Re: [EM] Chris BC reply
I agree that "minmax" is not a good name. It refers maybe too much to the algorithm that can be used to seek the winner. Voters should not worry about that. And if one adds the "(margins)" part in the name gets even more complicated and algorithm oriented. For me "minmax" and "minmax(margins)" are a quite practical names since I'm interested in the algorithmic approach but I agree that the general audience is not. Therefore public promotion campaigns might benefit of using some other name. "Simpson-Kramer" is more human oriented but a bit long. I don't know it's history. Did those guys invent the method or was it covered maybe already by Condorcet and Llull? The name gets even more complex if one adds the margins part to it => "Simpson-Kramer(margins)". If we are looking for a name for "minmax(margins)" then one could use some name that refers to the specific characteristics of that method. I sometime ago used name "Least Additional Votes" but I'm not sure if that is a good enough. Also simpler "Additional Votes" could do, or maybe "Additional Votes Method", or something on the pairwise comparisons like "Beats All" :-). Plenty of names to choose from if one needs to popularize the method. Juho On Feb 20, 2007, at 14:11 , Markus Schulze wrote: > Dear Dave Ketchum, > > you wrote (20 Feb 2007): > >> Could there be a better name than "minmax"? > > I recommend the name "Simpson-Kramer". > > Markus Schulze > > > > > > election-methods mailing list - see http://electorama.com/em for > list info ___ Inbox full of spam? Get leading spam protection and 1GB storage with All New Yahoo! Mail. http://uk.docs.yahoo.com/nowyoucan.html election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Chris BC reply
Dear Dave Ketchum, you wrote (20 Feb 2007): > Could there be a better name than "minmax"? I recommend the name "Simpson-Kramer". Markus Schulze election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Chris BC reply
Thanks, I learned a bit but: I think cycles should not be hard to explain. We get to A>B>C>A when the pairs are near ties and the wins of the pairs proceed around the circle, either right or left. Minmax resolution of cycles does read easier than other methods. That the winner does not have to come from the Smith set should shock only those who expect too much from that label. Could there be a better name than "minmax"? DWK On Mon, 19 Feb 2007 19:04:09 +0200 Juho wrote: > On Feb 19, 2007, at 10:42 , Michael Ossipoff wrote: > > >> >>Juho wrote: >> >>(There are good methods also on the other side of the fence, >> >>>like minmax(margins).) >>> >>I reply: >> >>But, when saying that minmax(margins) is good, you've got to say >>what it's good for. I've told what the wv methods are good for: The >>best ones meet SFC, GSFC, and SDSC. >> >>Mike Ossipoff >> > > Ok, fair enough. > > My sympathies towards minmax(margins) come primarily from the way it > handles sincere votes. I'll address the behaviour with sincere votes > based on the two categorization criteria that I mentioned in my > previous mail. > > A) how to measure preference strength between two candidates > > Margins is a quite natural way of measuring the preference strength. > When comparing to winning votes I must say that defeat 0%-50% feels > worse than defeat 49%-50%, and that defeat 25%-75% feels quite > similar to 0%-50%. (One can always discuss what the intentions of > those voters that indicated a tie are, or if there are other better > ways to measure the preference strength than these two, but in any > case margins is quite decent.) > > B) is there a philosophy to "fix" only the cyclic preferences and > keep the "straight" ones > > Minmax does not follow this principle. It rather evaluates each > candidate in turn. I like this approach since trying to "linearize" > the preferences that are circular doesn't sound to me as natural. The > result that minmax gives is as follows. Elect the candidate that > would beat all the others. If there is no such candidate, elect the > one that would need least additional votes to beat the others. This > sounds like a natural utility function to me - at least for some > purposes (I accept that different utility functions may be best for > different elections). > > I also find the path based explanations a bit clumsy since in real > life after the election it does not appear very natural to think that > the elected candidate is bad because there is a path where she could > be changed to X that could be in turn changed to Y etc. It is maybe > more natural to just see how the elected candidate looks with respect > to the other candidates (without imagined winner change paths). > > Respect of the Smith set sounds natural when one images a picture of > the canidates and their preference relations drawn on a paper. The > most natural way to draw the figure is to draw the Smith set > candidates first in a group and only then the others below the Smith > set. It looks natural that one elects the winner from the Smith set. > But while respecting the fact that candidates outside the Smith set > lost to the Smith set candidates the description above totally > ignored the cyclic defeats. From minmax point of view they are just > as bad as the non cyclic defeats. > > The disrespect of the Smith set leads to the possibility of electing > even the Condorcet loser in some extreme situations. This is the case > e.g. when there is a very strong loop between three candidates (Smith > set), and all these candidates beat a fourth candidate with a very > small margin. Electing the Condorcet loser sounds quite irrational at > first sight. One must however note that the Condorcet loser would in > this case need only few votes to beat all the others, i.e. it is not > that far of being a Condorcet winner. The others are much farther > from that target. The minmax utility function measures the distance > to being a Condorcet winner, and as already noted above this is a > quite natural utility function (at least for some uses). Electing the > Condorcet loser can thus be seen as a positive thing in some > situations (and methods that do not do so could be rejected based on > this criterion). > > C) other stuff > > Minmax is good also in the sense that it is easy to explain. "Least > number of additional votes to beat all others" is an explanation that > most peope understand and may agree to. It is better to have this > kind of understandable explanations to the results of the election > than just saying that there was a cycle (people don't understand what > that is) and it was solved by a very complex algorithm in favour of > some candidate (people don't understand this either). > > The fact that the result for each candidate is a single number is > good since then people can see e.g. how much their favourite
Re: [EM] Chris BC reply
On Feb 19, 2007, at 10:42 , Michael Ossipoff wrote: > > > Juho wrote: > > (There are good methods also on the other side of the fence, >> like minmax(margins).) > > I reply: > > But, when saying that minmax(margins) is good, you've got to say > what it's good for. I've told what the wv methods are good for: The > best ones meet SFC, GSFC, and SDSC. > > Mike Ossipoff Ok, fair enough. My sympathies towards minmax(margins) come primarily from the way it handles sincere votes. I'll address the behaviour with sincere votes based on the two categorization criteria that I mentioned in my previous mail. A) how to measure preference strength between two candidates Margins is a quite natural way of measuring the preference strength. When comparing to winning votes I must say that defeat 0%-50% feels worse than defeat 49%-50%, and that defeat 25%-75% feels quite similar to 0%-50%. (One can always discuss what the intentions of those voters that indicated a tie are, or if there are other better ways to measure the preference strength than these two, but in any case margins is quite decent.) B) is there a philosophy to "fix" only the cyclic preferences and keep the "straight" ones Minmax does not follow this principle. It rather evaluates each candidate in turn. I like this approach since trying to "linearize" the preferences that are circular doesn't sound to me as natural. The result that minmax gives is as follows. Elect the candidate that would beat all the others. If there is no such candidate, elect the one that would need least additional votes to beat the others. This sounds like a natural utility function to me - at least for some purposes (I accept that different utility functions may be best for different elections). I also find the path based explanations a bit clumsy since in real life after the election it does not appear very natural to think that the elected candidate is bad because there is a path where she could be changed to X that could be in turn changed to Y etc. It is maybe more natural to just see how the elected candidate looks with respect to the other candidates (without imagined winner change paths). Respect of the Smith set sounds natural when one images a picture of the canidates and their preference relations drawn on a paper. The most natural way to draw the figure is to draw the Smith set candidates first in a group and only then the others below the Smith set. It looks natural that one elects the winner from the Smith set. But while respecting the fact that candidates outside the Smith set lost to the Smith set candidates the description above totally ignored the cyclic defeats. From minmax point of view they are just as bad as the non cyclic defeats. The disrespect of the Smith set leads to the possibility of electing even the Condorcet loser in some extreme situations. This is the case e.g. when there is a very strong loop between three candidates (Smith set), and all these candidates beat a fourth candidate with a very small margin. Electing the Condorcet loser sounds quite irrational at first sight. One must however note that the Condorcet loser would in this case need only few votes to beat all the others, i.e. it is not that far of being a Condorcet winner. The others are much farther from that target. The minmax utility function measures the distance to being a Condorcet winner, and as already noted above this is a quite natural utility function (at least for some uses). Electing the Condorcet loser can thus be seen as a positive thing in some situations (and methods that do not do so could be rejected based on this criterion). C) other stuff Minmax is good also in the sense that it is easy to explain. "Least number of additional votes to beat all others" is an explanation that most peope understand and may agree to. It is better to have this kind of understandable explanations to the results of the election than just saying that there was a cycle (people don't understand what that is) and it was solved by a very complex algorithm in favour of some candidate (people don't understand this either). The fact that the result for each candidate is a single number is good since then people can see e.g. how much their favourite lost to the winner. Referring to a complex algorithm and complex conditions that would have changed the outcome is not as helpful and does not explain which candidates got good/bad results. One value for each candidate makes it also easy to display the results, e.g. the intermediate results in TV during the vote counting process. One can also easily see if some candidate still has possibilities to win with the remaining votes that have not yet been calculated (luckily with minmax(margins) one can actually see the exact answer: number of additional votes needed (to beat all or at least to pass the best result so far)). The co
Re: [EM] Chris BC reply
Juho wrote: (There are good methods also on the other side of the fence, >like minmax(margins).) I reply: But, when saying that minmax(margins) is good, you've got to say what it's good for. I've told what the wv methods are good for: The best ones meet SFC, GSFC, and SDSC. Mike Ossipoff election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Chris BC reply
On Feb 18, 2007, at 2:32 , Chris Benham wrote: > There is group of pairwise methods that use "winning votes" to measure > "defeat strength" that as I understand it always give > the same winner unless there are more than three candidates in a top > cycle. That situation would be very very rare and almost > certainly would never happen in a public political election, so for > practical intents and purposes the differences between them > are insignificant and they are one method. > > The most prominent member of this group is Schulze (aka Beatpath), but > others are the Winning Votes versions of Ranked Pairs, > River, and Smith//MinMax. Correct me if I'm wrong, but isn't this all > that you are referring to by "a set of methods"? Good description. This nicely defines one category of Condorcet methods that are almost identical (for most practical purposes). My simple categorization of the basic Condorcet methods is as follows. A) how to measure preference strength between two candidates => margins and winning votes are the common alternatives (but I don't exclude others) B) is there a philosophy to "fix" only the cyclic preferences and keep the "straight" ones => leads e.g. to respect of the Smith set In this categorization Chris Benham's set is A = winning votes, B = yes. (There are good methods also on the other side of the fence, like minmax(margins).) Juho Laatu ___ All new Yahoo! Mail "The new Interface is stunning in its simplicity and ease of use." - PC Magazine http://uk.docs.yahoo.com/nowyoucan.html election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Chris BC reply
Michael Ossipoff wrote: > > Chris quotes me: > > Pasting from Mike's web page : > Beatpath Criterion (BC): > BC is only applied to rank methods. Its purpose is as a test for > compliance with SFC, GSFC, WDSC, & SDSC. Any rank method that meets BC > meets those 4 criteria. > BC: > No one should win who has a pairwise defeat that isn't the weakest > defeat in some cycle. (The strength of B's defeat by A is the number > of people voting A over B). > *** > BC is met only by SD, SSD, RP, and a few closely related methods. > BC generalizes & underlies the 4 majority-based defensive strategy > criteria (WDSC, SDSC, SFC, & GSFC). Any rank method that meets BC also > meets those 5 criteria. > > > Michael Ossipoff wrote: > So I prefer my own preference-based wordings of my defensive strategy > criteria. However, I myself have used a votes-only, rank-methods-only > test for compliance with my criteria: Steve Epplely’s Beatpath > Criterion. Any rank method that meets BC meets all four majority > defensive strategy criteria (SFC, GSFC,. WDSC, & SDSC). You could say > that no nonrank method meets BC, or you could say that it’s only > applied to rank methods. But it’s a convenient way to test for > compliance with all the majority defensive strategy criteria. BC’s > wording doesn’t make it obvious why it should be met, and so I prefer > my criteria, as criteria. I use BC as a test. > > Chris says: > > This "Beatpath Criterion" is more or less just Schulze(Winning Votes) > dressed up as a criterion. > I reply now: > > BC is a criterion, more than it’s “Schulze’s method dressed-up as a > criterion“. That’s because, if “Schulze’s method” were a criterion, it > would be met only by one method. A narrow criterion indeed. BC, on the > other hand, is met by a set of methods (including, but certainly not > limited to, “Schulze’s method”). There is group of pairwise methods that use "winning votes" to measure "defeat strength" that as I understand it always give the same winner unless there are more than three candidates in a top cycle. That situation would be very very rare and almost certainly would never happen in a public political election, so for practical intents and purposes the differences between them are insignificant and they are one method. The most prominent member of this group is Schulze (aka Beatpath), but others are the Winning Votes versions of Ranked Pairs, River, and Smith//MinMax. Correct me if I'm wrong, but isn't this all that you are referring to by "a set of methods"? > BC is for my own use. I don’t offer it as a criterion. Well, its labelled as a criterion and posted on your webpage. > That’s why Benham caught me off-guard when he told me that BC, which > I’d been using, isn’t useful. I meant that I don't think it is generally useful for the task of evaluating voting methods, for discerning or discovering which is/are the best. Because if someone thinks that it is a big black mark for a method if it doesn't meet all four of WDSC, SDSC,SFC, GSFC then their mind is mostly made up. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] Chris BC reply
Chris quotes me: Pasting from Mike's web page : Beatpath Criterion (BC): BC is only applied to rank methods. Its purpose is as a test for compliance with SFC, GSFC, WDSC, & SDSC. Any rank method that meets BC meets those 4 criteria. BC: No one should win who has a pairwise defeat that isn't the weakest defeat in some cycle. (The strength of B's defeat by A is the number of people voting A over B). *** BC is met only by SD, SSD, RP, and a few closely related methods. BC generalizes & underlies the 4 majority-based defensive strategy criteria (WDSC, SDSC, SFC, & GSFC). Any rank method that meets BC also meets those 5 criteria. Michael Ossipoff wrote: So I prefer my own preference-based wordings of my defensive strategy criteria. However, I myself have used a votes-only, rank-methods-only test for compliance with my criteria: Steve Epplelys Beatpath Criterion. Any rank method that meets BC meets all four majority defensive strategy criteria (SFC, GSFC,. WDSC, & SDSC). You could say that no nonrank method meets BC, or you could say that its only applied to rank methods. But its a convenient way to test for compliance with all the majority defensive strategy criteria. BCs wording doesnt make it obvious why it should be met, and so I prefer my criteria, as criteria. I use BC as a test. Chris says: This "Beatpath Criterion" is more or less just Schulze(Winning Votes) I reply now: How about a bit more less than more Maybe Chris knows what he means by more or less. You could say that anything is more or less anything, though it might be more on the less side. If you dressed-up BeatpathWinner as a criterion, various wv methods that meet BC wouldnt meet BeatpathWinner. Chris continues: dressed up as a criterion. I reply now: No, not dressed up as a criterion. BC is a criterion. No one has proposed it as a method. It is different from BeatpathWinner. As is often the case with criteria and methods, a number of methods meet BC, but only one method is BeatpathWinner. BC is not BeatpathWinner, and BC is a criterion. Chris continues: I don't think this is very useful I reply now: That depends on what you want to use it for, stupid. I stated what I use it for. I said that I use it for demonstrating compliance with all four of the majority defensive strategy criteria. Its very useful for that. I never said that it was useful for anything else, stupid. Chris continues: because (a) anybody who insists that a voting method meets this (i.e. the 4 criteria it tests for) has (98%) ended their search for the best voting method, and I reply now: Hey, Einstein, what if someone wants me to show them that, say, BeatpathWinner meets the four majority defensive strategy criteria.? There are properties that I claim desirable. Can you find it in your heart to forgive me if I want a way to demonstrate which methods comply? Chris continues: (b) some people like one or some but not all of the 4 criteria, so it is much better to be able to test for them individually. I reply now: People have asked me to demonstrate that certain methods meet all four of the majority defensive strategy criteria. Mike Ossipoff election-methods mailing list - see http://electorama.com/em for list info
