score? Have you not reinvented
 Dasgupta-Maskin?
    Colin


 On 31/03/2022 05:58, Richard, the VoteFair guy wrote:

 Here I'm suggesting a way to improve the recently (fall 2021)
 created
 "Ranked Robin" method, which is described at Electowiki at this
 link:

   https://electowiki.org/wiki/Ranked_Robin

 The improvement is to replace the first-level tie breaker -- which
 looks at margins calculated from the pairwise matrix -- with
 "pairwise
 support counts" -- which are easily described without using any
 numbers from the pairwise matrix.

 Starting from the beginning ...

 Currently the Ranked Robin method is described this way:

 "Elect the candidate who pairwise beats the greatest number of
 candidates."

 That's the method described by Ramon Llull (in 1299).

 According to Electowiki that's been improved to become the Copeland
 method, which elects "the candidate with the most (pairwise
 victories
 minus pairwise defeats)."

 According to Wikipedia the Copeland method doesn't do the
 subtraction
 and instead adds "half the number of candidates with whom he or she
 has a preference tie."

 All of these Copeland method variations produce lots of ties.

 So of course the Ranked Robin method needs tie breakers.  Here's
 the
 first-level tie breaker as it's currently specified:

 "For each finalist, subtract the number of votes preferring each
 other
 finalist from the number of votes preferring them over each other
 finalist. The finalist with the greatest total difference is
 elected."

 A big disadvantage of this Ranked Robin tie breaker is that it uses
 numbers from the pairwise matrix.  Yet one of the stated goals
 of the
 Ranked Robin method is to avoid confusing voters with the pairwise
 matrix.

 Therefore I suggest replacing this tie-breaker method with the
 use of
 "pairwise support counts."  These counts are part of the "Instant
 Pairwise Elimination" (IPE) method, which is described at
 Electowiki
 at this link:

   https://electowiki.org/wiki/Instant_Pairwise_Elimination

 It says:

 "If an elimination round has no pairwise-losing candidate, then the
 method eliminates the candidate with the largest pairwise
 opposition
 count, which is determined by counting on each ballot the number of
 not-yet-eliminated candidates who are ranked above that
 candidate, and
 adding those numbers across all the ballots. If there is a tie
 for the
 largest pairwise opposition count, the method eliminates the
 candidate
 with the smallest pairwise support count, which similarly counts
 support rather than opposition. ..."

 Of course the second-level tie-breaker would be to use pairwise
 opposition counts.  (The pairwise support counts and pairwise
 opposition counts are not always symmetrical.)

 Notice that the numbers in the pairwise matrix do not need to be
 mentioned.

 Yes, the software will calculate the pairwise support counts
 from the
 numbers in the pairwise matrix.  But that fact doesn't need to be
 mentioned -- to the voters, or in the legal description.

 The resulting improved Ranked Robin method can be described as
 follows:

 "The [improved] Ranked Robin method elects the candidate who has
 the
 most number of one-on-one wins against every other candidate
 plus half
 the number of one-on-one ties. [*]  If more than one candidate
 has the
 same largest number, the method elects from those tied
 candidates the
 candidate with the highest pairwise support count.  The pairwise
 support count for each of the tied candidates is the sum, across
 all
 the ballots, of the number of tied [**] candidates who are ranked
 lower than the candidate whose pairwise support count is being
 counted."

 [*] The wording can be adjusted depending on which Copeland
 variation
 is desired.  Adding the words "minus the number of one-on-one
 losses"
 would specify the other variation.

 [**] Importantly, the ballot marks for the non-tied candidates
 must be
 ignored when resolving the tie.

 When the election results are displayed, they might look something
 like this, where the names are from the Ranked Robin article,
 and the
 numbers don't apply to any particular case:


     Matchup win and loss counts:

     Ava: 4 wins (against ...) and 2 losses (to ...)

     Bianca: 4 wins (against ...) and 2 losses (to ...)

     Cedric: 3 wins (against ...) and 3 losses (to ...)

     Deegan: 3 wins (against ...) and 3 losses (to ...)

     Eli: 2 wins (against ...) and 4 losses (to ...)

     Fabio: 0 wins and 6 losses


     The result is a tie between Ava and Bianca because they each
 have
 4 wins, and that's more than any other candidate.  Considering just
 these tied candidates, their pairwise support counts are:

     Ava: 213

     Bianca: 123

     So Ava wins!


 Notice there's no need to show a pairwise matrix!

 To prevent a potential source of confusion, the Wikipedia article
 about the Borda count begins with the words "The Borda count is a
 family of positional voting rules which gives each candidate,
 for each
 ballot, a number of points corresponding to the number of
 candidates
 ranked lower."  The last portion of this sentence describes
 pairwise
 support counts, but it has nothing to do with the Borda count.  The
 Wikipedia article for "positional voting" correctly says:
 "Positional
 voting is a ranked voting electoral system in which the options or
 candidates receive points based on their rank position on each
 ballot
 and the one with the most points overall wins."  The remainder of
 Wikipedia's Borda count article correctly specifies positional
 voting
 in the descriptions and examples.  The Borda count article at
 Electowiki does not include this first-sentence mistake.  I'm
 going to
 let someone else figure out how the first sentence in Wikipedia
 should
 be worded.  (I'd rather fight other battles.)

 I'm calling attention to this difference between pairwise support
 counts and the Borda count because this issue has previously caused
 confusion in this forum.

 Getting back to the Ranked Robin method, this improved version
 is not
 likely to significantly increase the failure rates of the most
 important failure criteria, and it's likely to reduce some
 failure rates.

 Currently the Ranked Robin article claims that the method passes
 some
 fairness criteria that it actually doesn't pass.  When the Ranked
 Robin article is improved to include a concise description of the
 method (which should be near the beginning), some experts here can
 identify which of the listed "pass" criteria need to be moved to
 the
 listed "fail" criteria.

 Interestingly, the Ranked Robin method and its name were created by
 people who have previously promoted only STAR voting.  I'm pleased
 that they are finally recognizing that STAR ballots are not
 going to
 replace ranked choice ballots throughout the US.  And that they
 recognize the need to promote a method that takes advantage of the
 Forward Party's recommendation of "ranked choice voting."

 Looking at the broader perspective ...

 The current version of Ranked Robin already has these advantages:

 * Uses pairwise vote counting, which looks deeper into the ballot
 preferences compared to instant-runoff voting.

 * Is precinct summable.

 * Allows voters to mark more than one candidate at the same ranking
 level.

 I suggest making it even easier to understand by using pairwise
 support counts.  This improvement will eliminate the need to
 educate
 voters about the pairwise matrix.  And I believe this change will
 still provide a similar level of fairness.

 Certainly, in multiple ways, it's much better than
 instant-runoff voting.

 Richard Fobes
 The VoteFair guy
 ----
 Election-Methods mailing list - see https://electorama.com/em
 for list
 info

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

On 4/1/2022 6:24 PM, Forest Simmons wrote: > ... > Here are two versions of decloned Copeland that are not prone to ties: > > 1.Elect the candidate that, on the greatest number of ballots, > pairwise defeats the candidate designated "worst." > ... > 2. Elect the candidate that, on the fewest number of ballots, is > pairwise defeated by the candidate designated "best." Both of these ways of resolving Copeland ties are more difficult to understand -- for most voters -- than the current version. As a further barrier to understanding, these definitions involve recursion. That's even more difficult to understand than a pairwise matrix. The goal of the Ranked Robin method (according to the description on Electowiki) is to provide a method that is reasonably easy to understand, yet uses ranked choice ballots and yields reasonably fair results. As I said, I'm proposing that the method be made even easier to understand by using pairwise support counts, which are directly countable from the ballots, without involving a pairwise matrix. Regarding your desire to protect against clone failures, those are just one special kind of "irrelevant alternative," as in IIA (independence of irrelevant alternatives). Personally I'm more concerned about reducing all kinds of irrelevant alternatives. In this case I'm concerned that attempts to fully eliminate clone independence failures might have the side effect of increasing the rates of other kinds of IIA failures. Richard Fobes The VoteFair guy On 4/1/2022 6:24 PM, Forest Simmons wrote: > Besides being prone to ties, Copeland also suffers from Clone > Dependence, which makes it inferior to IRV in that regard. > > Here are two versions of decloned Copeland that are not prone to ties: > > 1.Elect the candidate that, on the greatest number of ballots, pairwise > defeats the candidate designated "worst." > > That is the burial resistant version of decloned Copeland. > > The other version, that may be more appealing to some people, is this: > > 2. Elect the candidate that, on the fewest number of ballots, is > pairwise defeated by the candidate designated "best." > > Both of these methods are monotonic, clone free, and "Round Robin > Efficient." > > It is practically impossible for either method to yield a tied result in > an actual political election involving hundreds of ballots. > > Because of that fact, the obligatory tie breaker does not need the > special scrutiny that is so important for ordinary clone dependent Copeland. > > Random Favorite would be the simplest ... and perfectly adequate tie > breaker. > > At the other end of the spectrum, method one could serve as the tie > breaker for method two, and vice-versa. > > Between those possibilities there are many others that are also > perfectly adequate. > > -Forest > > > > > El jue., 31 de mar. de 2022 12:04 p. m., Colin Champion > <colin.champion@routemaster.app <mailto:colin.champion@routemaster.app>> > escribió: > > Richard – there are two ways of using a Borda tiebreak, sometimes > written "Llull//Borda" and "Llull,Borda". It sounds like you > understood me to be attributing "Llull,Borda" to you while you were > actually advocating "Llull//Borda". (I have no idea which of these > was Dasgupta and Maskin’s preference – I don’t think they were > clear.) Certainly Llull//Borda reduces to a plurality choice between > two tied candidates. > Other tiebreaks (eg. minimax) can be used in the same two ways, > which is why a fairly general notation exists. I can't say I like it > as a notation, since it's far from self-explanatory. > Colin > > On 31/03/2022 18:10, Richard, the VoteFair guy wrote: >> On 3/30/2022 11:51 PM, Colin Champion wrote: >> > ... is the candidate with the highest support count not the >> > candidate with the highest Borda score? Have you not reinvented >> > Dasgupta-Maskin? >> >> Borda count is a positional voting method: >> >> https://en.wikipedia.org/wiki/Positional_voting >> >> As a tie breaker, only the candidates who are tied are considered >> in this count. >> >> When the tie is between just two candidates, the Borda count would >> still use the (positional) numbers assigned by the voters. >> >> In contrast, I'm recommending a counting method that disregards >> which position contains the mark being counted. So a >> two-candidate tie becomes simple plurality counting. >> >> To repeat, I'm suggesting breaking a tie by using pairwise support >> counts. On one ballot the pairwise support count is the number of >> candidates who are ranked lower than the candidate getting the >> support count. Those counts are added across all the ballots to >> yield that candidate's pairwise support count. >> >> A big advantage is that it can be counted directly from the >> ballots, without first creating a pairwise matrix. Although >> software would use the pairwise matrix approach, voters and the >> legal description and the tabulated results would not mention the >> pairwise matrix. >> >> Richard Fobes >> The VoteFair guy >> >> >> On 3/30/2022 11:51 PM, Colin Champion wrote: >>> Richard – is the candidate with the highest support count not the >>> candidate with the highest Borda score? Have you not reinvented >>> Dasgupta-Maskin? >>> Colin >>> >>> >>> On 31/03/2022 05:58, Richard, the VoteFair guy wrote: >>>> Here I'm suggesting a way to improve the recently (fall 2021) >>>> created >>>> "Ranked Robin" method, which is described at Electowiki at this >>>> link: >>>> >>>> https://electowiki.org/wiki/Ranked_Robin >>>> >>>> The improvement is to replace the first-level tie breaker -- which >>>> looks at margins calculated from the pairwise matrix -- with >>>> "pairwise >>>> support counts" -- which are easily described without using any >>>> numbers from the pairwise matrix. >>>> >>>> Starting from the beginning ... >>>> >>>> Currently the Ranked Robin method is described this way: >>>> >>>> "Elect the candidate who pairwise beats the greatest number of >>>> candidates." >>>> >>>> That's the method described by Ramon Llull (in 1299). >>>> >>>> According to Electowiki that's been improved to become the Copeland >>>> method, which elects "the candidate with the most (pairwise >>>> victories >>>> minus pairwise defeats)." >>>> >>>> According to Wikipedia the Copeland method doesn't do the >>>> subtraction >>>> and instead adds "half the number of candidates with whom he or she >>>> has a preference tie." >>>> >>>> All of these Copeland method variations produce lots of ties. >>>> >>>> So of course the Ranked Robin method needs tie breakers. Here's >>>> the >>>> first-level tie breaker as it's currently specified: >>>> >>>> "For each finalist, subtract the number of votes preferring each >>>> other >>>> finalist from the number of votes preferring them over each other >>>> finalist. The finalist with the greatest total difference is >>>> elected." >>>> >>>> A big disadvantage of this Ranked Robin tie breaker is that it uses >>>> numbers from the pairwise matrix. Yet one of the stated goals >>>> of the >>>> Ranked Robin method is to avoid confusing voters with the pairwise >>>> matrix. >>>> >>>> Therefore I suggest replacing this tie-breaker method with the >>>> use of >>>> "pairwise support counts." These counts are part of the "Instant >>>> Pairwise Elimination" (IPE) method, which is described at >>>> Electowiki >>>> at this link: >>>> >>>> https://electowiki.org/wiki/Instant_Pairwise_Elimination >>>> >>>> It says: >>>> >>>> "If an elimination round has no pairwise-losing candidate, then the >>>> method eliminates the candidate with the largest pairwise >>>> opposition >>>> count, which is determined by counting on each ballot the number of >>>> not-yet-eliminated candidates who are ranked above that >>>> candidate, and >>>> adding those numbers across all the ballots. If there is a tie >>>> for the >>>> largest pairwise opposition count, the method eliminates the >>>> candidate >>>> with the smallest pairwise support count, which similarly counts >>>> support rather than opposition. ..." >>>> >>>> Of course the second-level tie-breaker would be to use pairwise >>>> opposition counts. (The pairwise support counts and pairwise >>>> opposition counts are not always symmetrical.) >>>> >>>> Notice that the numbers in the pairwise matrix do not need to be >>>> mentioned. >>>> >>>> Yes, the software will calculate the pairwise support counts >>>> from the >>>> numbers in the pairwise matrix. But that fact doesn't need to be >>>> mentioned -- to the voters, or in the legal description. >>>> >>>> The resulting improved Ranked Robin method can be described as >>>> follows: >>>> >>>> "The [improved] Ranked Robin method elects the candidate who has >>>> the >>>> most number of one-on-one wins against every other candidate >>>> plus half >>>> the number of one-on-one ties. [*] If more than one candidate >>>> has the >>>> same largest number, the method elects from those tied >>>> candidates the >>>> candidate with the highest pairwise support count. The pairwise >>>> support count for each of the tied candidates is the sum, across >>>> all >>>> the ballots, of the number of tied [**] candidates who are ranked >>>> lower than the candidate whose pairwise support count is being >>>> counted." >>>> >>>> [*] The wording can be adjusted depending on which Copeland >>>> variation >>>> is desired. Adding the words "minus the number of one-on-one >>>> losses" >>>> would specify the other variation. >>>> >>>> [**] Importantly, the ballot marks for the non-tied candidates >>>> must be >>>> ignored when resolving the tie. >>>> >>>> When the election results are displayed, they might look something >>>> like this, where the names are from the Ranked Robin article, >>>> and the >>>> numbers don't apply to any particular case: >>>> >>>> >>>> Matchup win and loss counts: >>>> >>>> Ava: 4 wins (against ...) and 2 losses (to ...) >>>> >>>> Bianca: 4 wins (against ...) and 2 losses (to ...) >>>> >>>> Cedric: 3 wins (against ...) and 3 losses (to ...) >>>> >>>> Deegan: 3 wins (against ...) and 3 losses (to ...) >>>> >>>> Eli: 2 wins (against ...) and 4 losses (to ...) >>>> >>>> Fabio: 0 wins and 6 losses >>>> >>>> >>>> The result is a tie between Ava and Bianca because they each >>>> have >>>> 4 wins, and that's more than any other candidate. Considering just >>>> these tied candidates, their pairwise support counts are: >>>> >>>> Ava: 213 >>>> >>>> Bianca: 123 >>>> >>>> So Ava wins! >>>> >>>> >>>> Notice there's no need to show a pairwise matrix! >>>> >>>> To prevent a potential source of confusion, the Wikipedia article >>>> about the Borda count begins with the words "The Borda count is a >>>> family of positional voting rules which gives each candidate, >>>> for each >>>> ballot, a number of points corresponding to the number of >>>> candidates >>>> ranked lower." The last portion of this sentence describes >>>> pairwise >>>> support counts, but it has nothing to do with the Borda count. The >>>> Wikipedia article for "positional voting" correctly says: >>>> "Positional >>>> voting is a ranked voting electoral system in which the options or >>>> candidates receive points based on their rank position on each >>>> ballot >>>> and the one with the most points overall wins." The remainder of >>>> Wikipedia's Borda count article correctly specifies positional >>>> voting >>>> in the descriptions and examples. The Borda count article at >>>> Electowiki does not include this first-sentence mistake. I'm >>>> going to >>>> let someone else figure out how the first sentence in Wikipedia >>>> should >>>> be worded. (I'd rather fight other battles.) >>>> >>>> I'm calling attention to this difference between pairwise support >>>> counts and the Borda count because this issue has previously caused >>>> confusion in this forum. >>>> >>>> Getting back to the Ranked Robin method, this improved version >>>> is not >>>> likely to significantly increase the failure rates of the most >>>> important failure criteria, and it's likely to reduce some >>>> failure rates. >>>> >>>> Currently the Ranked Robin article claims that the method passes >>>> some >>>> fairness criteria that it actually doesn't pass. When the Ranked >>>> Robin article is improved to include a concise description of the >>>> method (which should be near the beginning), some experts here can >>>> identify which of the listed "pass" criteria need to be moved to >>>> the >>>> listed "fail" criteria. >>>> >>>> Interestingly, the Ranked Robin method and its name were created by >>>> people who have previously promoted only STAR voting. I'm pleased >>>> that they are finally recognizing that STAR ballots are not >>>> going to >>>> replace ranked choice ballots throughout the US. And that they >>>> recognize the need to promote a method that takes advantage of the >>>> Forward Party's recommendation of "ranked choice voting." >>>> >>>> Looking at the broader perspective ... >>>> >>>> The current version of Ranked Robin already has these advantages: >>>> >>>> * Uses pairwise vote counting, which looks deeper into the ballot >>>> preferences compared to instant-runoff voting. >>>> >>>> * Is precinct summable. >>>> >>>> * Allows voters to mark more than one candidate at the same ranking >>>> level. >>>> >>>> I suggest making it even easier to understand by using pairwise >>>> support counts. This improvement will eliminate the need to >>>> educate >>>> voters about the pairwise matrix. And I believe this change will >>>> still provide a similar level of fairness. >>>> >>>> Certainly, in multiple ways, it's much better than >>>> instant-runoff voting. >>>> >>>> Richard Fobes >>>> The VoteFair guy >>>> ---- >>>> Election-Methods mailing list - see https://electorama.com/em >>>> for list >>>> info >>> > > ---- > Election-Methods mailing list - see https://electorama.com/em for > list info > > > > ---- > Election-Methods mailing list - see https://electorama.com/em for list info >

Hi Richard, You wrote to Forest: > Regarding your desire to protect against clone failures, those are just > one special kind of "irrelevant alternative," as in IIA (independence of > irrelevant alternatives).  Personally I'm more concerned about reducing > all kinds of irrelevant alternatives.  In this case I'm concerned that > attempts to fully eliminate clone independence failures might have the > side effect of increasing the rates of other kinds of IIA failures. This is an interesting idea. It's a little hard for me to conceive of why this would be the case. But clone independence is a difficult standard to meet, and based on randomly generated scenarios one would likely conclude that "clones," as such, are pretty rare. (This sets aside of course the possibility that clones could be deliberately created as a nomination strategy.) There are no doubt other approaches we can take to minimize IIA failures. I see some correlation, via simulations, between compromise incentive and the potential for "loser withdrawal" to change the outcome. I guess this is not so surprising since they're conceptually related: A compromising voter likely wants to pretend that a (expected) losing candidate didn't enter the race at all, in hopes of getting a better outcome. It's like an "irrelevant alternative" drops out, but only from some ballots, and only if a certain kind of change can result from it. Kevin

 Richard – there are two ways of using a Borda tiebreak, sometimes
 written "Llull//Borda" and "Llull,Borda". It sounds like you
 understood me to be attributing "Llull,Borda" to you while you were
 actually advocating "Llull//Borda". (I have no idea which of these
 was Dasgupta and Maskin’s preference – I don’t think they were
 clear.) Certainly Llull//Borda reduces to a plurality choice between
 two tied candidates.
    Other tiebreaks (eg. minimax) can be used in the same two ways,
 which is why a fairly general notation exists. I can't say I like it
 as a notation, since it's far from self-explanatory.
       Colin

 On 31/03/2022 18:10, Richard, the VoteFair guy wrote:

 On 3/30/2022 11:51 PM, Colin Champion wrote:

 Borda count is a positional voting method:

 https://en.wikipedia.org/wiki/Positional_voting

 As a tie breaker, only the candidates who are tied are considered
 in this count.

 When the tie is between just two candidates, the Borda count would
 still use the (positional) numbers assigned by the voters.

 In contrast, I'm recommending a counting method that disregards
 which position contains the mark being counted.  So a
 two-candidate tie becomes simple plurality counting.

 To repeat, I'm suggesting breaking a tie by using pairwise support
 counts.  On one ballot the pairwise support count is the number of
 candidates who are ranked lower than the candidate getting the
 support count.  Those counts are added across all the ballots to
 yield that candidate's pairwise support count.

 A big advantage is that it can be counted directly from the
 ballots, without first creating a pairwise matrix.  Although
 software would use the pairwise matrix approach, voters and the
 legal description and the tabulated results would not mention the
 pairwise matrix.

 Richard Fobes
 The VoteFair guy


 On 3/30/2022 11:51 PM, Colin Champion wrote:

 Richard – is the candidate with the highest support count not the
 candidate with the highest Borda score? Have you not reinvented
 Dasgupta-Maskin?
    Colin


 On 31/03/2022 05:58, Richard, the VoteFair guy wrote:

 Here I'm suggesting a way to improve the recently (fall 2021)
 created
 "Ranked Robin" method, which is described at Electowiki at this
 link:

   https://electowiki.org/wiki/Ranked_Robin

 The improvement is to replace the first-level tie breaker -- which
 looks at margins calculated from the pairwise matrix -- with
 "pairwise
 support counts" -- which are easily described without using any
 numbers from the pairwise matrix.

 Starting from the beginning ...

 Currently the Ranked Robin method is described this way:

 "Elect the candidate who pairwise beats the greatest number of
 candidates."

 That's the method described by Ramon Llull (in 1299).

 According to Electowiki that's been improved to become the

 method, which elects "the candidate with the most (pairwise
 victories
 minus pairwise defeats)."

 According to Wikipedia the Copeland method doesn't do the
 subtraction
 and instead adds "half the number of candidates with whom he or

 has a preference tie."

 All of these Copeland method variations produce lots of ties.

 So of course the Ranked Robin method needs tie breakers.  Here's
 the
 first-level tie breaker as it's currently specified:

 "For each finalist, subtract the number of votes preferring each
 other
 finalist from the number of votes preferring them over each other
 finalist. The finalist with the greatest total difference is
 elected."

 A big disadvantage of this Ranked Robin tie breaker is that it

 numbers from the pairwise matrix.  Yet one of the stated goals
 of the
 Ranked Robin method is to avoid confusing voters with the pairwise
 matrix.

 Therefore I suggest replacing this tie-breaker method with the
 use of
 "pairwise support counts."  These counts are part of the "Instant
 Pairwise Elimination" (IPE) method, which is described at
 Electowiki
 at this link:

   https://electowiki.org/wiki/Instant_Pairwise_Elimination

 It says:

 "If an elimination round has no pairwise-losing candidate, then

 method eliminates the candidate with the largest pairwise
 opposition
 count, which is determined by counting on each ballot the number

 not-yet-eliminated candidates who are ranked above that
 candidate, and
 adding those numbers across all the ballots. If there is a tie
 for the
 largest pairwise opposition count, the method eliminates the
 candidate
 with the smallest pairwise support count, which similarly counts
 support rather than opposition. ..."

 Of course the second-level tie-breaker would be to use pairwise
 opposition counts.  (The pairwise support counts and pairwise
 opposition counts are not always symmetrical.)

 Notice that the numbers in the pairwise matrix do not need to be
 mentioned.

 Yes, the software will calculate the pairwise support counts
 from the
 numbers in the pairwise matrix.  But that fact doesn't need to be
 mentioned -- to the voters, or in the legal description.

 The resulting improved Ranked Robin method can be described as
 follows:

 "The [improved] Ranked Robin method elects the candidate who has
 the
 most number of one-on-one wins against every other candidate
 plus half
 the number of one-on-one ties. [*]  If more than one candidate
 has the
 same largest number, the method elects from those tied
 candidates the
 candidate with the highest pairwise support count.  The pairwise
 support count for each of the tied candidates is the sum, across
 all
 the ballots, of the number of tied [**] candidates who are ranked
 lower than the candidate whose pairwise support count is being
 counted."

 [*] The wording can be adjusted depending on which Copeland
 variation
 is desired.  Adding the words "minus the number of one-on-one
 losses"
 would specify the other variation.

 [**] Importantly, the ballot marks for the non-tied candidates
 must be
 ignored when resolving the tie.

 When the election results are displayed, they might look something
 like this, where the names are from the Ranked Robin article,
 and the
 numbers don't apply to any particular case:


     Matchup win and loss counts:

     Ava: 4 wins (against ...) and 2 losses (to ...)

     Bianca: 4 wins (against ...) and 2 losses (to ...)

     Cedric: 3 wins (against ...) and 3 losses (to ...)

     Deegan: 3 wins (against ...) and 3 losses (to ...)

     Eli: 2 wins (against ...) and 4 losses (to ...)

     Fabio: 0 wins and 6 losses


     The result is a tie between Ava and Bianca because they each
 have
 4 wins, and that's more than any other candidate.  Considering

 these tied candidates, their pairwise support counts are:

     Ava: 213

     Bianca: 123

     So Ava wins!


 Notice there's no need to show a pairwise matrix!

 To prevent a potential source of confusion, the Wikipedia article
 about the Borda count begins with the words "The Borda count is a
 family of positional voting rules which gives each candidate,
 for each
 ballot, a number of points corresponding to the number of
 candidates
 ranked lower."  The last portion of this sentence describes
 pairwise
 support counts, but it has nothing to do with the Borda count.

 Wikipedia article for "positional voting" correctly says:
 "Positional
 voting is a ranked voting electoral system in which the options or
 candidates receive points based on their rank position on each
 ballot
 and the one with the most points overall wins."  The remainder of
 Wikipedia's Borda count article correctly specifies positional
 voting
 in the descriptions and examples.  The Borda count article at
 Electowiki does not include this first-sentence mistake.  I'm
 going to
 let someone else figure out how the first sentence in Wikipedia
 should
 be worded.  (I'd rather fight other battles.)

 I'm calling attention to this difference between pairwise support
 counts and the Borda count because this issue has previously

 confusion in this forum.

 Getting back to the Ranked Robin method, this improved version
 is not
 likely to significantly increase the failure rates of the most
 important failure criteria, and it's likely to reduce some
 failure rates.

 Currently the Ranked Robin article claims that the method passes
 some
 fairness criteria that it actually doesn't pass.  When the Ranked
 Robin article is improved to include a concise description of the
 method (which should be near the beginning), some experts here can
 identify which of the listed "pass" criteria need to be moved to
 the
 listed "fail" criteria.

 Interestingly, the Ranked Robin method and its name were created

 people who have previously promoted only STAR voting.  I'm pleased
 that they are finally recognizing that STAR ballots are not
 going to
 replace ranked choice ballots throughout the US.  And that they
 recognize the need to promote a method that takes advantage of the
 Forward Party's recommendation of "ranked choice voting."

 Looking at the broader perspective ...

 The current version of Ranked Robin already has these advantages:

 * Uses pairwise vote counting, which looks deeper into the ballot
 preferences compared to instant-runoff voting.

 * Is precinct summable.

 * Allows voters to mark more than one candidate at the same

 level.

 I suggest making it even easier to understand by using pairwise
 support counts.  This improvement will eliminate the need to
 educate
 voters about the pairwise matrix.  And I believe this change will
 still provide a similar level of fairness.

 Certainly, in multiple ways, it's much better than
 instant-runoff voting.

 Richard Fobes
 The VoteFair guy
 ----
 Election-Methods mailing list - see https://electorama.com/em
 for list
 info

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

El sáb., 2 de abr. de 2022 9:41 p. m., Richard, the VoteFair guy < electionmethods@votefair.org> escribió: > On 4/1/2022 6:24 PM, Forest Simmons wrote: > > ... > > Here are two versions of decloned Copeland that are not prone to ties: > > > > 1.Elect the candidate that, on the greatest number of ballots, > > pairwise defeats the candidate designated "worst." > > ... > > 2. Elect the candidate that, on the fewest number of ballots, is > > pairwise defeated by the candidate designated "best." > > Both of these ways of resolving Copeland ties are more difficult to > understand -- for most voters -- than the current version. > These are not ways of resolving Copeland ties ... rather they are two succinctly stated complete versions of Copeland that only vanishingly rarely require any tie breaker at all, let alone one as elaborate as you are suggesting. > > As a further barrier to understanding, these definitions involve > recursion. Recursion? Who said recursion? Where did you get that impression? Where is the recursion in ... ... elect the candidate that, on the fewest number of ballots, is pairwise defeated by the ballot favorite .... To spell it out in complete detail ... just open each ballot B and, after identifying the first preference X on each ballot B, give a demerit to each candidate Y defeated pairwise by candidate X. After tallying all of the ballots in this same fashion, elect the candidate with the fewest demerits. [That's all there is ... don't try reading something complicated into it ;-) If another method seems simpler, it's only because you are more familiar with it.] A Condorcet candidate will have no demerits because, by definition a Condorcet candidate is not defeated pairwise. The key to clone independence is focusing on defeats incurred by the ballot favorites, rather than giving all pairwise defeats equal weight. That's even more difficult to procedurally understand than a pairwise > matrix. > The goal of the Ranked Robin method (according to the description on > Electowiki) is to provide a method that is reasonably easy to > understand, yet uses ranked choice ballots and yields reasonably fair > results. > > As I said, I'm proposing that the method be made even easier to > understand by using pairwise support counts, which are directly > countable from the ballots, without involving a pairwise matrix. > > Regarding your desire to protect against clone failures, those are just > one special kind of "irrelevant alternative," as in IIA (independence of > irrelevant alternatives). Personally I'm more concerned about reducing > all kinds of irrelevant alternatives. In this case I'm concerned that > attempts to fully eliminate clone independence failures might have the > side effect of increasing the rates of other kinds of IIA failures. > > Richard Fobes > The VoteFair guy > > > On 4/1/2022 6:24 PM, Forest Simmons wrote: > > Besides being prone to ties, Copeland also suffers from Clone > > Dependence, which makes it inferior to IRV in that regard. > > > > Here are two versions of decloned Copeland that are not prone to ties: > > > > 1.Elect the candidate that, on the greatest number of ballots, pairwise > > defeats the candidate designated "worst." > > > > That is the burial resistant version of decloned Copeland. > > > > The other version, that may be more appealing to some people, is this: > > > > 2. Elect the candidate that, on the fewest number of ballots, is > > pairwise defeated by the candidate designated "best." > > > > Both of these methods are monotonic, clone free, and "Round Robin > > Efficient." > > > > It is practically impossible for either method to yield a tied result in > > an actual political election involving hundreds of ballots. > > > > Because of that fact, the obligatory tie breaker does not need the > > special scrutiny that is so important for ordinary clone dependent > Copeland. > > > > Random Favorite would be the simplest ... and perfectly adequate tie > > breaker. > > > > At the other end of the spectrum, method one could serve as the tie > > breaker for method two, and vice-versa. > > > > Between those possibilities there are many others that are also > > perfectly adequate. > > > > -Forest > > > > > > > > > > El jue., 31 de mar. de 2022 12:04 p. m., Colin Champion > > <colin.champion@routemaster.app <mailto:colin.champion@routemaster.app>> > > escribió: > > > > Richard – there are two ways of using a Borda tiebreak, sometimes > > written "Llull//Borda" and "Llull,Borda". It sounds like you > > understood me to be attributing "Llull,Borda" to you while you were > > actually advocating "Llull//Borda". (I have no idea which of these > > was Dasgupta and Maskin’s preference – I don’t think they were > > clear.) Certainly Llull//Borda reduces to a plurality choice between > > two tied candidates. > > Other tiebreaks (eg. minimax) can be used in the same two ways, > > which is why a fairly general notation exists. I can't say I like it > > as a notation, since it's far from self-explanatory. > > Colin > > > > On 31/03/2022 18:10, Richard, the VoteFair guy wrote: > >> On 3/30/2022 11:51 PM, Colin Champion wrote: > >> > ... is the candidate with the highest support count not the > >> > candidate with the highest Borda score? Have you not reinvented > >> > Dasgupta-Maskin? > >> > >> Borda count is a positional voting method: > >> > >> https://en.wikipedia.org/wiki/Positional_voting > >> > >> As a tie breaker, only the candidates who are tied are considered > >> in this count. > >> > >> When the tie is between just two candidates, the Borda count would > >> still use the (positional) numbers assigned by the voters. > >> > >> In contrast, I'm recommending a counting method that disregards > >> which position contains the mark being counted. So a > >> two-candidate tie becomes simple plurality counting. > >> > >> To repeat, I'm suggesting breaking a tie by using pairwise support > >> counts. On one ballot the pairwise support count is the number of > >> candidates who are ranked lower than the candidate getting the > >> support count. Those counts are added across all the ballots to > >> yield that candidate's pairwise support count. > >> > >> A big advantage is that it can be counted directly from the > >> ballots, without first creating a pairwise matrix. Although > >> software would use the pairwise matrix approach, voters and the > >> legal description and the tabulated results would not mention the > >> pairwise matrix. > >> > >> Richard Fobes > >> The VoteFair guy > >> > >> > >> On 3/30/2022 11:51 PM, Colin Champion wrote: > >>> Richard – is the candidate with the highest support count not the > >>> candidate with the highest Borda score? Have you not reinvented > >>> Dasgupta-Maskin? > >>> Colin > >>> > >>> > >>> On 31/03/2022 05:58, Richard, the VoteFair guy wrote: > >>>> Here I'm suggesting a way to improve the recently (fall 2021) > >>>> created > >>>> "Ranked Robin" method, which is described at Electowiki at this > >>>> link: > >>>> > >>>> https://electowiki.org/wiki/Ranked_Robin > >>>> > >>>> The improvement is to replace the first-level tie breaker -- which > >>>> looks at margins calculated from the pairwise matrix -- with > >>>> "pairwise > >>>> support counts" -- which are easily described without using any > >>>> numbers from the pairwise matrix. > >>>> > >>>> Starting from the beginning ... > >>>> > >>>> Currently the Ranked Robin method is described this way: > >>>> > >>>> "Elect the candidate who pairwise beats the greatest number of > >>>> candidates." > >>>> > >>>> That's the method described by Ramon Llull (in 1299). > >>>> > >>>> According to Electowiki that's been improved to become the > Copeland > >>>> method, which elects "the candidate with the most (pairwise > >>>> victories > >>>> minus pairwise defeats)." > >>>> > >>>> According to Wikipedia the Copeland method doesn't do the > >>>> subtraction > >>>> and instead adds "half the number of candidates with whom he or > she > >>>> has a preference tie." > >>>> > >>>> All of these Copeland method variations produce lots of ties. > >>>> > >>>> So of course the Ranked Robin method needs tie breakers. Here's > >>>> the > >>>> first-level tie breaker as it's currently specified: > >>>> > >>>> "For each finalist, subtract the number of votes preferring each > >>>> other > >>>> finalist from the number of votes preferring them over each other > >>>> finalist. The finalist with the greatest total difference is > >>>> elected." > >>>> > >>>> A big disadvantage of this Ranked Robin tie breaker is that it > uses > >>>> numbers from the pairwise matrix. Yet one of the stated goals > >>>> of the > >>>> Ranked Robin method is to avoid confusing voters with the pairwise > >>>> matrix. > >>>> > >>>> Therefore I suggest replacing this tie-breaker method with the > >>>> use of > >>>> "pairwise support counts." These counts are part of the "Instant > >>>> Pairwise Elimination" (IPE) method, which is described at > >>>> Electowiki > >>>> at this link: > >>>> > >>>> https://electowiki.org/wiki/Instant_Pairwise_Elimination > >>>> > >>>> It says: > >>>> > >>>> "If an elimination round has no pairwise-losing candidate, then > the > >>>> method eliminates the candidate with the largest pairwise > >>>> opposition > >>>> count, which is determined by counting on each ballot the number > of > >>>> not-yet-eliminated candidates who are ranked above that > >>>> candidate, and > >>>> adding those numbers across all the ballots. If there is a tie > >>>> for the > >>>> largest pairwise opposition count, the method eliminates the > >>>> candidate > >>>> with the smallest pairwise support count, which similarly counts > >>>> support rather than opposition. ..." > >>>> > >>>> Of course the second-level tie-breaker would be to use pairwise > >>>> opposition counts. (The pairwise support counts and pairwise > >>>> opposition counts are not always symmetrical.) > >>>> > >>>> Notice that the numbers in the pairwise matrix do not need to be > >>>> mentioned. > >>>> > >>>> Yes, the software will calculate the pairwise support counts > >>>> from the > >>>> numbers in the pairwise matrix. But that fact doesn't need to be > >>>> mentioned -- to the voters, or in the legal description. > >>>> > >>>> The resulting improved Ranked Robin method can be described as > >>>> follows: > >>>> > >>>> "The [improved] Ranked Robin method elects the candidate who has > >>>> the > >>>> most number of one-on-one wins against every other candidate > >>>> plus half > >>>> the number of one-on-one ties. [*] If more than one candidate > >>>> has the > >>>> same largest number, the method elects from those tied > >>>> candidates the > >>>> candidate with the highest pairwise support count. The pairwise > >>>> support count for each of the tied candidates is the sum, across > >>>> all > >>>> the ballots, of the number of tied [**] candidates who are ranked > >>>> lower than the candidate whose pairwise support count is being > >>>> counted." > >>>> > >>>> [*] The wording can be adjusted depending on which Copeland > >>>> variation > >>>> is desired. Adding the words "minus the number of one-on-one > >>>> losses" > >>>> would specify the other variation. > >>>> > >>>> [**] Importantly, the ballot marks for the non-tied candidates > >>>> must be > >>>> ignored when resolving the tie. > >>>> > >>>> When the election results are displayed, they might look something > >>>> like this, where the names are from the Ranked Robin article, > >>>> and the > >>>> numbers don't apply to any particular case: > >>>> > >>>> > >>>> Matchup win and loss counts: > >>>> > >>>> Ava: 4 wins (against ...) and 2 losses (to ...) > >>>> > >>>> Bianca: 4 wins (against ...) and 2 losses (to ...) > >>>> > >>>> Cedric: 3 wins (against ...) and 3 losses (to ...) > >>>> > >>>> Deegan: 3 wins (against ...) and 3 losses (to ...) > >>>> > >>>> Eli: 2 wins (against ...) and 4 losses (to ...) > >>>> > >>>> Fabio: 0 wins and 6 losses > >>>> > >>>> > >>>> The result is a tie between Ava and Bianca because they each > >>>> have > >>>> 4 wins, and that's more than any other candidate. Considering > just > >>>> these tied candidates, their pairwise support counts are: > >>>> > >>>> Ava: 213 > >>>> > >>>> Bianca: 123 > >>>> > >>>> So Ava wins! > >>>> > >>>> > >>>> Notice there's no need to show a pairwise matrix! > >>>> > >>>> To prevent a potential source of confusion, the Wikipedia article > >>>> about the Borda count begins with the words "The Borda count is a > >>>> family of positional voting rules which gives each candidate, > >>>> for each > >>>> ballot, a number of points corresponding to the number of > >>>> candidates > >>>> ranked lower." The last portion of this sentence describes > >>>> pairwise > >>>> support counts, but it has nothing to do with the Borda count. > The > >>>> Wikipedia article for "positional voting" correctly says: > >>>> "Positional > >>>> voting is a ranked voting electoral system in which the options or > >>>> candidates receive points based on their rank position on each > >>>> ballot > >>>> and the one with the most points overall wins." The remainder of > >>>> Wikipedia's Borda count article correctly specifies positional > >>>> voting > >>>> in the descriptions and examples. The Borda count article at > >>>> Electowiki does not include this first-sentence mistake. I'm > >>>> going to > >>>> let someone else figure out how the first sentence in Wikipedia > >>>> should > >>>> be worded. (I'd rather fight other battles.) > >>>> > >>>> I'm calling attention to this difference between pairwise support > >>>> counts and the Borda count because this issue has previously > caused > >>>> confusion in this forum. > >>>> > >>>> Getting back to the Ranked Robin method, this improved version > >>>> is not > >>>> likely to significantly increase the failure rates of the most > >>>> important failure criteria, and it's likely to reduce some > >>>> failure rates. > >>>> > >>>> Currently the Ranked Robin article claims that the method passes > >>>> some > >>>> fairness criteria that it actually doesn't pass. When the Ranked > >>>> Robin article is improved to include a concise description of the > >>>> method (which should be near the beginning), some experts here can > >>>> identify which of the listed "pass" criteria need to be moved to > >>>> the > >>>> listed "fail" criteria. > >>>> > >>>> Interestingly, the Ranked Robin method and its name were created > by > >>>> people who have previously promoted only STAR voting. I'm pleased > >>>> that they are finally recognizing that STAR ballots are not > >>>> going to > >>>> replace ranked choice ballots throughout the US. And that they > >>>> recognize the need to promote a method that takes advantage of the > >>>> Forward Party's recommendation of "ranked choice voting." > >>>> > >>>> Looking at the broader perspective ... > >>>> > >>>> The current version of Ranked Robin already has these advantages: > >>>> > >>>> * Uses pairwise vote counting, which looks deeper into the ballot > >>>> preferences compared to instant-runoff voting. > >>>> > >>>> * Is precinct summable. > >>>> > >>>> * Allows voters to mark more than one candidate at the same > ranking > >>>> level. > >>>> > >>>> I suggest making it even easier to understand by using pairwise > >>>> support counts. This improvement will eliminate the need to > >>>> educate > >>>> voters about the pairwise matrix. And I believe this change will > >>>> still provide a similar level of fairness. > >>>> > >>>> Certainly, in multiple ways, it's much better than > >>>> instant-runoff voting. > >>>> > >>>> Richard Fobes > >>>> The VoteFair guy > >>>> ---- > >>>> Election-Methods mailing list - see https://electorama.com/em > >>>> for list > >>>> info > >>> > > > > ---- > > Election-Methods mailing list - see https://electorama.com/em for > > list info > > > > > > > > ---- > > Election-Methods mailing list - see https://electorama.com/em for list > info > > > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >

 On 4/1/2022 6:24 PM, Forest Simmons wrote:

 ties:

 Both of these ways of resolving Copeland ties are more difficult to
 understand -- for most voters -- than the current version.

 As a further barrier to understanding, these definitions involve
 recursion.

   That's even more difficult to procedurally understand than a
 pairwise matrix.


 The goal of the Ranked Robin method (according to the description on
 Electowiki) is to provide a method that is reasonably easy to
 understand, yet uses ranked choice ballots and yields reasonably fair
 results.

 As I said, I'm proposing that the method be made even easier to
 understand by using pairwise support counts, which are directly
 countable from the ballots, without involving a pairwise matrix.

 Regarding your desire to protect against clone failures, those are just
 one special kind of "irrelevant alternative," as in IIA
 (independence of
 irrelevant alternatives).  Personally I'm more concerned about reducing
 all kinds of irrelevant alternatives.  In this case I'm concerned that
 attempts to fully eliminate clone independence failures might have the
 side effect of increasing the rates of other kinds of IIA failures.

 Richard Fobes
 The VoteFair guy


 On 4/1/2022 6:24 PM, Forest Simmons wrote:

 pairwise

 result in

 Copeland.

 <mailto:colin.champion@routemaster.app>
 <mailto:colin.champion@routemaster.app
 <mailto:colin.champion@routemaster.app>>>

 Richard – there are two ways of using a Borda tiebreak, sometimes
 written "Llull//Borda" and "Llull,Borda". It sounds like you
 understood me to be attributing "Llull,Borda" to you while you

 were

 actually advocating "Llull//Borda". (I have no idea which of these
 was Dasgupta and Maskin’s preference – I don’t think they were
 clear.) Certainly Llull//Borda reduces to a plurality choice

 between

 two tied candidates.
    Other tiebreaks (eg. minimax) can be used in the same two ways,
 which is why a fairly general notation exists. I can't say I

 like it

 as a notation, since it's far from self-explanatory.
       Colin

 On 31/03/2022 18:10, Richard, the VoteFair guy wrote:

 On 3/30/2022 11:51 PM, Colin Champion wrote:

 Borda count is a positional voting method:

 https://en.wikipedia.org/wiki/Positional_voting

 As a tie breaker, only the candidates who are tied are considered
 in this count.

 When the tie is between just two candidates, the Borda count

 would

 still use the (positional) numbers assigned by the voters.

 In contrast, I'm recommending a counting method that disregards
 which position contains the mark being counted.  So a
 two-candidate tie becomes simple plurality counting.

 To repeat, I'm suggesting breaking a tie by using pairwise

 support

 counts.  On one ballot the pairwise support count is the

 number of

 candidates who are ranked lower than the candidate getting the
 support count.  Those counts are added across all the ballots to
 yield that candidate's pairwise support count.

 A big advantage is that it can be counted directly from the
 ballots, without first creating a pairwise matrix.  Although
 software would use the pairwise matrix approach, voters and the
 legal description and the tabulated results would not mention the
 pairwise matrix.

 Richard Fobes
 The VoteFair guy


 On 3/30/2022 11:51 PM, Colin Champion wrote:

 Richard – is the candidate with the highest support count

 not the

 candidate with the highest Borda score? Have you not reinvented
 Dasgupta-Maskin?
    Colin


 On 31/03/2022 05:58, Richard, the VoteFair guy wrote:

 Here I'm suggesting a way to improve the recently (fall 2021)
 created
 "Ranked Robin" method, which is described at Electowiki at this
 link:

   https://electowiki.org/wiki/Ranked_Robin

 The improvement is to replace the first-level tie breaker

 -- which

 looks at margins calculated from the pairwise matrix -- with
 "pairwise
 support counts" -- which are easily described without using any
 numbers from the pairwise matrix.

 Starting from the beginning ...

 Currently the Ranked Robin method is described this way:

 "Elect the candidate who pairwise beats the greatest number of
 candidates."

 That's the method described by Ramon Llull (in 1299).

 According to Electowiki that's been improved to become the

 Copeland

 method, which elects "the candidate with the most (pairwise
 victories
 minus pairwise defeats)."

 According to Wikipedia the Copeland method doesn't do the
 subtraction
 and instead adds "half the number of candidates with whom

 he or she

 has a preference tie."

 All of these Copeland method variations produce lots of ties.

 So of course the Ranked Robin method needs tie breakers.

 Here's

 the
 first-level tie breaker as it's currently specified:

 "For each finalist, subtract the number of votes preferring

 each

 other
 finalist from the number of votes preferring them over each

 other

 finalist. The finalist with the greatest total difference is
 elected."

 A big disadvantage of this Ranked Robin tie breaker is that

 it uses

 numbers from the pairwise matrix.  Yet one of the stated goals
 of the
 Ranked Robin method is to avoid confusing voters with the

 pairwise

 matrix.

 Therefore I suggest replacing this tie-breaker method with the
 use of
 "pairwise support counts."  These counts are part of the

 "Instant

 Pairwise Elimination" (IPE) method, which is described at
 Electowiki
 at this link:

   https://electowiki.org/wiki/Instant_Pairwise_Elimination

 It says:

 "If an elimination round has no pairwise-losing candidate,

 then the

 method eliminates the candidate with the largest pairwise
 opposition
 count, which is determined by counting on each ballot the

 number of

 not-yet-eliminated candidates who are ranked above that
 candidate, and
 adding those numbers across all the ballots. If there is a tie
 for the
 largest pairwise opposition count, the method eliminates the
 candidate
 with the smallest pairwise support count, which similarly

 counts

 support rather than opposition. ..."

 Of course the second-level tie-breaker would be to use pairwise
 opposition counts.  (The pairwise support counts and pairwise
 opposition counts are not always symmetrical.)

 Notice that the numbers in the pairwise matrix do not need

 to be

 mentioned.

 Yes, the software will calculate the pairwise support counts
 from the
 numbers in the pairwise matrix.  But that fact doesn't need

 to be

 mentioned -- to the voters, or in the legal description.

 The resulting improved Ranked Robin method can be described as
 follows:

 "The [improved] Ranked Robin method elects the candidate

 who has

 the
 most number of one-on-one wins against every other candidate
 plus half
 the number of one-on-one ties. [*]  If more than one candidate
 has the
 same largest number, the method elects from those tied
 candidates the
 candidate with the highest pairwise support count.  The

 pairwise

 support count for each of the tied candidates is the sum,

 across

 all
 the ballots, of the number of tied [**] candidates who are

 ranked

 lower than the candidate whose pairwise support count is being
 counted."

 [*] The wording can be adjusted depending on which Copeland
 variation
 is desired.  Adding the words "minus the number of one-on-one
 losses"
 would specify the other variation.

 [**] Importantly, the ballot marks for the non-tied candidates
 must be
 ignored when resolving the tie.

 When the election results are displayed, they might look

 something

 like this, where the names are from the Ranked Robin article,
 and the
 numbers don't apply to any particular case:


     Matchup win and loss counts:

     Ava: 4 wins (against ...) and 2 losses (to ...)

     Bianca: 4 wins (against ...) and 2 losses (to ...)

     Cedric: 3 wins (against ...) and 3 losses (to ...)

     Deegan: 3 wins (against ...) and 3 losses (to ...)

     Eli: 2 wins (against ...) and 4 losses (to ...)

     Fabio: 0 wins and 6 losses


     The result is a tie between Ava and Bianca because they

 each

 have
 4 wins, and that's more than any other candidate.

 Considering just

 these tied candidates, their pairwise support counts are:

     Ava: 213

     Bianca: 123

     So Ava wins!


 Notice there's no need to show a pairwise matrix!

 To prevent a potential source of confusion, the Wikipedia

 article

 about the Borda count begins with the words "The Borda

 count is a

 family of positional voting rules which gives each candidate,
 for each
 ballot, a number of points corresponding to the number of
 candidates
 ranked lower."  The last portion of this sentence describes
 pairwise
 support counts, but it has nothing to do with the Borda

 count.  The

 Wikipedia article for "positional voting" correctly says:
 "Positional
 voting is a ranked voting electoral system in which the

 options or

 candidates receive points based on their rank position on each
 ballot
 and the one with the most points overall wins."  The

 remainder of

 Wikipedia's Borda count article correctly specifies positional
 voting
 in the descriptions and examples.  The Borda count article at
 Electowiki does not include this first-sentence mistake.  I'm
 going to
 let someone else figure out how the first sentence in Wikipedia
 should
 be worded.  (I'd rather fight other battles.)

 I'm calling attention to this difference between pairwise

 support

 counts and the Borda count because this issue has

 previously caused

 confusion in this forum.

 Getting back to the Ranked Robin method, this improved version
 is not
 likely to significantly increase the failure rates of the most
 important failure criteria, and it's likely to reduce some
 failure rates.

 Currently the Ranked Robin article claims that the method

 passes

 some
 fairness criteria that it actually doesn't pass.  When the

 Ranked

 Robin article is improved to include a concise description

 of the

 method (which should be near the beginning), some experts

 here can

 identify which of the listed "pass" criteria need to be

 moved to

 the
 listed "fail" criteria.

 Interestingly, the Ranked Robin method and its name were

 created by

 people who have previously promoted only STAR voting.  I'm

 pleased

 that they are finally recognizing that STAR ballots are not
 going to
 replace ranked choice ballots throughout the US.  And that they
 recognize the need to promote a method that takes advantage

 of the

 Forward Party's recommendation of "ranked choice voting."

 Looking at the broader perspective ...

 The current version of Ranked Robin already has these

 advantages:

 * Uses pairwise vote counting, which looks deeper into the

 ballot

 preferences compared to instant-runoff voting.

 * Is precinct summable.

 * Allows voters to mark more than one candidate at the same

 ranking

 level.

 I suggest making it even easier to understand by using pairwise
 support counts.  This improvement will eliminate the need to
 educate
 voters about the pairwise matrix.  And I believe this

 change will

 still provide a similar level of fairness.

 Certainly, in multiple ways, it's much better than
 instant-runoff voting.

 Richard Fobes
 The VoteFair guy
 ----
 Election-Methods mailing list - see https://electorama.com/em
 for list
 info

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

 list info

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

On 4/5/2022 9:03 PM, Forest Simmons wrote: > Recursion? Who said recursion? Where did you get that impression? > Where is the recursion in ... > > ... elect the candidate that, on the fewest number of ballots, > is pairwise defeated by the ballot favorite .... Forest, thank you for clarifying that your word "best" refers to "the ballot favorite." However, I still don't yet understand how the counting works. How can any ballot yield a defeat of the candidate who is ranked highest on that ballot? For example, suppose there is a ballot: A > B > C How would this one ballot be counted? Specifically, who is "pairwise defeated by the ballot favorite"? Thanks! Richard Fobes The VoteFair guy On 4/5/2022 9:03 PM, Forest Simmons wrote: > > > El sáb., 2 de abr. de 2022 9:41 p. m., Richard, the VoteFair guy > <electionmethods@votefair.org <mailto:electionmethods@votefair.org>> > escribió: > > On 4/1/2022 6:24 PM, Forest Simmons wrote: > > ... > > Here are two versions of decloned Copeland that are not prone to > ties: > > > > 1.Elect the candidate that, on the greatest number of ballots, > > pairwise defeats the candidate designated "worst." > > ... > > 2. Elect the candidate that, on the fewest number of ballots, is > > pairwise defeated by the candidate designated "best." > > Both of these ways of resolving Copeland ties are more difficult to > understand -- for most voters -- than the current version. > > > These are not ways of resolving Copeland ties ... rather they are two > succinctly stated complete versions of Copeland that only vanishingly > rarely require any tie breaker at all, let alone one as elaborate as you > are suggesting. > > > As a further barrier to understanding, these definitions involve > recursion. > > > Recursion? Who said recursion? Where did you get that impression? Where > is the recursion in ... > > ... elect the candidate that, on the fewest number of ballots, > is pairwise defeated by the ballot favorite .... > > To spell it out in complete detail ... just open each ballot B and, > after identifying the first preference X on each ballot B, give a > demerit to each candidate Y defeated pairwise by candidate X. > > After tallying all of the ballots in this same fashion, elect the > candidate with the fewest demerits. > > [That's all there is ... don't try reading something complicated into it > ;-) > If another method seems simpler, it's only because you are more familiar > with it.] > > A Condorcet candidate will have no demerits because, by definition a > Condorcet candidate is not defeated pairwise. > > The key to clone independence is focusing on defeats incurred by the > ballot favorites, rather than giving all pairwise defeats equal weight. > > > That's even more difficult to procedurally understand than a > pairwise matrix. > > > The goal of the Ranked Robin method (according to the description on > Electowiki) is to provide a method that is reasonably easy to > understand, yet uses ranked choice ballots and yields reasonably fair > results. > > As I said, I'm proposing that the method be made even easier to > understand by using pairwise support counts, which are directly > countable from the ballots, without involving a pairwise matrix. > > Regarding your desire to protect against clone failures, those are just > one special kind of "irrelevant alternative," as in IIA > (independence of > irrelevant alternatives). Personally I'm more concerned about reducing > all kinds of irrelevant alternatives. In this case I'm concerned that > attempts to fully eliminate clone independence failures might have the > side effect of increasing the rates of other kinds of IIA failures. > > Richard Fobes > The VoteFair guy > > > On 4/1/2022 6:24 PM, Forest Simmons wrote: > > Besides being prone to ties, Copeland also suffers from Clone > > Dependence, which makes it inferior to IRV in that regard. > > > > Here are two versions of decloned Copeland that are not prone to ties: > > > > 1.Elect the candidate that, on the greatest number of ballots, > pairwise > > defeats the candidate designated "worst." > > > > That is the burial resistant version of decloned Copeland. > > > > The other version, that may be more appealing to some people, is this: > > > > 2. Elect the candidate that, on the fewest number of ballots, is > > pairwise defeated by the candidate designated "best." > > > > Both of these methods are monotonic, clone free, and "Round Robin > > Efficient." > > > > It is practically impossible for either method to yield a tied > result in > > an actual political election involving hundreds of ballots. > > > > Because of that fact, the obligatory tie breaker does not need the > > special scrutiny that is so important for ordinary clone dependent > Copeland. > > > > Random Favorite would be the simplest ... and perfectly adequate tie > > breaker. > > > > At the other end of the spectrum, method one could serve as the tie > > breaker for method two, and vice-versa. > > > > Between those possibilities there are many others that are also > > perfectly adequate. > > > > -Forest > > > > > > > > > > El jue., 31 de mar. de 2022 12:04 p. m., Colin Champion > > <colin.champion@routemaster.app > <mailto:colin.champion@routemaster.app> > <mailto:colin.champion@routemaster.app > <mailto:colin.champion@routemaster.app>>> > > escribió: > > > > Richard – there are two ways of using a Borda tiebreak, sometimes > > written "Llull//Borda" and "Llull,Borda". It sounds like you > > understood me to be attributing "Llull,Borda" to you while you > were > > actually advocating "Llull//Borda". (I have no idea which of these > > was Dasgupta and Maskin’s preference – I don’t think they were > > clear.) Certainly Llull//Borda reduces to a plurality choice > between > > two tied candidates. > > Other tiebreaks (eg. minimax) can be used in the same two ways, > > which is why a fairly general notation exists. I can't say I > like it > > as a notation, since it's far from self-explanatory. > > Colin > > > > On 31/03/2022 18:10, Richard, the VoteFair guy wrote: > >> On 3/30/2022 11:51 PM, Colin Champion wrote: > >> > ... is the candidate with the highest support count not the > >> > candidate with the highest Borda score? Have you not reinvented > >> > Dasgupta-Maskin? > >> > >> Borda count is a positional voting method: > >> > >> https://en.wikipedia.org/wiki/Positional_voting > >> > >> As a tie breaker, only the candidates who are tied are considered > >> in this count. > >> > >> When the tie is between just two candidates, the Borda count > would > >> still use the (positional) numbers assigned by the voters. > >> > >> In contrast, I'm recommending a counting method that disregards > >> which position contains the mark being counted. So a > >> two-candidate tie becomes simple plurality counting. > >> > >> To repeat, I'm suggesting breaking a tie by using pairwise > support > >> counts. On one ballot the pairwise support count is the > number of > >> candidates who are ranked lower than the candidate getting the > >> support count. Those counts are added across all the ballots to > >> yield that candidate's pairwise support count. > >> > >> A big advantage is that it can be counted directly from the > >> ballots, without first creating a pairwise matrix. Although > >> software would use the pairwise matrix approach, voters and the > >> legal description and the tabulated results would not mention the > >> pairwise matrix. > >> > >> Richard Fobes > >> The VoteFair guy > >> > >> > >> On 3/30/2022 11:51 PM, Colin Champion wrote: > >>> Richard – is the candidate with the highest support count > not the > >>> candidate with the highest Borda score? Have you not reinvented > >>> Dasgupta-Maskin? > >>> Colin > >>> > >>> > >>> On 31/03/2022 05:58, Richard, the VoteFair guy wrote: > >>>> Here I'm suggesting a way to improve the recently (fall 2021) > >>>> created > >>>> "Ranked Robin" method, which is described at Electowiki at this > >>>> link: > >>>> > >>>> https://electowiki.org/wiki/Ranked_Robin > >>>> > >>>> The improvement is to replace the first-level tie breaker > -- which > >>>> looks at margins calculated from the pairwise matrix -- with > >>>> "pairwise > >>>> support counts" -- which are easily described without using any > >>>> numbers from the pairwise matrix. > >>>> > >>>> Starting from the beginning ... > >>>> > >>>> Currently the Ranked Robin method is described this way: > >>>> > >>>> "Elect the candidate who pairwise beats the greatest number of > >>>> candidates." > >>>> > >>>> That's the method described by Ramon Llull (in 1299). > >>>> > >>>> According to Electowiki that's been improved to become the > Copeland > >>>> method, which elects "the candidate with the most (pairwise > >>>> victories > >>>> minus pairwise defeats)." > >>>> > >>>> According to Wikipedia the Copeland method doesn't do the > >>>> subtraction > >>>> and instead adds "half the number of candidates with whom > he or she > >>>> has a preference tie." > >>>> > >>>> All of these Copeland method variations produce lots of ties. > >>>> > >>>> So of course the Ranked Robin method needs tie breakers. > Here's > >>>> the > >>>> first-level tie breaker as it's currently specified: > >>>> > >>>> "For each finalist, subtract the number of votes preferring > each > >>>> other > >>>> finalist from the number of votes preferring them over each > other > >>>> finalist. The finalist with the greatest total difference is > >>>> elected." > >>>> > >>>> A big disadvantage of this Ranked Robin tie breaker is that > it uses > >>>> numbers from the pairwise matrix. Yet one of the stated goals > >>>> of the > >>>> Ranked Robin method is to avoid confusing voters with the > pairwise > >>>> matrix. > >>>> > >>>> Therefore I suggest replacing this tie-breaker method with the > >>>> use of > >>>> "pairwise support counts." These counts are part of the > "Instant > >>>> Pairwise Elimination" (IPE) method, which is described at > >>>> Electowiki > >>>> at this link: > >>>> > >>>> https://electowiki.org/wiki/Instant_Pairwise_Elimination > >>>> > >>>> It says: > >>>> > >>>> "If an elimination round has no pairwise-losing candidate, > then the > >>>> method eliminates the candidate with the largest pairwise > >>>> opposition > >>>> count, which is determined by counting on each ballot the > number of > >>>> not-yet-eliminated candidates who are ranked above that > >>>> candidate, and > >>>> adding those numbers across all the ballots. If there is a tie > >>>> for the > >>>> largest pairwise opposition count, the method eliminates the > >>>> candidate > >>>> with the smallest pairwise support count, which similarly > counts > >>>> support rather than opposition. ..." > >>>> > >>>> Of course the second-level tie-breaker would be to use pairwise > >>>> opposition counts. (The pairwise support counts and pairwise > >>>> opposition counts are not always symmetrical.) > >>>> > >>>> Notice that the numbers in the pairwise matrix do not need > to be > >>>> mentioned. > >>>> > >>>> Yes, the software will calculate the pairwise support counts > >>>> from the > >>>> numbers in the pairwise matrix. But that fact doesn't need > to be > >>>> mentioned -- to the voters, or in the legal description. > >>>> > >>>> The resulting improved Ranked Robin method can be described as > >>>> follows: > >>>> > >>>> "The [improved] Ranked Robin method elects the candidate > who has > >>>> the > >>>> most number of one-on-one wins against every other candidate > >>>> plus half > >>>> the number of one-on-one ties. [*] If more than one candidate > >>>> has the > >>>> same largest number, the method elects from those tied > >>>> candidates the > >>>> candidate with the highest pairwise support count. The > pairwise > >>>> support count for each of the tied candidates is the sum, > across > >>>> all > >>>> the ballots, of the number of tied [**] candidates who are > ranked > >>>> lower than the candidate whose pairwise support count is being > >>>> counted." > >>>> > >>>> [*] The wording can be adjusted depending on which Copeland > >>>> variation > >>>> is desired. Adding the words "minus the number of one-on-one > >>>> losses" > >>>> would specify the other variation. > >>>> > >>>> [**] Importantly, the ballot marks for the non-tied candidates > >>>> must be > >>>> ignored when resolving the tie. > >>>> > >>>> When the election results are displayed, they might look > something > >>>> like this, where the names are from the Ranked Robin article, > >>>> and the > >>>> numbers don't apply to any particular case: > >>>> > >>>> > >>>> Matchup win and loss counts: > >>>> > >>>> Ava: 4 wins (against ...) and 2 losses (to ...) > >>>> > >>>> Bianca: 4 wins (against ...) and 2 losses (to ...) > >>>> > >>>> Cedric: 3 wins (against ...) and 3 losses (to ...) > >>>> > >>>> Deegan: 3 wins (against ...) and 3 losses (to ...) > >>>> > >>>> Eli: 2 wins (against ...) and 4 losses (to ...) > >>>> > >>>> Fabio: 0 wins and 6 losses > >>>> > >>>> > >>>> The result is a tie between Ava and Bianca because they > each > >>>> have > >>>> 4 wins, and that's more than any other candidate. > Considering just > >>>> these tied candidates, their pairwise support counts are: > >>>> > >>>> Ava: 213 > >>>> > >>>> Bianca: 123 > >>>> > >>>> So Ava wins! > >>>> > >>>> > >>>> Notice there's no need to show a pairwise matrix! > >>>> > >>>> To prevent a potential source of confusion, the Wikipedia > article > >>>> about the Borda count begins with the words "The Borda > count is a > >>>> family of positional voting rules which gives each candidate, > >>>> for each > >>>> ballot, a number of points corresponding to the number of > >>>> candidates > >>>> ranked lower." The last portion of this sentence describes > >>>> pairwise > >>>> support counts, but it has nothing to do with the Borda > count. The > >>>> Wikipedia article for "positional voting" correctly says: > >>>> "Positional > >>>> voting is a ranked voting electoral system in which the > options or > >>>> candidates receive points based on their rank position on each > >>>> ballot > >>>> and the one with the most points overall wins." The > remainder of > >>>> Wikipedia's Borda count article correctly specifies positional > >>>> voting > >>>> in the descriptions and examples. The Borda count article at > >>>> Electowiki does not include this first-sentence mistake. I'm > >>>> going to > >>>> let someone else figure out how the first sentence in Wikipedia > >>>> should > >>>> be worded. (I'd rather fight other battles.) > >>>> > >>>> I'm calling attention to this difference between pairwise > support > >>>> counts and the Borda count because this issue has > previously caused > >>>> confusion in this forum. > >>>> > >>>> Getting back to the Ranked Robin method, this improved version > >>>> is not > >>>> likely to significantly increase the failure rates of the most > >>>> important failure criteria, and it's likely to reduce some > >>>> failure rates. > >>>> > >>>> Currently the Ranked Robin article claims that the method > passes > >>>> some > >>>> fairness criteria that it actually doesn't pass. When the > Ranked > >>>> Robin article is improved to include a concise description > of the > >>>> method (which should be near the beginning), some experts > here can > >>>> identify which of the listed "pass" criteria need to be > moved to > >>>> the > >>>> listed "fail" criteria. > >>>> > >>>> Interestingly, the Ranked Robin method and its name were > created by > >>>> people who have previously promoted only STAR voting. I'm > pleased > >>>> that they are finally recognizing that STAR ballots are not > >>>> going to > >>>> replace ranked choice ballots throughout the US. And that they > >>>> recognize the need to promote a method that takes advantage > of the > >>>> Forward Party's recommendation of "ranked choice voting." > >>>> > >>>> Looking at the broader perspective ... > >>>> > >>>> The current version of Ranked Robin already has these > advantages: > >>>> > >>>> * Uses pairwise vote counting, which looks deeper into the > ballot > >>>> preferences compared to instant-runoff voting. > >>>> > >>>> * Is precinct summable. > >>>> > >>>> * Allows voters to mark more than one candidate at the same > ranking > >>>> level. > >>>> > >>>> I suggest making it even easier to understand by using pairwise > >>>> support counts. This improvement will eliminate the need to > >>>> educate > >>>> voters about the pairwise matrix. And I believe this > change will > >>>> still provide a similar level of fairness. > >>>> > >>>> Certainly, in multiple ways, it's much better than > >>>> instant-runoff voting. > >>>> > >>>> Richard Fobes > >>>> The VoteFair guy > >>>> ---- > >>>> Election-Methods mailing list - see https://electorama.com/em > >>>> for list > >>>> info > >>> > > > > ---- > > Election-Methods mailing list - see https://electorama.com/em for > > list info > > > > > > > > ---- > > Election-Methods mailing list - see https://electorama.com/em for > list info > > > ---- > Election-Methods mailing list - see https://electorama.com/em for > list info >