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 4/1/2022 12:04 AM, Colin Champion wrote: > Llull,Borda computes Borda scores on the entire field and > elects the Llull winner with the highest Borda score. > > Llull//Borda simulates a Borda-count runoff between the > Llull winners. This can be done using totals computed from > the original ballots. > > When I did a big simulation last year ... > ... I called Llull,Borda "Llull with a full Borda tiebreak" > and Llull//Borda "Llull with a restricted Borda tiebreak" ... Thanks, then the current definition of the Ranked Robin method is Copeland//Borda -- not Copeland,Borda. In contrast, I'm suggesting using pairwise support counts, which are described this way: On one ballot the pairwise support count is the number of candidates who are ranked lower than the candidate getting the support count. These counts are added across all the ballots to yield that candidate's pairwise support count. A big advantage of this method is that there is no need to teach voters about pairwise vote counting beyond the win-lose kind, namely which candidate got more votes than the other candidate in the pair. In turn, this means there's no need to mention the pairwise matrix, which is confusing to many people. More importantly, this improved version does not suffer from the ability to vote tactically, which is a big weakness of the Borda Count. Richard Fobes The VoteFair guy On 4/1/2022 12:04 AM, Colin Champion wrote: > Richard - I realise this wasn't very helpful... > Llull,Borda computes Borda scores on the entire field and elects the > Llull winner with the highest Borda score. > Llull//Borda simulates a Borda-count runoff between the Llull > winners. This can be done using totals computed from the original ballots. > When I did a big simulation last year, I was aware that there were > two ways of using tiebreaks but not aware of the "//" notation; I called > Llull,Borda "Llull with a full Borda tiebreak" and Llull//Borda "Llull > with a restricted Borda tiebreak"; and at least I can remember which of > these is which. > Colin > > On 31/03/2022 19:55, Colin Champion wrote: >> 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 >

On 03.04.2022 06:24, Richard, the VoteFair guy wrote: > On 4/1/2022 12:04 AM, Colin Champion wrote: >> Llull,Borda computes Borda scores on the entire field and >> elects the Llull winner with the highest Borda score. >> >> Llull//Borda simulates a Borda-count runoff between the >> Llull winners. This can be done using totals computed from >> the original ballots. >> >> When I did a big simulation last year ... >> ... I called Llull,Borda "Llull with a full Borda tiebreak" >> and Llull//Borda "Llull with a restricted Borda tiebreak" ... > > Thanks, then the current definition of the Ranked Robin method is > Copeland//Borda -- not Copeland,Borda. > > In contrast, I'm suggesting using pairwise support counts, > which are described this way: > > On one ballot the pairwise support count is the number of candidates who > are ranked lower than the candidate getting the support count.  These > counts are added across all the ballots to yield that candidate's > pairwise support count. > > A big advantage of this method is that there is no need to teach voters > about pairwise vote counting beyond the win-lose kind, namely which > candidate got more votes than the other candidate in the pair. > > In turn, this means there's no need to mention the pairwise matrix, > which is confusing to many people. > > More importantly, this improved version does not suffer from the ability > to vote tactically, which is a big weakness of the Borda Count. Could you give an example without truncation or equal rank, where your count elects a different candidate than the Borda count restricted to the same candidates? If the outcomes are the same then I don't think your count would be any less (or more) strategically vulnerable than the Borda count. -km

On 4/4/2022 3:49 AM, Kristofer Munsterhjelm wrote: > Could you give an example without truncation or equal rank, where your > count elects a different candidate than the Borda count restricted to > the same candidates? The big weakness of the Borda count is that many voters choose to mark their ballot using "equal ranks" (multiple candidates ranked at the same level) and truncated ballots. If, somehow, all voters can be forced to rank each candidate at a different rank, and assuming the number of ranks equals the number of candidates, then the Borda count produces very nice results. In other words, your constraints rule out the very reason I'm suggesting the switch from Borda count to pairwise support counts (for the Ranked Robin method). If you want evidence that pairwise support/opposition counts are better than the Borda count (without marking constraints), then here's a link to the scatter plot that shows Instant Pairwise Elimination (IPE) and Borda count having significantly different failure rates for CI (clone independence) and IIA (independence of irrelevant alternatives): https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg In a general way IPE is an upside-down version of the improved version of Ranked Robin that I'm suggesting. IPE eliminates pairwise losing candidates when they occur during the elimination rounds, and otherwise eliminates the candidate with the highest pairwise opposition count. In contrast, the Ranked Robin method finds the Copeland winner and uses as the tiebreaker the Borda count among the tied candidates. I'm suggesting a different tiebreaker, namely the tied candidate with the largest pairwise support count. This is the change that avoids the Borda-count vulnerability to tactical voting. Richard Fobes The VoteFair guy On 4/4/2022 3:49 AM, Kristofer Munsterhjelm wrote: > On 03.04.2022 06:24, Richard, the VoteFair guy wrote: >> On 4/1/2022 12:04 AM, Colin Champion wrote: >>> Llull,Borda computes Borda scores on the entire field and >>> elects the Llull winner with the highest Borda score. >>> >>> Llull//Borda simulates a Borda-count runoff between the >>> Llull winners. This can be done using totals computed from >>> the original ballots. >>> >>> When I did a big simulation last year ... >>> ... I called Llull,Borda "Llull with a full Borda tiebreak" >>> and Llull//Borda "Llull with a restricted Borda tiebreak" ... >> >> Thanks, then the current definition of the Ranked Robin method is >> Copeland//Borda -- not Copeland,Borda. >> >> In contrast, I'm suggesting using pairwise support counts, >> which are described this way: >> >> On one ballot the pairwise support count is the number of candidates who >> are ranked lower than the candidate getting the support count. These >> counts are added across all the ballots to yield that candidate's >> pairwise support count. >> >> A big advantage of this method is that there is no need to teach voters >> about pairwise vote counting beyond the win-lose kind, namely which >> candidate got more votes than the other candidate in the pair. >> >> In turn, this means there's no need to mention the pairwise matrix, >> which is confusing to many people. >> >> More importantly, this improved version does not suffer from the ability >> to vote tactically, which is a big weakness of the Borda Count. > > Could you give an example without truncation or equal rank, where your > count elects a different candidate than the Borda count restricted to > the same candidates? > > If the outcomes are the same then I don't think your count would be any > less (or more) strategically vulnerable than the Borda count. > > -km >

On 05.04.2022 02:23, Richard, the VoteFair guy wrote: > On 4/4/2022 3:49 AM, Kristofer Munsterhjelm wrote: >> Could you give an example without truncation or equal rank, where your >> count elects a different candidate than the Borda count restricted to >> the same candidates? > > The big weakness of the Borda count is that many voters choose to mark > their ballot using "equal ranks" (multiple candidates ranked at the same > level) and truncated ballots. > > If, somehow, all voters can be forced to rank each candidate at a > different rank, and assuming the number of ranks equals the number of > candidates, then the Borda count produces very nice results. I wouldn't say that it does. Consider this simple example with complete ballots: 66: A>B 34: B>A A wins by the majority criterion and has got a 66% supermajority. Now clone B into B1 and B2, and by convention say the positional score values are n-1 for first place and 0 for last: 66: A>B1>B2 34: B1>B2>A A obtains 2*66 = 132 points. B1 obtains 1*66 + 2*34 = 134 points and wins. An almost two thirds supermajority is wiped out by cloning, which I wouldn't really call a nice outcome. For a more general result, some algebra then gives that k clones can overturn a supermajority ever so slightly smaller than k/(k+1), e.g. 74: A>B1>B2>B3 26: B1>B2>B3>A B1 obtains 226 points to A's 222 points and wins. This also suggests that if equal rank existed, it wouldn't be used by tactical voters because there's more power to be had by ranking the viable opposition last (e.g. the A-voters responding by voting A>B3>B2>B1 above). > In other words, your constraints rule out the very reason I'm suggesting > the switch from Borda count to pairwise support counts (for the Ranked > Robin method). > > If you want evidence that pairwise support/opposition counts are better > than the Borda count (without marking constraints), then here's a link > to the scatter plot that shows Instant Pairwise Elimination (IPE) and > Borda count having significantly different failure rates for CI (clone > independence) and IIA (independence of irrelevant alternatives): > > https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg > > In a general way IPE is an upside-down version of the improved version > of Ranked Robin that I'm suggesting. I don't think IPE is really comparable to Borda, though. According to its Electowiki page, IPE proceeds by eliminating the Condorcet loser whenever one exists. So in all of the clone examples above (which have no Condorcet cycles anywhere in the rank order), the majority candidate would be the winner in IPE but not in Borda. Every (majoritarian deterministic) ranked voting method can be made to fail IIA by starting with an election where there's a Condorcet cycle. But Condorcet methods never fail when there's no such Condorcet cycle. So it would seem reasonable that a method that passes Condorcet loser and majority (like IPE does) would fail IIA less than a method that passes neither, like Borda, all else equal. So in an apples-to-apples comparison, the right comparison wouldn't be Borda vs IPE, but a Borda variant that uses the pairwise count vs one that uses your count. Or Ranked Robin with one tiebreaker vs with the other. -km