Re: [EM] About non-monotonicity and non-responding to previous posts...
Dave Ketchum wrote: Trying some fresh thinking for Condorcet, and what anyone should be able to see in the X*X array. I am ignoring labels such as Schulze and Ranked Pairs - this is human-doable and minimal effort - especially with normally having a CW and most cycles having the minimal three members. 1. Look at any pair of candidates. Loser is not the CW (there can be a tie in any comparison here - NOT likely in a normal election, but we have to be prepared with responses for such). 2. If there are other possible CWs, repeat step 1 with latest winner and one of them. 3. If there are other candidates latest winner has not been compared with, compare it with each of them. 4. If winner wins each of these, it is CW. 5. Winner and each who beat it in step 4 are cycle members. Also, any candidate beating any of these is also a cycle member. IF there is a CW, it should win - anything else is a complication, even if some math makes claims for the something else. Otherwise a simple cycle resolution should apply. Simply canceling the smallest margin has been thought of - that value means minimum difference in vote counts between actual and what is assumed. Note that each cycle member would be CW if remaining cycle members were ignored. As to voting: Equal ranks permitted. Write-ins permitted, and such a candidate wins with the same vote counts as if nominated. As to clones, strategy, primaries, and runoffs - all seem best ignored, though only a nuisance if some are determined to involve such. Okay, so let's see which *simple* cycle breaker provides as much as possible. To do that, we'll need to find out what simplicity means, and how to define as much as possible. That could be interesting in itself. Ranked Pairs (or River) seems nice, but even it may be too complex. Sports usually employ Copeland (but modified); perhaps that could be used - but Copeland is indecisive. One can add Smith compliance by checking for a CW among the first n ranked in the output, then n-1, then n-2 and so on, but that might also be too complex. Of course, if simplicity is paramount (i.e. we want very simple) we could just go with break it by whoever beats the Plurality winner by the greatest amount or plain old minmax (candidate with least worst defeat wins) or LR (greatest sum of victories wins). Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] About non-monotonicity and non-responding to previous posts...
What I wrote last time is about as simple as you get. Canceling the smallest margin cancels a three-member cycle, leaving the strongest member as CW. Could take more canceling for more complex, and thus rarer, cycles. Dave Ketchum On Nov 10, 2009, at 7:54 AM, Kristofer Munsterhjelm wrote: Dave Ketchum wrote: Trying some fresh thinking for Condorcet, and what anyone should be able to see in the X*X array. I am ignoring labels such as Schulze and Ranked Pairs - this is human-doable and minimal effort - especially with normally having a CW and most cycles having the minimal three members. 1. Look at any pair of candidates. Loser is not the CW (there can be a tie in any comparison here - NOT likely in a normal election, but we have to be prepared with responses for such). 2. If there are other possible CWs, repeat step 1 with latest winner and one of them. 3. If there are other candidates latest winner has not been compared with, compare it with each of them. 4. If winner wins each of these, it is CW. 5. Winner and each who beat it in step 4 are cycle members. Also, any candidate beating any of these is also a cycle member. IF there is a CW, it should win - anything else is a complication, even if some math makes claims for the something else. Otherwise a simple cycle resolution should apply. Simply canceling the smallest margin has been thought of - that value means minimum difference in vote counts between actual and what is assumed. Note that each cycle member would be CW if remaining cycle members were ignored. As to voting: Equal ranks permitted. Write-ins permitted, and such a candidate wins with the same vote counts as if nominated. As to clones, strategy, primaries, and runoffs - all seem best ignored, though only a nuisance if some are determined to involve such. Okay, so let's see which *simple* cycle breaker provides as much as possible. To do that, we'll need to find out what simplicity means, and how to define as much as possible. That could be interesting in itself. Ranked Pairs (or River) seems nice, but even it may be too complex. Sports usually employ Copeland (but modified); perhaps that could be used - but Copeland is indecisive. One can add Smith compliance by checking for a CW among the first n ranked in the output, then n-1, then n-2 and so on, but that might also be too complex. Of course, if simplicity is paramount (i.e. we want very simple) we could just go with break it by whoever beats the Plurality winner by the greatest amount or plain old minmax (candidate with least worst defeat wins) or LR (greatest sum of victories wins). Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] About non-monotonicity and non-responding to previous posts...
Trying some fresh thinking for Condorcet, and what anyone should be able to see in the X*X array. I am ignoring labels such as Schulze and Ranked Pairs - this is human-doable and minimal effort - especially with normally having a CW and most cycles having the minimal three members. 1. Look at any pair of candidates. Loser is not the CW (there can be a tie in any comparison here - NOT likely in a normal election, but we have to be prepared with responses for such). 2. If there are other possible CWs, repeat step 1 with latest winner and one of them. 3. If there are other candidates latest winner has not been compared with, compare it with each of them. 4. If winner wins each of these, it is CW. 5. Winner and each who beat it in step 4 are cycle members. Also, any candidate beating any of these is also a cycle member. IF there is a CW, it should win - anything else is a complication, even if some math makes claims for the something else. Otherwise a simple cycle resolution should apply. Simply canceling the smallest margin has been thought of - that value means minimum difference in vote counts between actual and what is assumed. Note that each cycle member would be CW if remaining cycle members were ignored. As to voting: Equal ranks permitted. Write-ins permitted, and such a candidate wins with the same vote counts as if nominated. As to clones, strategy, primaries, and runoffs - all seem best ignored, though only a nuisance if some are determined to involve such. Dave Ketchum On Nov 8, 2009, at 6:33 AM, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: On Nov 5, 2009, at 1:35 PM, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: i don't think a sequence of elimination rounds would be okay, but the method of picking the biggest loser for each round needs to be debated. i am not sure what would be best. Are you referring to IRV here? no. i mean if there is a Condorcet cycle, as an alternative to Schulze or Ranked Pairs or whatever, you could start with the Smith Set and, with some meaningful metric, eliminate a candidate deemed to be the biggest loser, then rerun the superficial Condorcet tally (just see if there is a Condorcet winner among the candidates left) and repeat until a Condorcet winner is apparent from the candidates left over. I've been browsing old posts of this list, and I've encountered the idea or method of sprucing up, which may be of interest in this respect: http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2004-December/014372.html The relevant post for determining cycles is here: http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2004-December/014373.html and basically says that, in public elections, and in every election if the base method passes certain criteria, the question of how to resolve cycles can be reduced to drawing the borders of three regions of a triangle. The complexity of the question has thus been reduced quite a bit, even if it is now very abstract. On another note, Condorcet cycles don't have to be resolved through elimination. Also, there may be subsets of the Smith or Schwartz set, such as the uncovered (Landau, Fishburn) set, that have just one candidate even when the former sets have multiple, that can be used to resolve the cycles. Picking uncovered candidates confers protection against certain forms of strategy, as well. All of this is theoretical, since the methods are too clumsy for public proposal, but one has to start somewhere :-) You're right. If I were to guess, I'd say that in most situations, unless the electorate is small or uncertain, there will be a CW; however, once the method has been adopted, parties will try to coordinate strategies to induce a cycle, really? Terry B (also a Burlington resident) told me that, and i find that to be an untested hypothesis. since the parties do not know who will benefit from a cycle (who can tell the future?), i really have my doubts about that. They'll try, but that doesn't necessarily mean they'll succeed. If the method resists the initial strategy, they would eventually give up. In the case of STV, vote management did work (but it was very risky), and so the parties continued, adding noise to the system. I do think the good methods (River, MAM/Ranked Pairs, Schulze, etc) will manage to resist the initial attempts at coordinated strategy, but it does emphasize that you need some resistance to strategy in order to survive the metaphorical birth of fire. Some strategies could be maintained longer than others. Those that involve manipulation of the candidate set would be easier for a party than those that involve electoral strategy, for instance; so a method should be cloneproof (which the three I mentioned are), and should be independent of as many alternatives as possible (the three
Re: [EM] About non-monotonicity and non-responding to previous posts...
robert bristow-johnson wrote: On Nov 5, 2009, at 1:35 PM, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: i don't think a sequence of elimination rounds would be okay, but the method of picking the biggest loser for each round needs to be debated. i am not sure what would be best. Are you referring to IRV here? no. i mean if there is a Condorcet cycle, as an alternative to Schulze or Ranked Pairs or whatever, you could start with the Smith Set and, with some meaningful metric, eliminate a candidate deemed to be the biggest loser, then rerun the superficial Condorcet tally (just see if there is a Condorcet winner among the candidates left) and repeat until a Condorcet winner is apparent from the candidates left over. I've been browsing old posts of this list, and I've encountered the idea or method of sprucing up, which may be of interest in this respect: http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2004-December/014372.html The relevant post for determining cycles is here: http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2004-December/014373.html and basically says that, in public elections, and in every election if the base method passes certain criteria, the question of how to resolve cycles can be reduced to drawing the borders of three regions of a triangle. The complexity of the question has thus been reduced quite a bit, even if it is now very abstract. On another note, Condorcet cycles don't have to be resolved through elimination. Also, there may be subsets of the Smith or Schwartz set, such as the uncovered (Landau, Fishburn) set, that have just one candidate even when the former sets have multiple, that can be used to resolve the cycles. Picking uncovered candidates confers protection against certain forms of strategy, as well. All of this is theoretical, since the methods are too clumsy for public proposal, but one has to start somewhere :-) You're right. If I were to guess, I'd say that in most situations, unless the electorate is small or uncertain, there will be a CW; however, once the method has been adopted, parties will try to coordinate strategies to induce a cycle, really? Terry B (also a Burlington resident) told me that, and i find that to be an untested hypothesis. since the parties do not know who will benefit from a cycle (who can tell the future?), i really have my doubts about that. They'll try, but that doesn't necessarily mean they'll succeed. If the method resists the initial strategy, they would eventually give up. In the case of STV, vote management did work (but it was very risky), and so the parties continued, adding noise to the system. I do think the good methods (River, MAM/Ranked Pairs, Schulze, etc) will manage to resist the initial attempts at coordinated strategy, but it does emphasize that you need some resistance to strategy in order to survive the metaphorical birth of fire. Some strategies could be maintained longer than others. Those that involve manipulation of the candidate set would be easier for a party than those that involve electoral strategy, for instance; so a method should be cloneproof (which the three I mentioned are), and should be independent of as many alternatives as possible (the three are all independent of candidates not in the Smith set, and River is also independent of Pareto-dominated alternatives). The voters themselves might also strategize. Such strategy would be less coordinated, but this is where the critics of Condorcet focus their efforts: if a large share of the electorate bury candidates (vote A ... B instead of A B ... because B is a threat), then you can get bad outcomes. The question here is whether the public will actually do that. in Burlington Vermont, Repubs who voted for their candidate as their first pick actually helped elect (with IRV) the candidate they liked the least and that would not have happened if it was Condorcet. they are mistaken in their belief that their candidate (the FPTP winner) should have won, but i can understand their voter regret in that their vote for their guy actually caused the election of the candidate they liked the least. Yes, it brings to mind a few pictures I saw on the web. http://www.braindoll.net/vote/#Which%20version%20is%20best%20%28or:%20Grudgeless%20Match%20between%20the%20Tomorrow%20Twins%29.3.1 FPTP's football field is nearly vertical, IRV's is better but still has a hill in it (minor parties are safe as long as they're minor, but when they start getting large, they'll interfere with the runoff process). Condorcet's is flat :-) There's certainly precedence for this, not with Condorcet there is. it's never been used in a government election. I meant more broadly. The parties will *try*, but will they succeed? Depends on the method. Unlike FairVote et al, we don't have a strong voice saying Hey public, if you think
Re: [EM] About non-monotonicity and non-responding to previous posts...
On Nov 8, 2009, at 6:33 AM, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: On Nov 5, 2009, at 1:35 PM, Kristofer Munsterhjelm wrote: ... Unlike FairVote et al, we don't have a strong voice saying Hey public, if you think Plurality sucks, implement [method here]. but if FairVote won't keep all of their eggs in the IRV basket, then we need someone to do the same for Condorcet. FairVote doesn't? I thought their problem was that they had committed to IRV as the electoral method from heaven, and thus they have to stick with it rather than, for instance, say Oh, oops, we were wrong, turns out that system is actually better. when i'm typing away and composing sentences in my head, sometimes i make the mistake of the Wicked Bible. usually the spurious omission or spurious inclusion of the word not has the tendency to change the meaning of a sentence to something not intended. FairVote *does* put all of their eggs in the IRV basket. and i have many times taken issue with them about it. i've sorta tired of repeatedly refuting Rob Ritchie recently. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] About non-monotonicity and non-responding to previous posts...
On Nov 5, 2009, at 1:35 PM, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: ... simplicity and sufficient transparency is important to have public confidence. otherwise i would probably just jump on the Schulze bandwagon. Ranked Pairs might be good here. If you can get the one you're explaining it to, to understand the pairwise way of thinking, then it easily follows that if you're going to build a ranking for society itself piece by piece, the stronger defeats should be considered before the weaker ones, and there you have Ranked Pairs. On the other hand, more organizations use Schulze than Ranked Pairs, so it comes down to which inspires greater confidence: simplicity or a record of use. i don't think a sequence of elimination rounds would be okay, but the method of picking the biggest loser for each round needs to be debated. i am not sure what would be best. Are you referring to IRV here? no. i mean if there is a Condorcet cycle, as an alternative to Schulze or Ranked Pairs or whatever, you could start with the Smith Set and, with some meaningful metric, eliminate a candidate deemed to be the biggest loser, then rerun the superficial Condorcet tally (just see if there is a Condorcet winner among the candidates left) and repeat until a Condorcet winner is apparent from the candidates left over. Do Condorcet winners appear often enough in reality that it is not a problem? since no government yet uses Condorcet, i don't think any of us know the answer. You're right. If I were to guess, I'd say that in most situations, unless the electorate is small or uncertain, there will be a CW; however, once the method has been adopted, parties will try to coordinate strategies to induce a cycle, really? Terry B (also a Burlington resident) told me that, and i find that to be an untested hypothesis. since the parties do not know who will benefit from a cycle (who can tell the future?), i really have my doubts about that. because that's the only way they can game the system. that's right. i see Condorcet as the least gameable (and the most compliant to the fundamental concept of democracy) than any of the others. *which* Condorcet (which boils down to which methods shall we use to resolve a cycle or tie) is a secondary issue, in my opinion. *any* Condorcet (with a reasonably meaningful method to resolve a cycle, i.e. let's not draw lots nor give it to a candidate outside of the Smith set) is better than IRV or Borda. and certainly better than FPTP. my rejection of Range voting is because the ballot requires more information from the voter than the simple ranked ballot of Condorcet, IRV or Borda. asking the voter to rate their candidate on a scale is asking too much and they would have to be thinking about what would happen if they rate *anyone* other than their primary pick with anything other than zero. the voter should feel free to pick their first pick, back it up with a second pick and not worry that their second pick somehow hurts their first. or that their first pick somehow hurts the interest of their second pick against some third candidate that they like even less. i think that Range voters will give the guy they like a 10 and everyone else a 0 in an effort to not harm the guy they like. then no more information is gathered from the voter than you get with FPTP. the ranked order ballot, where the voter only needs to ask themselves who do i prefer more, candidate A or candidate B? extracts exactly the right amount of information from the voter (i think that ties should be allowed and we shall assume of course that any candidate not ranked is tied for last place). in Burlington Vermont, Repubs who voted for their candidate as their first pick actually helped elect (with IRV) the candidate they liked the least and that would not have happened if it was Condorcet. they are mistaken in their belief that their candidate (the FPTP winner) should have won, but i can understand their voter regret in that their vote for their guy actually caused the election of the candidate they liked the least. There's certainly precedence for this, not with Condorcet there is. it's never been used in a government election. in how the various parties in STV New York tried to employ vote management to get more than their fair share of the local council. but for there to be a paradox, you would need a situation where there is no predictable voter alignment along a single dimensioned political spectrum. you would need to have (in 2000) a lot of Nader voters who choose Bush over Gore as their second choice, and Bush voters that sincerely choose Nader over Gore, something i really do not expect. Perhaps the existence of Condorcet would permit variety to the point that the political spectrum becomes multidimensional? that would be fine. and, if
