So this would be about Tideman Ranked-Pairs, or Schulze, or some other Condorcet-compliant method. It doesn't make much difference if the measure of Defeat Strength is Margins (supporting votes minus opposing votes), but what if Winning Votes is the measure of Defeat Strength in either RP or Schulze? How should a pair of candidates that are equally-ranked on a ballot be counted? Do you count it (as a winning vote) for *both* candidates? For neither candidate? (I dislike the idea of a half-vote for both candidates. And I hate the idea of not allowing equal-ranking in a Condorcet RCV election.) What is the right way to do this? It seems the most consistent might be to count an equally-ranked votes for **neither** candidate, since we consider unranked candidates as tied for last place on the ballot, and we would count those as votes. But what do you guys think? If we allow for equal-ranking in a Condorcet-compliant RCV, how do we deal with it in terms of vote totals?
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Hi Robert, In a WV method you can't trace beatpaths through a loss. So if A defeats B you can only trace from A to B, and the strength of the defeat is equal to the number of voters who preferred A>B. (If you added half a vote to A in the case of an equal ranking between A and B, this gives the same effect as margins, assuming you applied this rule everywhere.) Normally these methods do not show a difference based on whether an equal ranking was explicit, vs. implied via truncation. I would say this is mostly because explicit vs. implicit ranking isn't really native/inherent to the idea of Condorcet. But I'd suggest also because a distinction in treatment doesn't help the voter. A "half vote" treatment turns equal ranking into a "neither here nor there" strategy, where ranking your favorite candidates equal-top is prima facie not optimal regardless of your priorities. Kevin
Le lundi 20 mai 2019 à 16:06:32 UTC−5, robert bristow-johnson <[hidden email]> a écrit :
So this would be about Tideman Ranked-Pairs, or Schulze, or some other Condorcet-compliant method. It doesn't make much difference if the measure of Defeat Strength is Margins (supporting votes minus opposing votes), but what if Winning Votes is the measure of Defeat Strength in either RP or Schulze? How should a pair of candidates that are equally-ranked on a ballot be counted? Do you count it (as a winning vote) for *both* candidates? For neither candidate? (I dislike the idea of a half-vote for both candidates. And I hate the idea of not allowing equal-ranking in a Condorcet RCV election.) What is the right way to do this? It seems the most consistent might be to count an equally-ranked votes for **neither** candidate, since we consider unranked candidates as tied for last place on the ballot, and we would count those as votes. But what do you guys think? If we allow for equal-ranking in a Condorcet-compliant RCV, how do we deal with it in terms of vote totals?
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I agree with that (but i don't think it speaks to the point). You **can** include a tie in a beatpath, no? And, if it's RP with WV instead of margins, a tie can be used in the ranking graph, no? But this is not about ties in the vote totals. This is about whether we count ties on an individual ballot toward vote totals or do not count them. > So if A defeats B you can only trace from A to B, and the strength of the defeat is equal to the number of voters who preferred A>B. Only for WV. For Margins, the strength of the defeat is the number of voters who prefer A>B minus the number of voters who prefer B>A. Now for Margins, that net margin is unchanged if we count equal ranks as votes for both or votes for neither. But it **does** make a difference if we're measuring defeat strength using WV. > (If you added half a vote to A in the case of an equal ranking between A and B, this gives the same effect as margins, assuming you applied this rule everywhere.) for Margins, adding half a vote (to both A and B) or no vote to either or one vote for both makes no difference in the defeat strength. but it makes a difference for WV. > Normally these methods do not show a difference based on whether an equal ranking was explicit, vs. implied via truncation. If we don't count equal ranking as votes for either
candidate, you're correct. But if we *do* count equal ranked (active ranking, higher than unranked), there is a difference for WV. If two candidates were equally ranked (and not unranked), that WV is in the beatpath. It could end up counting in the net beatpath score, no? This last statement I can't figure out. bestest, r b-j > --
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Hi Robert, I'll add a bit below but the long story made short is that under WV, you traditionally don't add any tally to the pairwise matrix for a single ballot's tied rankings, no matter whether the equality is implicit or explicit. Also, the conventional wisdom is that voters don't want to create strong defeats among the candidates they like. So if you had different treatment for implicit or explicit equality, you might if anything want to add the tally for ties among truncated candidates, not explicitly ranked candidates. (But I don't actually think you should do that.)
Le lundi 20 mai 2019 à 23:06:57 UTC−5, robert bristow-johnson <[hidden email]> a écrit :
---------------------------- Original Message ---------------------------- >> Hi Robert, >I agree with that (but i don't think it speaks to the point). You **can** include a tie in a beatpath, no? And, if it's >RP with WV instead of margins, a tie can be used in the ranking graph, no? Generally no... With RP in particular I can't imagine it, because you are locking defeats in descending order of strength. Even if you assign a defeat strength to a tie, there is no way to say in which direction it can be locked. I wonder if you're thinking of the Schwartz set which has kind of a tricky definition. To be in the Schwartz set you need a path of wins to those candidates that have such a path to you. So you don't need a path to everyone. Tied contests can help you, but you don't actually trace through them. >But this is not
about ties in the vote totals. This is about whether we count ties on an individual ballot toward vote totals or do not count them. >> So if A defeats B you can only trace from A to B, and the strength of the defeat is equal to the number of voters who preferred A>B. >Only for
WV. For Margins, the strength of the defeat is the number of voters who prefer A>B minus the number >of voters who prefer B>A. Now for Margins, that net margin is unchanged if we count equal ranks as votes for both or votes for neither. >But it **does** make a difference if we're measuring defeat strength using WV. >> (If you added half a vote to A in the case of an equal ranking between A and B, this gives the same effect as margins, assuming you applied this rule everywhere.) >for Margins, adding half a vote (to both A and B) or no vote to either or one
vote for both makes no difference in the defeat strength. but it makes a difference for WV. What I mean is that if you always add half votes for (both types of) equality under WV, the method will give the same result as margins. >> Normally these methods do not show a difference based on whether an equal ranking was explicit, vs. implied via truncation. >If we don't count equal ranking as votes for either
candidate, you're correct. But if we *do* count equal ranked >(active ranking, higher than unranked), there is a difference for WV. If two candidates were equally ranked (and >not unranked), that WV is in the beatpath. It could end up counting in the net beatpath score, no? If you used such a rule then yes. But typically there is no concept of ranked vs. unranked. >> I would say this is mostly because explicit vs. implicit ranking isn't really native/inherent to the idea of Condorcet. >>But I'd suggest also because a distinction in treatment doesn't help the voter. A "half vote" treatment turns equal >>ranking into a "neither here nor there"
strategy, where ranking your favorite candidates equal-top is prima facie >>not optimal regardless of your priorities. >This last statement I can't figure out. Compare this with the concept of giving half-approvals under Approval. In most scenarios it's not possible to calculate that giving a candidate half an approval is strategically optimal. Similarly if you use a treatment of equal ranking such that a vote for A=B is simply midway, in effect, between voting A>B and B>A, then you should imagine that one of A>B or B>A must be a better vote than equality. I see this as a loss because ordinarily WV comes quite close to meeting the principle that you can rank your true favorite candidate equal-top with your compromise choice without thereby making the compromise choice lose to somebody worse. Kevin ---- Election-Methods mailing list - see https://electorama.com/em for list info |
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Robert, Jobst Heitzig's River method is identical to Tideman's method, except that one additionally ignores (without locking) defeats against candidates against whom some defeat has already been locked. This is possibly the easiest of the three to work out by hand.The other two he is referring to are Schulze and Tideman RP.?? Nearly all the time it will elect the same candidate and as far as I know is at least as good. I strongly suggest that the measure of defeat strength should be
Losing Votes and that ballots that equal-rank A and B above bottom
should contribute a whole vote On 21/05/2019 6:36 am, robert
bristow-johnson wrote:
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maybe someone needs to explain this more to me. i can think of a plausible example where it may differ from RP, but i can't think of what the motivating principle is. if River and RP disagree, why is the River winner a better choice?
well, we know when there are only 3 in the Smith Set, that Schulze and Tideman pick the same winner. dunno about this River method, though.
that's an interesting proposal i hadn't heard before. i'll be interested in hearing the motivation of it. i presume you mean that the defeat strength should be a strictly decreasing function of the losing votes, perhaps -LV (and the greatest defeat strength is the least negative -LV). in principle, why is this better than Winning Votes or Margins? (seems like Margins is the midpoint compromise between WV and LV since it is WV-LV.)
> I'll be posting more on this soonish, but since you asked the question
I i am digesting. Thank you, Chris.
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i had been asked: i'm not as good as you guys in dreaming up the number of ballots ranked however: ex. A>B>C>D but could you have a defeat matrix where A>B>C but C>A by a smaller defeat strength than A>B or B>C. But D>A by an even smaller defeat strength, however D<B and D>C? i dunno how to dream up ballot combinations to do that.
i think it's more complicated than RP. it's RP with an additional exception.
i have to say i am still not convinced of WV. probably Schulze-Margins is still the best, but RP-Margins good enough and possibly easier to sell to policy makers and the public. i like Margins in principle: The percentage Margin is (WV-LV)/(WV+LV) and is a measure of the decisiveness of defeat, without respect to the size of the election. So 5% defeat is a more decisive defeat than a 4% defeat. But if you consider every Condorcet pair as it's own little election, then the salience of the election would be the number of voters that weigh in on it, which is WV+LV. So if the net defeat strength (the index to rank the pairs) is the product of how important the election is with the decisiveness of defeat you get: (WV+LV) x (WV-LV)/(WV+LV) = WV - LV it just seems to me that Margins is better than WV. but say, WV, is a good idea for defeat strength. is LV a better idea? hmmmm. --
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Yes, I thought I sent my last email to the list. On 23/05/2019 9:48 am, robert
bristow-johnson wrote:
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Hi Robert,
A few comments on this exchange... >> Another Condorcet-compliant method that might interest you, from a Kevin >> Venzke webpage: >> >>> *Jobst Heitzig's River method* is identical to Tideman's method, >>> except that one additionally ignores (without locking) defeats against >>> candidates against whom some defeat has already been locked. This is >>> possibly the easiest of the three to work out by hand. >maybe someone needs to explain this more to me. i can think of a plausible example where it may differ from >RP, but i can't think of what the motivating principle is. if River and RP disagree, why is the River winner a better choice? There are theoretical arguments for each method, but for me the appeal of River is not that it gives a better winner but that it's easier to find the result. You don't have to look at as many pairwise contests as with RP. >> The other two he is referring to are Schulze and Tideman RP. Nearly all >> the time it will elect the same candidate and as far as I know is at >> least as good. >well, we know when there are only 3 in the Smith Set, that Schulze and Tideman pick the same winner. >dunno about this River method, though. Yes, it's the same. >i have to say i am still not convinced of WV. probably Schulze-Margins is still the best, but >RP-Margins good enough and possibly easier to sell to policy makers and the public. I really wonder. Could you sell A winning the below election? Especially to someone who doesn't know about pairwise matrices. The IRV or Bucklin advocate will find this absurd I would guess. 7 A>B. 5 B. 8 C. >i like Margins in principle: The percentage Margin is (WV-LV)/(WV+LV) and is a measure of the >decisiveness of defeat, without respect to the size of the election. So 5% defeat is a more decisive >defeat than a 4% defeat. >But if you consider every Condorcet pair as it's own little election, then the salience of the election >would be the number of voters that weigh in on it, which is WV+LV. I feel the loser of the most "salient" election should not be elected. I think this is in the same vein as saying that elections shouldn't be vulnerable to spoilers. E.g. if less salient contests affect the outcome it's likely they do so without benefit to the winners of those contests. (As there is only one prize to give out.) Kevin ---- Election-Methods mailing list - see https://electorama.com/em for list info |
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All criterias (Winning Votes, Margins, Relative Margins) have advantages and are acceptable. The fine choice depends on the interpretation you told voters that would be made of blank ballots. If a blank rank means "all bad", WV is perfect. If it means "all the same" Margin is good, and if it means "I don't know but I trust other voters to express a valid opinion about this option", then RM is perfect. Just tell voters the chosen interpretation of blank tanks in advance so they can fill a sincere ballot... Envoyé de mon iPhone
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I think all unranked candidates are tied for last place, no? Are there any variants of RCV that this is different? Whether equally-ranked candidates are counted as votes for *both* candidates or for *neither* candidates cannot make a difference for Margins. But it seems to me that it makes a difference if Winning Votes is the measure of defeat strength. regrads, r b-j
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Hi Stéphane,
Le jeudi 23 mai 2019 à 18:24:24 UTC−5, Stéphane Rouillon <[hidden email]> a écrit : >All criterias (Winning Votes, Margins, Relative Margins) have advantages and are acceptable. The fine >choice depends on the interpretation you told voters that would be made of blank ballots. If a blank rank >means "all bad", WV is perfect. If it means "all the same" Margin is good, and if it means "I don't know but >I trust other voters to express a valid opinion about this option", then RM is perfect. Just tell voters the >chosen interpretation of blank tanks in advance so they can fill a sincere ballot... For WV the truncated candidates can be presumed "all bad" (or unknown) but for explicit equal rankings, at the top, "all good" would describe it as well. It's true it's different in meaning from "all the same" but I think the main difference is in the practical effect of the vote. Kevin ---- Election-Methods mailing list - see https://electorama.com/em for list info |
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I think the problem with Schulze versus Ranked Pairs or River is that Schulze is more complicated to understand/explain, and also it's not even obviously a method. Also, realistically you'll probably never encounter an election where any of these three would give a different result. I've often heard people say that these methods can give different results, but I don't think I've ever seen an example, and this suggests to me that it would have to be pretty contrived and complex. But about Schulze not obviously being a method - have a look at the Wikipedia article under "Computation" - https://en.wikipedia.org/wiki/Schulze_method#Computation And it's that last bit that sticks out: "It can be proven that and together imply .^{[1]}^{:§4.1} Therefore, it is guaranteed (1) that the above definition of "better" really defines a transitive relation and (2) that there is always at least one candidate with for every other candidate ." "It can be proven..." I don't necessarily mind if it takes a complex proof to show that a method obeys certain criterion like monotonicity etc. But this is just about it being a method that can elect a winner. How complex is this proof? I'm just taking it on trust that it works as a method. With Ranked Pairs or River, it's pretty trivial. And on Warren Smith's rangevoting.org, https://rangevoting.org/SchulzeComplic.html "(4) If the strongest path from L to W, is stronger than, or at least as strong as, the strongest path from W to L, and if this is simultaneously true for every L, then W is a "Schulze winner." Schulze proved the theorem that such a W always exists (at least using "margins"; I am confused re the "winning-votes" enhancement)." So even Warren is confused about the proof for winning votes. And bear in mind, this isn't a proof about some property of the method, but that it is even a method. Toby From: robert bristow-johnson <[hidden email]> To: [hidden email] Sent: Wednesday, 22 May 2019, 23:14 Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on the ballot? ---------------------------- Original Message ---------------------------- Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equally-ranks on ballot? From: "Chris Benham" <[hidden email]> Date: Wed, May 22, 2019 2:35 pm To: [hidden email] -------------------------------------------------------------------------- > Another Condorcet-compliant method that might interest you, from a Kevin > Venzke webpage: > >> *Jobst Heitzig's River method* is identical to Tideman's method, >> except that one additionally ignores (without locking) defeats against >> candidates against whom some defeat has already been locked. This is >> possibly the easiest of the three to work out by hand. maybe someone needs to explain this more to me. i can think of a plausible example where it may differ from RP, but i can't think of what the motivating principle is. if River and RP disagree, why is the River winner a
better choice? > The other two he is referring to are Schulze and Tideman RP. Nearly all > the time it will elect the same candidate and as far as I know is at > least as good. well, we know when there are only 3 in the Smith Set, that Schulze and Tideman pick the same winner. dunno about this River method, though. > I strongly suggest that the measure of defeat strength should be Losing > Votes and that ballots that equal-rank A and B above bottom should > contribute a whole vote > to each in the A-B pairwise comparison. Ballots that rank A and B > equal-bottom (or truncate both A and B) should contribute nothing to the > A-B pairwise comparison. that's an interesting proposal i hadn't heard before. i'll be interested in hearing the motivation of it. i presume you mean that the defeat strength should be a strictly decreasing function of the losing votes, perhaps -LV (and the greatest
defeat strength is the least negative -LV). in principle, why is this better than Winning Votes or Margins? (seems like Margins is the midpoint compromise between WV and LV since it is WV-LV.) > I'll be posting more on this soonish, but since you asked the question
I > thought I'd just give you some food for thought to be going along with. i am digesting. Thank you, Chris. Election-Methods mailing list - see https://electorama.com/em for list info ---- Election-Methods mailing list - see https://electorama.com/em for list info |
In reply to this post by robert bristow-johnson
On 24/05/2019 12:59, Richard Lung
wrote:
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On 24/05/2019 12:43, Richard Lung
wrote:
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Good question Robert! Does anyone know of a publication that addresses this topic? On the site that Canadian MP Ron McKinnon published to promote Ranked Pairs, it appears the approach is to add voters' indifferent votes to both candidates when computing winning votes. The “majority vote” is the number of votes in which the given majority candidate is more-preferred-than the given minority candidate plus the no-preference value. The “minority vote” is the number of votes in which the minority-candidate is more-preferred-than the given majority candidate plus the no-preference value. (Click "Ranking the Pairs", then click "Notes") While I have ideas about the reasoning for the approach, I don't know for certain. I'll email him about it. MP's tend to be busy, so it may take a while to get a response. To speed things up, does anyone have a connection to Mr. McKinnon or the expert(s) he worked with? I would be interested in learning more about their reasoning for this approach. All the best, Carl On Mon, May 20, 2019, 4:06 PM robert bristow-johnson <[hidden email]> wrote:
On Mon, May 20, 2019, 4:06 PM robert bristow-johnson <[hidden email]> wrote:
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I've emailed that McKinnon guy soon after I discovered his page and I downloaded his pdf doc. Got no response. So, on an RCV ballot, every candidate unmarked is tied for last place on that ballot. If tied *marked* candidates get their tied votes counted as votes for both candidates, then marking all these unliked candidates the same lowest ranking level would count differently than if the voter instead left these unliked candidates unmarked. If the RP (or Schulze) election went into a cycle that involved any of these candidates, and if the defeat strength was WV, not Margins, the candidates tied at the bottom would get votes if they were ranked and tied that they would not get if they were unranked and tied, correct? And it would make no difference if it were Margins. I am still mulling over if that differentiation of ranked-and-tied to unranked-and-tied is something I would want or not. I know it makes no difference if there is no cycle or even if there was a cycle but only Margins is used as the measure of defeat strength. -------- Original message -------- From: Carl Schroedl <[hidden email]> Date: 5/25/2019 12:20 (GMT-08:00) To: [hidden email] Cc: EM <[hidden email]> Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equally-ranks on ballot? Good question Robert! Does anyone know of a publication that addresses this topic? On the site that Canadian MP Ron McKinnon published to promote Ranked Pairs, it appears the approach is to add voters' indifferent votes to both candidates when computing winning votes. The “majority vote” is the number of votes in which the given majority candidate is more-preferred-than the given minority candidate plus the no-preference value. The “minority vote” is the number of votes in which the minority-candidate is more-preferred-than the given majority candidate plus the no-preference value. (Click "Ranking the Pairs", then click "Notes") While I have ideas about the reasoning for the approach, I don't know for certain. I'll email him about it. MP's tend to be busy, so it may take a while to get a response. To speed things up, does anyone have a connection to Mr. McKinnon or the expert(s) he worked with? I would be interested in learning more about their reasoning for this approach. All the best, Carl On Mon, May 20, 2019, 4:06 PM robert bristow-johnson <[hidden email]> wrote:
On Mon, May 20, 2019, 4:06 PM robert bristow-johnson <[hidden email]> wrote:
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> On 24 May 2019, at 02:24, Stéphane Rouillon <[hidden email]> wrote:
> > All criterias (Winning Votes, Margins, Relative Margins) have advantages and are acceptable. The fine choice depends on the interpretation you told voters that would be made of blank ballots. If a blank rank means "all bad", WV is perfect. If it means "all the same" Margin is good, and if it means "I don't know but I trust other voters to express a valid opinion about this option", then RM is perfect. Just tell voters the chosen interpretation of blank tanks in advance so they can fill a sincere ballot... I like the approach of telling people clearly what their vote and not giving any preference between two candidates means. In Margins a tie can be said to mean "they are equally good", and in Relative Margins "I support the opinion of those voters that rank them". Winning Votes is quite difficult to explain since it says that the strength of preference is discontinuous with fully ranked votes (51-49 is a strong victory but 49-51 is a heavy loss). I tried to write good explanations on how Winning Votes and Losing Votes (that is also discontinuous) treat pairwise ties and rankings, but the end results were not very intuitive, so I will not include any of that mess here :-). I however want to discuss about another pairwise preference function. It could be called Moderated Margins. While Relative Margins says that ties mean that "others shall decide, and they shall use the strength of my vote too", Margins says "others shall decide, but without the strength of my vote" (the voter doesn't want to influence the strength of the final decision in any way), and Moderated Margins says "others shall decide, but I vote to make their final decision weaker" (lack of opinions should men that the outcome is weak). Relative Margins says that preference 30-10 should be seen as stronger than 60-40. Margins says that 30-10 should be seen as equally strong. Moderated Margins says that 30-10 should be seen as weaker than 60-40 (maybe "less decisive" since so many voters didn't tell their opinion). In Moderated Margins a tie can be said to mean "I want them to be more equal" or "against any preference". I.e. this voter wants to flatten the final preferences, and make the final preference strength weaker. Mathematically Moderated Margins can be defined so that 50% participation in the pairwise competition (when 50% of the preferences in the ballots are ties) should mean that the strength of the result should be only 50% of the strength it would otherwise be (Margins can be seen as the starting point here). While Relative Margins results can be seen to be Margins results, where the Margins result will be divided by participation (percentage), in Moderated Margins the Margins result will be multiplied with participation. In that sense they are mirroring each others at the opposite sides of the Margins philosophy. One could imagine also election methods where voters would be offered the option to cast different kind of ties. They could be e.g. relative, normal and moderated ties, or "others to decide", "I'm neutral", "make them equal". But probably that gets too complicated for any regular election. These options try to capture the sincere opinion of the voter. Strategic implications ffs. I modelled the preference functions in OSX's Grapher (file available if someone is interested). It was a nice way to visualise and study these and other preference functions in 3D. I'll explain the nature of preference functions and their 3D modelling a bit more. preference functions (f(x,y)) are defined in triangle (0%,0%), (100%,0%), (0%,100%) of the x-y-plane x and y coordinates refer to percentage of ballots that prefer A over B and B over A respectively values of f are in range [-1, 1] positive value => A preferred over B negative value => B preferred over A 0 => A and B are tied 1 => A preferred over B with maximal strength -1 => B preferred over A with maximal strength "tied" line from (0%,0%) to (50%,50%) all discussed preference functions (f) give the same value (0) f(x,x) = 0 "fully ranked" line from (100%,0%) to (0%,100%) all discussed preference functions (f), except Winning Votes, give the same result f(x,100%-x) = x at this line all ballots rank A over B or B over A values are linear in the sense that f(50%+2*x,50%-2*x) is always twice as strong preference as f(50%+x,50%-x) this linear approach is just a typical way to present the preference strengths (could be something else too) the triangle can be divided in two smaller triangles (0%,0%), (100%,0%), (50%,50%) (0%,0%), (50%,50%), (0%,100%) all discussed preference functions are "symmetric" with respect to A and B i.e. the two smaller triangles have the same form they are rotated 180° in 3D around the tie line f(x,y) = - f(y,x) in one of the smaller triangles A always wins, and in the other one B always wins f(x,y)>0 when x>y f(x,y)<0 when x<y p = participation values in range [0, 1] percentage of ballots that have ranked A over B or B over A p = x + y m = margin values in range [-1, 1] m = x - y r = ratio values in range [-1, 1] r = (x-y)/(x+y) = m/p Margins f(x,y) = x-y = m = r*p Relative Margins f(x,y) = (x-y)/(x+y) (defined as 0 when (x+y)=0) = m/p = r Moderated Margins f(x,y) = (x-y)*(x+y) = m*p = r*p^2 Winning Votes f(x,y) = if x>y then x elseif x<y then -y else 0 Losing Votes f(x,y) = if x>y then 1-y elseif x<y then -1+x else 0 ---- Election-Methods mailing list - see https://electorama.com/em for list info |
Juho,
Publish this... I'll cosign! Envoyé de mon iPhone Le 28 mai 2019 à 02:54, Juho Laatu <[hidden email]> a écrit : >> On 24 May 2019, at 02:24, Stéphane Rouillon <[hidden email]> wrote: >> >> All criterias (Winning Votes, Margins, Relative Margins) have advantages and are acceptable. The fine choice depends on the interpretation you told voters that would be made of blank ballots. If a blank rank means "all bad", WV is perfect. If it means "all the same" Margin is good, and if it means "I don't know but I trust other voters to express a valid opinion about this option", then RM is perfect. Just tell voters the chosen interpretation of blank tanks in advance so they can fill a sincere ballot... > > I like the approach of telling people clearly what their vote and not giving any preference between two candidates means. In Margins a tie can be said to mean "they are equally good", and in Relative Margins "I support the opinion of those voters that rank them". Winning Votes is quite difficult to explain since it says that the strength of preference is discontinuous with fully ranked votes (51-49 is a strong victory but 49-51 is a heavy loss). I tried to write good explanations on how Winning Votes and Losing Votes (that is also discontinuous) treat pairwise ties and rankings, but the end results were not very intuitive, so I will not include any of that mess here :-). > > I however want to discuss about another pairwise preference function. It could be called Moderated Margins. While Relative Margins says that ties mean that "others shall decide, and they shall use the strength of my vote too", Margins says "others shall decide, but without the strength of my vote" (the voter doesn't want to influence the strength of the final decision in any way), and Moderated Margins says "others shall decide, but I vote to make their final decision weaker" (lack of opinions should men that the outcome is weak). Relative Margins says that preference 30-10 should be seen as stronger than 60-40. Margins says that 30-10 should be seen as equally strong. Moderated Margins says that 30-10 should be seen as weaker than 60-40 (maybe "less decisive" since so many voters didn't tell their opinion). > > In Moderated Margins a tie can be said to mean "I want them to be more equal" or "against any preference". I.e. this voter wants to flatten the final preferences, and make the final preference strength weaker. Mathematically Moderated Margins can be defined so that 50% participation in the pairwise competition (when 50% of the preferences in the ballots are ties) should mean that the strength of the result should be only 50% of the strength it would otherwise be (Margins can be seen as the starting point here). While Relative Margins results can be seen to be Margins results, where the Margins result will be divided by participation (percentage), in Moderated Margins the Margins result will be multiplied with participation. In that sense they are mirroring each others at the opposite sides of the Margins philosophy. > > One could imagine also election methods where voters would be offered the option to cast different kind of ties. They could be e.g. relative, normal and moderated ties, or "others to decide", "I'm neutral", "make them equal". But probably that gets too complicated for any regular election. These options try to capture the sincere opinion of the voter. Strategic implications ffs. > > I modelled the preference functions in OSX's Grapher (file available if someone is interested). It was a nice way to visualise and study these and other preference functions in 3D. I'll explain the nature of preference functions and their 3D modelling a bit more. > > preference functions (f(x,y)) are defined in triangle (0%,0%), (100%,0%), (0%,100%) of the x-y-plane > x and y coordinates refer to percentage of ballots that prefer A over B and B over A respectively > values of f are in range [-1, 1] > positive value => A preferred over B > negative value => B preferred over A > 0 => A and B are tied > 1 => A preferred over B with maximal strength > -1 => B preferred over A with maximal strength > "tied" line from (0%,0%) to (50%,50%) > all discussed preference functions (f) give the same value (0) > f(x,x) = 0 > "fully ranked" line from (100%,0%) to (0%,100%) > all discussed preference functions (f), except Winning Votes, give the same result > f(x,100%-x) = x > at this line all ballots rank A over B or B over A > values are linear in the sense that f(50%+2*x,50%-2*x) is always twice as strong preference as f(50%+x,50%-x) > this linear approach is just a typical way to present the preference strengths (could be something else too) > the triangle can be divided in two smaller triangles > (0%,0%), (100%,0%), (50%,50%) > (0%,0%), (50%,50%), (0%,100%) > all discussed preference functions are "symmetric" with respect to A and B > i.e. the two smaller triangles have the same form > they are rotated 180° in 3D around the tie line > f(x,y) = - f(y,x) > in one of the smaller triangles A always wins, and in the other one B always wins > f(x,y)>0 when x>y > f(x,y)<0 when x<y > > p = participation > values in range [0, 1] > percentage of ballots that have ranked A over B or B over A > p = x + y > m = margin > values in range [-1, 1] > m = x - y > r = ratio > values in range [-1, 1] > r = (x-y)/(x+y) = m/p > > Margins > f(x,y) = x-y > = m = r*p > Relative Margins > f(x,y) = (x-y)/(x+y) (defined as 0 when (x+y)=0) > = m/p = r > Moderated Margins > f(x,y) = (x-y)*(x+y) > = m*p = r*p^2 > Winning Votes > f(x,y) = if x>y then x elseif x<y then -y else 0 > Losing Votes > f(x,y) = if x>y then 1-y elseif x<y then -1+x else 0 > > > > > ---- > Election-Methods mailing list - see https://electorama.com/em for list info Election-Methods mailing list - see https://electorama.com/em for list info |
I'm not very active at that front. If you are more active and want to promote this kind of tie related questions, I might cosign :-).
BR, Juho > On 28 May 2019, at 17:55, Stéphane Rouillon <[hidden email]> wrote: > > Juho, > > Publish this... I'll cosign! > > Envoyé de mon iPhone > > Le 28 mai 2019 à 02:54, Juho Laatu <[hidden email]> a écrit : > >>> On 24 May 2019, at 02:24, Stéphane Rouillon <[hidden email]> wrote: >>> >>> All criterias (Winning Votes, Margins, Relative Margins) have advantages and are acceptable. The fine choice depends on the interpretation you told voters that would be made of blank ballots. If a blank rank means "all bad", WV is perfect. If it means "all the same" Margin is good, and if it means "I don't know but I trust other voters to express a valid opinion about this option", then RM is perfect. Just tell voters the chosen interpretation of blank tanks in advance so they can fill a sincere ballot... >> >> I like the approach of telling people clearly what their vote and not giving any preference between two candidates means. In Margins a tie can be said to mean "they are equally good", and in Relative Margins "I support the opinion of those voters that rank them". Winning Votes is quite difficult to explain since it says that the strength of preference is discontinuous with fully ranked votes (51-49 is a strong victory but 49-51 is a heavy loss). I tried to write good explanations on how Winning Votes and Losing Votes (that is also discontinuous) treat pairwise ties and rankings, but the end results were not very intuitive, so I will not include any of that mess here :-). >> >> I however want to discuss about another pairwise preference function. It could be called Moderated Margins. While Relative Margins says that ties mean that "others shall decide, and they shall use the strength of my vote too", Margins says "others shall decide, but without the strength of my vote" (the voter doesn't want to influence the strength of the final decision in any way), and Moderated Margins says "others shall decide, but I vote to make their final decision weaker" (lack of opinions should men that the outcome is weak). Relative Margins says that preference 30-10 should be seen as stronger than 60-40. Margins says that 30-10 should be seen as equally strong. Moderated Margins says that 30-10 should be seen as weaker than 60-40 (maybe "less decisive" since so many voters didn't tell their opinion). >> >> In Moderated Margins a tie can be said to mean "I want them to be more equal" or "against any preference". I.e. this voter wants to flatten the final preferences, and make the final preference strength weaker. Mathematically Moderated Margins can be defined so that 50% participation in the pairwise competition (when 50% of the preferences in the ballots are ties) should mean that the strength of the result should be only 50% of the strength it would otherwise be (Margins can be seen as the starting point here). While Relative Margins results can be seen to be Margins results, where the Margins result will be divided by participation (percentage), in Moderated Margins the Margins result will be multiplied with participation. In that sense they are mirroring each others at the opposite sides of the Margins philosophy. >> >> One could imagine also election methods where voters would be offered the option to cast different kind of ties. They could be e.g. relative, normal and moderated ties, or "others to decide", "I'm neutral", "make them equal". But probably that gets too complicated for any regular election. These options try to capture the sincere opinion of the voter. Strategic implications ffs. >> >> I modelled the preference functions in OSX's Grapher (file available if someone is interested). It was a nice way to visualise and study these and other preference functions in 3D. I'll explain the nature of preference functions and their 3D modelling a bit more. >> >> preference functions (f(x,y)) are defined in triangle (0%,0%), (100%,0%), (0%,100%) of the x-y-plane >> x and y coordinates refer to percentage of ballots that prefer A over B and B over A respectively >> values of f are in range [-1, 1] >> positive value => A preferred over B >> negative value => B preferred over A >> 0 => A and B are tied >> 1 => A preferred over B with maximal strength >> -1 => B preferred over A with maximal strength >> "tied" line from (0%,0%) to (50%,50%) >> all discussed preference functions (f) give the same value (0) >> f(x,x) = 0 >> "fully ranked" line from (100%,0%) to (0%,100%) >> all discussed preference functions (f), except Winning Votes, give the same result >> f(x,100%-x) = x >> at this line all ballots rank A over B or B over A >> values are linear in the sense that f(50%+2*x,50%-2*x) is always twice as strong preference as f(50%+x,50%-x) >> this linear approach is just a typical way to present the preference strengths (could be something else too) >> the triangle can be divided in two smaller triangles >> (0%,0%), (100%,0%), (50%,50%) >> (0%,0%), (50%,50%), (0%,100%) >> all discussed preference functions are "symmetric" with respect to A and B >> i.e. the two smaller triangles have the same form >> they are rotated 180° in 3D around the tie line >> f(x,y) = - f(y,x) >> in one of the smaller triangles A always wins, and in the other one B always wins >> f(x,y)>0 when x>y >> f(x,y)<0 when x<y >> >> p = participation >> values in range [0, 1] >> percentage of ballots that have ranked A over B or B over A >> p = x + y >> m = margin >> values in range [-1, 1] >> m = x - y >> r = ratio >> values in range [-1, 1] >> r = (x-y)/(x+y) = m/p >> >> Margins >> f(x,y) = x-y >> = m = r*p >> Relative Margins >> f(x,y) = (x-y)/(x+y) (defined as 0 when (x+y)=0) >> = m/p = r >> Moderated Margins >> f(x,y) = (x-y)*(x+y) >> = m*p = r*p^2 >> Winning Votes >> f(x,y) = if x>y then x elseif x<y then -y else 0 >> Losing Votes >> f(x,y) = if x>y then 1-y elseif x<y then -1+x else 0 >> >> >> >> >> ---- >> 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 |
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