Re: [EM] Beatpath GMC compliance a mistaken standard?
Paul Kislanko wrote: This still makes no sense to me, since C has no more a majority in case 2 than it had in case 1. If mutual majority selects (A B) in case 1 and (A B C) in case 2, it makes no sense at all and should never be mentioned again. Mutual majority can still be useful. Let's make an analogy to Condorcet. The Condorcet criterion elects the CW if there is one. In other words, if there is a CW and that CW is candidate X, then the set from which Condorcet methods elect is { X }. If there is no CW, and the candidates for election are {A B C ... X }, then the set from which Condorcet methods elect is {A B C ... X }. Thus, Condorcet is useful when there is indeed a CW, but does nothing when there isn't. So it is with mutual majority as well. When there's a set that a majority ranks above all the others, then a method that passes mutual majority must elect from that set. When there is no such set, the method is free to pick any candidate yet still pass mutual majority. In that light, mutual majority seems very reasonable indeed: if there is a set so that a majority prefers that set to all others outside the set, then a candidate within that set should be elected. It's simply majority transported to sets. (And on another note, sorry for not mailing you this directly as well, Paul, but airmail.net seems to think my ISP is a dirty spammer.) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
This is the post that confused me, and got everbody yelling at me because I was confused. I call attention to theis bit: 26 AB 25 BA 49 C Mutual Majority elects {A,B} Now add 5 A bullet votes: 26 AB 25 BA 49 C 5 A Now Mutual Majority elects {A,B,C}. -- My original question was how does that make sense? The only answers have been addressed to me, and haven't addressed the question. The assertion that mutual majority elects was made by Kevin Venzke, so I guess my question directed to him. -Original Message- From: election-methods-boun...@lists.electorama.com [mailto:election-methods-boun...@lists.electorama.com] On Behalf Of Kevin Venzke Sent: Saturday, January 10, 2009 1:25 PM To: election-meth...@electorama.com Subject: Re: [EM] Beatpath GMC compliance a mistaken standard? Hi Chris, --- En date de : Sam 10.1.09, Chris Benham cbenha...@yahoo.com.au a écrit : De: Chris Benham cbenha...@yahoo.com.au Objet: [EM] Beatpath GMC compliance a mistaken standard? À: EM election-methods@lists.electorama.com, Kevin Venzke step...@yahoo.fr Cc: Markus Schulze markus.schu...@alumni.tu-berlin.de Date: Samedi 10 Janvier 2009, 0h31 Kevin, You wrote (9 Jan 2009): Well, with Mutual Majority, when X may win, it's possible that by adding bullet votes for X, then every other candidate becomes able to win. No it isn't. (Can you give an example?) 26 AB 25 BA 49 C Mutual Majority elects {A,B} Now add 5 A bullet votes: 26 AB 25 BA 49 C 5 A Now Mutual Majority elects {A,B,C}. By the way, it's very easy to define a single-winner method that satisfies Mutual Majority and which elects A in the first scenario and C in the second. Is there any way to explain, why it isn't completely absurd, that adding bullet votes for X should cause other candidates to become eligible to win? No. Ok. Why is mono-add-plump important? Because as an election method algorithm that fails it simply can't have any credibility as a quasi-intelligent device (which is what it is supposed to be) and because satisfying it should be (and is) very cheap. I feel that cheapness isn't relevant to whether a criterion is important, and certainly not to whether failing it is absurd. I save the term absurd for ideas that are bad regardless of what else is available. Regarding your first reason: Why is it acceptable to fail mono-add-top or Participation, but not acceptable to fail mono-add-plump? I guess that you based this distinction almost entirely on the relative cheapness of the criteria. If we view CDTT somehow as an election method, then when it fails mono-add-plump, the bullet votes for X are not simply strengthening X, they are also *weakening* some pairwise victory of Y over Z, which X had relied upon in order to have a majority beatpath to Z. That just testifies to the absurdity of an algorithm specifically putting some special significance on majority beatpaths versus other beatpaths. You're saying it's absurd, but what is absurd about it? The only reason X is allowed to win in the first place is due to a decisive YZ win providing a path from X to Z. Why is it clear that X should be entitled to remain a possible winner irrespective of the status of this win? I agree it would be better if this were possible, but I don't see anything essential about it. Of course, you can always use the mechanics of the method to explain why something has happened. But it seems to me that the bullet voters aren't purely strengthening X, they are also weakening Y and thereby also X. This contention that bullet voters for X aren't purely strengthening X but are in some way also weakening X is completely absurd. The strengthening and weakening are in two different senses. The strengthening is in terms of bullet votes. The weakening is in terms of losing a majority beatpath to a candidate that the voters decisively prefer. This is an oddity inherent to beatpaths, really I think only to beatpaths that measure defeat strengths in a silly way. I don't agree. Just because the use of beatpaths doesn't naturally cause problems with mono-add-plump, doesn't mean there aren't other oddities. Why should a candidate's ability to win, ever depend on the strength of a contest between two other candidates? But I contend that here in my situation 2 election Beatpath GMC does exclude the clearly strongest candidate C. You're attacking a lot more than just beatpath GMC with this scenario. Excluding C is required by SFC (the 51 B voters are basically assured LNHarm when voting for C, since B might be the sincere CW) and also basically any WV method. Yes, you catch on quick. It's just a bit puzzling that this thread is phrased as an attack on beatpath GMC, if the bottom line is that beatpath GMC isn't compatible with the positional criterion. In other words the CDTT set can fail to include the candidate that on overwhelming common-sense (mostly
Re: [EM] Beatpath GMC compliance a mistaken standard?
--- On Sun, 11/1/09, Paul Kislanko kisla...@airmail.net wrote: Arrr. Explain, someone, anyone, how MM can change an (A B) to an (A B C) possible winner set by adding voters for A. One way to say this is that since in the first example there was a set of voters (26 AB, 25 BA) that had a mutual majority opinion on candidate set {A, B} the winner must come from this set. In the second example there is no such majority set of voters that would prefer some set of candidates, so the criterion says nothing. There is thus no requirement not to allow C to win. There is also no requirement to allow C to win. Note also that set {A, B, C} refers to all candidates, i.e. {A, B, C, D, ... ,Z} (if there are more candidates than the three mentioned three). There are methods that meet mutual majority and are not very good. A method that would elect a random candidate from the set of all candidates but limiting the choice using the mutual majority criterion would be problematic in in the way you mention. Bullet votes would add C to the set of potential winners. Typically methods that meet mutual majority have however also other rules (or algorithm) that would elect the most sensible candidate from the sets {A, B} and {A, B, C}. Mutual majority could be just one of the criteria that the method meets. The behaviour of the methods is also often smooth in the sense that if there is almost mutual majority then the method elects a candidate that is (almost) in the mutual majority candidate set. So, even if some criterion may not apply in some set of votes the criterion may still roughly point out the direction where the winner will be found. 26 AB 25 BA 49 C Mutual Majority elects {A,B} Now add 5 A bullet votes: 26 AB 25 BA 49 C 5 A Now Mutual Majority elects {A,B,C}. Here words Now Mutual Majority elects {A,B,C} are a bit confusing since mutual majority doesn't set any requirements on who should be elected (nor elect anyone). There also seems to be a hidden assumption that there are no other candidates than A, B and C. Maybe it would be clearer to just say that any candidate can be elected (A, B, C or any other). Juho P.S. Also my direct mail to you was returned back to me (and this happened also with Kristofer Munsterhjelm some time ago). -Original Message- From: election-methods-boun...@lists.electorama.com [mailto:election-methods-boun...@lists.electorama.com] On Behalf Of Kristofer Munsterhjelm Sent: Sunday, January 11, 2009 2:23 AM To: election-meth...@electorama.com Cc: 'Markus Schulze' Subject: Re: [EM] Beatpath GMC compliance a mistaken standard? Paul Kislanko wrote: This still makes no sense to me, since C has no more a majority in case 2 than it had in case 1. If mutual majority selects (A B) in case 1 and (A B C) in case 2, it makes no sense at all and should never be mentioned again. Mutual majority can still be useful. Let's make an analogy to Condorcet. The Condorcet criterion elects the CW if there is one. In other words, if there is a CW and that CW is candidate X, then the set from which Condorcet methods elect is { X }. If there is no CW, and the candidates for election are {A B C ... X }, then the set from which Condorcet methods elect is {A B C ... X }. Thus, Condorcet is useful when there is indeed a CW, but does nothing when there isn't. So it is with mutual majority as well. When there's a set that a majority ranks above all the others, then a method that passes mutual majority must elect from that set. When there is no such set, the method is free to pick any candidate yet still pass mutual majority. In that light, mutual majority seems very reasonable indeed: if there is a set so that a majority prefers that set to all others outside the set, then a candidate within that set should be elected. It's simply majority transported to sets. (And on another note, sorry for not mailing you this directly as well, Paul, but airmail.net seems to think my ISP is a dirty spammer.) Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Paul, Regarding mutual majority: The problem is that the BA voters cannot be counted as solidly committed to {A}. They can only be counted to {B} and {A,B}. The additional A bullet voters can only be counted to {A}. C was excluded in scenario 1 because {A,B} possessed a majority. The new A voters increase the requirement for a majority but don't increase the strength of {A,B}. And {A} alone is not strong enough. It's certainly possible to criticize that the BA voters should be allowed to help {A} somehow. Regarding minimal defense (and I apologize for confusing the issue if I did so, by bringing up a second criterion): --- En date de : Sam 10.1.09, Paul Kislanko kisla...@airmail.net a écrit : A criterion more similar to what you have in mind, and which I consider more essential and effective than mutual majority, is this rendition of minimal defense: If a majority of the voters vote for X and don't vote for Y, then Y must not win. Although, the effect of that criterion is that {A,B} are the possible winners in both scenarios. I am still not understanding. In the second scenario only A has a majority of voters' support. So how does B get included in the second scenario? A's majority support serves to disqualify C, but can't disqualify B, because too much of A's support is also B's support. There's no majority that votes for a common candidate and doesn't vote for B. A criterion which said: If any candidate receives votes from a majority of the voters, then the winner must be one of these candidates, would be controversial because in a scenario like this: 49 AB 3 B 48 C This hypothetical criterion would require that B be elected, when many of us would rather say that A should win this election, because A can defeat the other candidates pairwise. Also, if B wins, then the A voters will feel that it wasn't safe to vote for B. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? JL
Hi Juho, --- En date de : Dim 11.1.09, Juho Laatu juho4...@yahoo.co.uk a écrit : Now Mutual Majority elects {A,B,C}. Here words Now Mutual Majority elects {A,B,C} are a bit confusing since mutual majority doesn't set any requirements on who should be elected (nor elect anyone). ... Maybe it would be clearer to just say that any candidate can be elected (A, B, C or any other). Yes, that would be clearer. However, given the subject of the thread that this comes from, it was necessary to treat Mutual Majority as a method and not a criterion. If I thought it was a novel discovery that carelessly electing from the set of candidates permissible by Mutual Majority, could violate mono-add-plump, then I would have used better wording. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Beatpath GMC compliance a mistaken standard?
Kevin, You wrote (10 Jan 2009): 26 AB 25 BA 49 C Mutual Majority elects {A,B} Now add 5 A bullet votes: 26 AB 25 BA 49 C 5 A Now Mutual Majority elects {A,B,C}. Oops! (I knew that!) Sorry for falsely contradicting you. Why is mono-add-plump important? Because as an election method algorithm that fails it simply can't have any credibility as a quasi-intelligent device (which is what it is supposed to be) and because satisfying it should be (and is) very cheap. I feel that cheapness isn't relevant to whether a criterion is important, and certainly not to whether failing it is absurd. I save the term absurd for ideas that are bad regardless of what else is available. Well I don't. If none of the election criteria were incompatible with each other, wouldn't we say that nearly all of them are important? Regarding your first reason: Why is it acceptable to fail mono-add-top or Participation, but not acceptable to fail mono-add-plump? I guess that you based this distinction almost entirely on the relative cheapness of the criteria. No. With mono-add-top and Participation, the quasi-intelligent device in reviewing its decision to elect X gets (possibly relevant) information about other candidates besides X. With mono-add-plump it gets nothing but information about and purely in favour of X, so it has no excuse at all for changing its mind about electing X. If we view CDTT somehow as an election method, then when it fails mono-add-plump, the bullet votes for X are not simply strengthening X, they are also *weakening* some pairwise victory of Y over Z, which X had relied upon in order to have a majority beatpath to Z. That just testifies to the absurdity of an algorithm specifically putting some special significance on majority beatpaths versus other beatpaths. You're saying it's absurd, but what is absurd about it? It's absurd that ballots that plump for X should in any way be considered relevant to the strength of the pairwise comparison between two other candidates. This absurdity only arises from the algorithm specifically using (and relying on) a majority threshold. It would be better, as in less arbitrary, if you simply criticized that beatpath GMC is incompatible with ratings summation. So is Condorcet. I don't think it's particularly arbitrary to value electing a voted Shwartz winner. I'm still a bit confused as to why anyone would be interested in beatpath GMC. So essentially, Schwartz//Approval is preferable to any method that satisfies SMD, Schwartz, and beatpath GMC. Yes, much preferable to any method that satisfies beatpath GMC period I don't feel there's an advantage to tending to elect candidates with more approval, because in turn this should just make voters approve fewer candidates when they doubt how the method will use their vote. And why is that a negative? I value LNHarm as an absolute guarantee, but in inherently- vulnerable-to-Burial Condocet methods, I think it is better if they have a watch who you rank because you could help elect them Approval flavour. From your earlier post: In the three-candidate case, at least, I think it's a problem to elect a candidate who isn't in the CDTT. Why? 25: AB 26: BC 23: CA 26: C In this situation 2 election from my demonstration, can you seriously contend (with a straight face) that electing C is a problem? Refresh my memory: who first suggested Max. Approval Opposition as a way of measuring a candidate's strength? Chris Benham Stay connected to the people that matter most with a smarter inbox. Take a look http://au.docs.yahoo.com/mail/smarterinbox Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Juho Laatu wrote: --- On Sun, 11/1/09, Kristofer Munsterhjelm km-el...@broadpark.no wrote: Let's consider the first election first, with truncation extended to full preference: 26: A B C 25: B A C 49: C A = B A B C: 100 prefer {A B C} to the empty set This case is interesting (not that it would have any impact on the ongoing mutual majority discussion but just for theoretical interest). The number of candidates was not exactly stated in the example. If there are e.g. four candidates then the votes would be: 26: A B C = D 25: B A C = D 49: C A = B = D Set {A, B, C} has in this case no support. Let's assume that there are also other citizens (=potential candidates who are however not candidates) than the named candidates. The opinions of the first 26 voters could be as follows. 26: X1 A B X2 C = D = X3 X4 The point here is that the voters have not said that they would prefer A, B, C and D to the other citizens / potential candidates (X1, X2,...). It is ok to say that if there are no mutual majorities the winner can be elected from the whole set of candidates {A, B, C} or {A, B, C, D} or whatever set. One can not say that the voters would prefer the all the candidates (or those that are named on the ballots) to other citizens. What is the meaning of saying that they prefer these candidates to an empty set? There is no real meaning - it's just an artifact of taking the process to its conclusion. The only thing it means is that all voters who voted, voted for the candidates they voted for, which is a tautology. Smaller unanimity sets can only exist if there's a candidate or a candidate set that everybody ranks last. Also note that changing a vote from A B to X1 A B can dissolve what would otherwise be a majority for {A B}. Mutual majority isn't complete - it only says that in certain cases (majority support for a set), certain things should happen (the method should elect from the set). In that respect, it's kind of like independence of clones. You can make a method that technically passes mutual majority yet wouldn't be any good, just like you can prefix a method with remove clones yet it would be a bad method if a single voter didn't vote clones in strict clone order. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
--- On Sun, 11/1/09, Kristofer Munsterhjelm km-el...@broadpark.no wrote: Juho Laatu wrote: --- On Sun, 11/1/09, Kristofer Munsterhjelm km-el...@broadpark.no wrote: Let's consider the first election first, with truncation extended to full preference: 26: A B C 25: B A C 49: C A = B A B C: 100 prefer {A B C} to the empty set This case is interesting (not that it would have any impact on the ongoing mutual majority discussion but just for theoretical interest). The number of candidates was not exactly stated in the example. If there are e.g. four candidates then the votes would be: 26: A B C = D 25: B A C = D 49: C A = B = D Set {A, B, C} has in this case no support. Let's assume that there are also other citizens (=potential candidates who are however not candidates) than the named candidates. The opinions of the first 26 voters could be as follows. 26: X1 A B X2 C = D = X3 X4 The point here is that the voters have not said that they would prefer A, B, C and D to the other citizens / potential candidates (X1, X2,...). It is ok to say that if there are no mutual majorities the winner can be elected from the whole set of candidates {A, B, C} or {A, B, C, D} or whatever set. One can not say that the voters would prefer the all the candidates (or those that are named on the ballots) to other citizens. What is the meaning of saying that they prefer these candidates to an empty set? There is no real meaning - it's just an artifact of taking the process to its conclusion. The only thing it means is that all voters who voted, voted for the candidates they voted for, which is a tautology. Smaller unanimity sets can only exist if there's a candidate or a candidate set that everybody ranks last. Also note that changing a vote from A B to X1 A B can dissolve what would otherwise be a majority for {A B}. Mutual majority isn't complete - it only says that in certain cases (majority support for a set), certain things should happen (the method should elect from the set). In that respect, it's kind of like independence of clones. You can make a method that technically passes mutual majority yet wouldn't be any good, just like you can prefix a method with remove clones yet it would be a bad method if a single voter didn't vote clones in strict clone order. Yes. I wish we had a more stable definitions and terms for discussing about criteria and how they are applied (e.g. just to meet the criterion or also its spirit when working outside of the defined scope of the criterion). Since all criteria can not be met I'd also like to have terminology for almost meeting some criteria, and following the spirit in most cases although not fully and formally meeting the criterion. (One example. Minmax(margins) doesn't meet independence of clones nor mutual majority, but it is very close to meeting both. It elects the candidate with weakest opposition instead (= their strength over the defenders when compared pairwise to any of the other candidates), and wile following this good principle is forced to violate the other good principles.) All methods violate some criteria. Typically we need a good balance of the violations and appropriate level of violation of each criterion. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] The structuring of power and the composition of norms by communicative assent
Here's one comment. The topmost thoughts in my mind when thinking about this approach is that 1) the principles are good and 2) making the votes public limits the usability of the method. Traditionally secret votes have been a building block of democracies. Public votes work somewhere but not everywhere. Juho --- On Tue, 6/1/09, Michael Allan m...@zelea.com wrote: I completed a theory outline, and here I'm posting it for the record. Critique is also welcome. Please point out flaws or ommissions. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? JL
Hi Juho, --- En date de : Dim 11.1.09, Juho Laatu juho4...@yahoo.co.uk a écrit : If there is a set of voters that form a majority and they all prefer all candidates of set A to all candidates of set B then candidates of set B should not win. This helps A (as requested) by at least eliminating some of the candidates from competing with A. This criterion may also eliminate all candidates. In such situations the rule of course will not apply. I haven't really thought what implications there are. Any comments? I would say you're close to inventing again either MDD or beatpath GMC / CDTT. All you've essentially said is that if A has a majority over B, B can't win. Because, each candidate could make up their own set. Having multiple candidates in a set doesn't make any difference. Under MDD the candidates of set B cannot be elected unless all candidates can be placed in a set B. This is inherently not cloneproof. Under beatpath GMC / CDTT the candidates of set B cannot be elected unless they have a majority-strength beatpath to all the candidates of set A. However, lacking this, the candidates of set B can also be disqualified when the candidates of set A merely have a majority-strength beatpath to the candidates of set B. A few years ago I considered a set where it wouldn't be enough for set A to merely have a beatpath to set B, in order to disqualify those candidates. But from what I remember, there were monotonicity problems. I guess there are probably clone problems also. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? JL
Ok, that relaxed version of mutual majority degraded faster to basic majority than I expected. Need to think more if there is something to conclude from the BA votes. Juho --- On Mon, 12/1/09, Kevin Venzke step...@yahoo.fr wrote: From: Kevin Venzke step...@yahoo.fr Subject: Re: [EM] Beatpath GMC compliance a mistaken standard? JL To: election-meth...@electorama.com Date: Monday, 12 January, 2009, 12:20 AM Hi Juho, --- En date de : Dim 11.1.09, Juho Laatu juho4...@yahoo.co.uk a écrit : If there is a set of voters that form a majority and they all prefer all candidates of set A to all candidates of set B then candidates of set B should not win. This helps A (as requested) by at least eliminating some of the candidates from competing with A. This criterion may also eliminate all candidates. In such situations the rule of course will not apply. I haven't really thought what implications there are. Any comments? I would say you're close to inventing again either MDD or beatpath GMC / CDTT. All you've essentially said is that if A has a majority over B, B can't win. Because, each candidate could make up their own set. Having multiple candidates in a set doesn't make any difference. Under MDD the candidates of set B cannot be elected unless all candidates can be placed in a set B. This is inherently not cloneproof. Under beatpath GMC / CDTT the candidates of set B cannot be elected unless they have a majority-strength beatpath to all the candidates of set A. However, lacking this, the candidates of set B can also be disqualified when the candidates of set A merely have a majority-strength beatpath to the candidates of set B. A few years ago I considered a set where it wouldn't be enough for set A to merely have a beatpath to set B, in order to disqualify those candidates. But from what I remember, there were monotonicity problems. I guess there are probably clone problems also. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Chris, --- En date de : Dim 11.1.09, Chris Benham cbenha...@yahoo.com.au a écrit : Kevin, You wrote (10 Jan 2009): 26 AB 25 BA 49 C Mutual Majority elects {A,B} Now add 5 A bullet votes: 26 AB 25 BA 49 C 5 A Now Mutual Majority elects {A,B,C}. Oops! (I knew that!) Sorry for falsely contradicting you. I guessed you must have known that. Why is mono-add-plump important? Because as an election method algorithm that fails it simply can't have any credibility as a quasi-intelligent device (which is what it is supposed to be) and because satisfying it should be (and is) very cheap. I feel that cheapness isn't relevant to whether a criterion is important, and certainly not to whether failing it is absurd. I save the term absurd for ideas that are bad regardless of what else is available. Well I don't. If none of the election criteria were incompatible with each other, wouldn't we say that nearly all of them are important? I don't think so. There are reasons for criteria to be important other than how easy they are to satisfy. Otherwise why would we ever bother to satisfy the difficult criteria? Regarding your first reason: Why is it acceptable to fail mono-add-top or Participation, but not acceptable to fail mono-add-plump? I guess that you based this distinction almost entirely on the relative cheapness of the criteria. No. With mono-add-top and Participation, the quasi-intelligent device in reviewing its decision to elect X gets (possibly relevant) information about other candidates besides X. How can it be relevant? X was winning and X is the preferred candidate on the new ballots. With mono-add-plump it gets nothing but information about and purely in favour of X, so it has no excuse at all for changing its mind about electing X. I don't think the information is purely about X. The method also learns about indecision between Y and Z. If we view CDTT somehow as an election method, then when it fails mono-add-plump, the bullet votes for X are not simply strengthening X, they are also *weakening* some pairwise victory of Y over Z, which X had relied upon in order to have a majority beatpath to Z. That just testifies to the absurdity of an algorithm specifically putting some special significance on majority beatpaths versus other beatpaths. You're saying it's absurd, but what is absurd about it? It's absurd that ballots that plump for X should in any way be considered relevant to the strength of the pairwise comparison between two other candidates. This absurdity only arises from the algorithm specifically using (and relying on) a majority threshold. Instead of strength you could view it as decisiveness. This is moot anyway, isn't it? We have Mutual Majority and beatpath GMC displaying the same phenomenon. Clearly there's no problem since neither criterion requires failures of mono-add-plump. It would be better, as in less arbitrary, if you simply criticized that beatpath GMC is incompatible with ratings summation. So is Condorcet. I don't think it's particularly arbitrary to value electing a voted Shwartz winner. I'm still a bit confused as to why anyone would be interested in beatpath GMC. Well, it's a majority-rule criterion that is compatible with clone independence and monotonicity. In the three-candidate case it's also compatible with LNHarm. By adding a vote for your second choice, you can't inadvertently remove your first preference from the CDTT. So essentially, Schwartz//Approval is preferable to any method that satisfies SMD, Schwartz, and beatpath GMC. Yes, much preferable to any method that satisfies beatpath GMC period I don't feel there's an advantage to tending to elect candidates with more approval, because in turn this should just make voters approve fewer candidates when they doubt how the method will use their vote. And why is that a negative? I value LNHarm as an absolute guarantee, but in inherently- vulnerable-to-Burial Condocet methods, I think it is better if they have a watch who you rank because you could help elect them Approval flavour. This is a negative because it suggests that your positional criterion will be self-defeating. If you want to write a criterion about burial, that would probably be better. From your earlier post: In the three-candidate case, at least, I think it's a problem to elect a candidate who isn't in the CDTT. Why? Because in the three-candidate case this is likely to be a failure of MD or SFC, or close to it. 25: AB 26: BC 23: CA 26: C In this situation 2 election from my demonstration, can you seriously contend (with a straight face) that electing C is a problem? It's not ideal. You have to use the BC votes contrary to the wishes of those voters, and for little purpose that isn't self-defeating considering that voters will just truncate, accomplishing the same result as
Re: [EM] The structuring of power and the composition of norms by communicative assent
Juho Laatu wrote: ... The topmost thoughts in my mind when thinking about this approach is that 1) the principles are good and 2) making the votes public limits the usability of the method. Traditionally secret votes have been a building block of democracies. Public votes work somewhere but not everywhere. (1). Re good principles. I've heard it suggested that modern democracy is the political form that is best suited to capitalism.^[1][2] If we change it to something with a firmer base in principles - a more substansive democracy - will it continue to be friendly to business entrepreneurs? If not, what will happen? Has anyone explored that scenario? (Any references?) (2). Re public/private voting. Maybe there are two possibilities: i) Initial participation by a small group of public pioneers gradually changes attitudes. Open voting comes to be accepted as a natural form of expression in the public sphere. Participation levels grow. (There remains a core who will not/cannot vote openly. We can get empirical data on this.) ii) A private voting facility (secret ballot) is grafted onto the public medium. Anyone who is content to participate merely as a voter (not as a delegate, or legislative drafter, etc.) may vote without disclosure. So we could extend participation to those who will not/cannot vote openly. Results verification (and maybe voter authentication) would be complicated by this, but the overall function of the medium should be unaffected. [1] Jürgen Habermas. 1973. Legitimation Crisis. Translated by Thomas McCarthy, 1975. Beacon Hill, Boston. [2] John Dunn. 1992. Conclusion. In Democracy: the Unfinished Journey, 508 BC to AD 1993. Edited by John Dunn. Oxford University Press. -- Michael Allan Toronto, 647-436-4521 http://zelea.com/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Beatpath GMC compliance a mistaken standard?
Kevin, You wrote (11 Jan 2009): There are reasons for criteria to be important other than how easy they are to satisfy. Otherwise why would we ever bother to satisfy the difficult criteria? Well, if as I said none of the criteria were incompatible with each other then presumably none of the criteria would be difficult. With mono-add-top and Participation, the quasi-intelligent device in reviewing its decision to elect X gets (possibly relevant) information about other candidates besides X. How can it be relevant? X was winning and X is the preferred candidate on the new ballots. You know that Condorcet is incompatible with mono-add-top (and so of course Participation), so if we value compliance with the Condorcet criterion information about candidates ranked below X must sometimes be relevant. But even if the quasi-intelligent device is mistaken in treating them as relevant, then that is a much more understandable and much less serious a blunder than the mono-add-plump failure. It's absurd that ballots that plump for X should in any way be considered relevant to the strength of the pairwise comparison between two other candidates. This absurdity only arises from the algorithm specifically using (and relying on) a majority threshold. We have Mutual Majority and beatpath GMC displaying the same phenomenon. No. I don't accept that 'being tossed out of the favoured (not excluded from winning) set' is exactly the same phenomenon as 'being joined by others in the favoured set'. The latter is obviously far less serious. I don't feel there's an advantage to tending to elect candidates with more approval, because in turn this should just make voters approve fewer candidates when they doubt how the method will use their vote. And why is that a negative? I value LNHarm as an absolute guarantee, but in inherently- vulnerable-to-Burial Condocet methods, I think it is better if they have a watch who you rank because you could help elect them Approval flavour. This is a negative because it suggests that your positional criterion will be self-defeating. How can it possibly be self-defeating? What is there to defeat? From your earlier post: In the three-candidate case, at least, I think it's a problem to elect a candidate who isn't in the CDTT. Why? Because in the three-candidate case this is likely to be a failure of MD or SFC, or close to it. I'm happy to have MD, and I don't care about SFC or close failures of MD. I'm still a bit confused as to why anyone would be interested in beatpath GMC. Well, it's a majority-rule criterion that is compatible with clone independence and monotonicity. Other majority-rule criteria with those same properties will suffice. In the three-candidate case it's also compatible with LNHarm. By adding a vote for your second choice, you can't inadvertently remove your first preference from the CDTT. Well since Condorcet is incompatible with LNHarm, that doesn't explain why Condorcet fans should like it. Also I think this is mainly just putting a positive spin on gross unfairness to truncators and the related silly random-fill incentive. 25: AB 26: BC 23: CA 26: C 100 ballots (majority threshold = 51) BC 51-27, CA 75-25, AB 48-26. In Schulze(Winning Votes), and I think also in any method that meets beatpath GMC and mono-raise, the 26C truncators can virtually guarantee that C be elected by using the random-fill strategy. That is silly and unfair. Also, by artificially denying the clearly strongest candidate any method that doesn't elect C must be vulnerable to Pushover, certainly much more than those that do elect C. http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023590.html (not that that is a very relevant strategy problem for the methods like WV that have the much easier and safer random-fill strategy for the C(B=C) voters.) Chris Benham Stay connected to the people that matter most with a smarter inbox. Take a look http://au.docs.yahoo.com/mail/smarterinbox Election-Methods mailing list - see http://electorama.com/em for list info