Re: [Election-Methods] Matrix voting and cloneproof MMP questions
Dear Kristofer, you wrote (6 July 2008): I've been reading about the decoy list problem in mixed member proportionality. The strategy exists because the method can't do anything when a party doesn't have any list votes to compensate for constituency disproportionality. Thus, cloning (or should it be called splitting?) a party into two parties, one for the constituency candidates, and one for the list, pays off. But is it possible to make a sort of MMP where that strategy doesn't work? That MMP method would have to use some kind of reweighting for those voters who got their way with regards to the constituency members, I think, because if the method just tries to find correlated parties, the party could theoretically execute the strategy by running all the constituency candidates as independents. What kind of reweighting would that be? One idea would be to have a rule that says those with say x about the constituency vote gets 1-x in the list vote. Then vary x until the point of party proportionality is found. No matter what party someone who makes a difference with regards to the constituency candidate chooses, his vote loses power proportionally, and thus decoy lists wouldn't work. Wow, that's exactly what I have proposed recently for an STV-MMP system in Berlin. Please read these papers: http://m-schulze.webhop.net/schulze4.pdf http://m-schulze.webhop.net/schulze5.pdf Read especially page 3 of paper schulze5.pdf. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Matrix voting and cloneproof MMP questions
Dear Kristofer, if your goal to issue a smaller group representing the same opinions and debates than the larger group I think maintaining proportortionality is a good characteristic to make sure most positions of these debates survive the attrition. The reduction in size should facilitate the oral exchanges. I have a tendancy to view any election as an attempt to build a microcosm of a larger group in order to facilitate debates... For your second point, there is one way to enforce coherency (using a mathematical definition) within an MMP election. If one uses the same results to elect the individual representatives and to determine the corrected proportion obtained after electing list members. The simple way to enforce such coherence between these two proportions is to use a single ballot MMP, where voting for an individual is considered too as giving support in favor of this candate party list. From what I know two german landers use this system. Otherwise you have to relie on cultural honesty of the parties or electorate to avoid the decoy problem. Salutations, Stéphane Kristofer Munsterhjelm a écrit : I thought I could ask a few questions while otherwise being busy making my next simulator version :-) So here goes.. First, when a group elects a smaller group (as a parliament might do with a government, although real parliaments don't do it this way), should the method used to elect the smaller group be proportional? I think one could make a majoritarian version with cardinal ratings/Range. It'd work this way: for n positions, each voter submits n rated ballots. Then, with k candidates, make a k*n matrix, where position (a,b) is the sum of the ratings the voter assigned candidate a in the ballot for position b. We've now reduced the problem of picking (candidate, position) values so that the sum is maximized. The constraints on the problem are: only one value can be selected from each row (can't have the same candidate for two positions), and only one value can be selected from each column (can't have two candidates for the same position). I think that's solvable in polynomial time, but I haven't worked out the details. That's for majoritarian matrix votes with cardinal ratings (or Range - could also be median or whatever as long as the scores are commensurable). (On a related note, has anyone tried to use Range with LeGrand's Equilibrium Average instead of plain average?) Perhaps the same pick-the-best-sum reasoning could be extended to a Condorcetian matrix vote, using Kemeny score for the Condorcet matrix for the position in question instead of ratings sums/averages. But as far as I remember, Kemeny scores relate to social orderings, not just candidate choices, so maybe the Dodgson score instead -- but that may not be comparable in cases where different candidates are Condorcet winners in different elections, since those would all have Dodgson scores of 0 (no swapping required). In any case, the reduction above won't work if matrix voting methods ought to be proportional. I'm not sure whether it should be majoritarian or proportional, and one could argue for either - majoritarianism in that that's how real world parliamentary governments are formed (negotiations notwithstanding), and proportionality because some group may be very good at distinguishing suitable foreign ministers while some other, slightly larger group, might not do very well at that task but be good at distinguish suitable ministers of interior. Second, I've been reading about the decoy list problem in mixed member proportionality. The strategy exists because the method can't do anything when a party doesn't have any list votes to compensate for constituency disproportionality. Thus, cloning (or should it be called splitting?) a party into two parties, one for the constituency candidates, and one for the list, pays off. But is it possible to make a sort of MMP where that strategy doesn't work? That MMP method would have to use some kind of reweighting for those voters who got their way with regards to the constituency members, I think, because if the method just tries to find correlated parties, the party could theoretically execute the strategy by running all the constituency candidates as independents. What kind of reweighting would that be? One idea would be to have a rule that says those with say x about the constituency vote gets 1-x in the list vote. Then vary x until the point of party proportionality is found. No matter what party someone who makes a difference with regards to the constituency candidate chooses, his vote loses power proportionally, and thus decoy lists wouldn't work. No concrete methods here, but maybe someone else will add to them... or find flaws in my reasoning and correct them :-) Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see
Re: [Election-Methods] Matrix voting and cloneproof MMP questions
Stéphane Rouillon Sent: Sunday, July 06, 2008 6:02 PM For your second point, there is one way to enforce coherency (using a mathematical definition) within an MMP election. If one uses the same results to elect the individual representatives and to determine the corrected proportion obtained after electing list members. The simple way to enforce such coherence between these two proportions is to use a single ballot MMP, where voting for an individual is considered too as giving support in favor of this candidate party list. From what I know two German landers use this system. I am aware that some German Lander use single ballot MMP, but it is a fundamentally flawed system and should not be recommended. The problem is that the candidate votes (cast in single-member districts) do not provide an accurate reflection of the voters' overall support for the political parties because the candidate votes are distorted by local tactical voting. If you must use MMP (a poor voting system), it should always be a two-vote version. James No virus found in this outgoing message. Checked by AVG. Version: 7.5.526 / Virus Database: 270.4.5/1537 - Release Date: 06/07/2008 05:26 Election-Methods mailing list - see http://electorama.com/em for list info
[Election-Methods] Fun with Friends and Dice
Dear Jobst, Your ingenious use of coins was very inspiring to me. It encouraged me to come up with a dice throwing realization of our benchmark function f(x) = 1/(5-4x) in another solution of our challenge problem. Also, since our goal is mutually beneficial cooperation, let me define two ballots to be friends of each other iff they co-approve one or more candidates. First, I give the method without the benefit of the dice: 1. Draw a ballot at random. Let Y be its favorite, let Z be the most approved of its approved candidates, and let x be the percentage of ballots that are friends with this one. 2. Elect Z with probability f(x), else Y. Now here's the dice rolling version: 1. Draw a ballot at random. Let Y be its favorite, and let Z be the most approved of its approved candidates. 2. Roll a die until some number k other than six shows on top. If k = 1, then elect Z, else ... 3. Draw a new ballot at random. If this new ballot is a friend of the first ballot, go back to step 2, else ... 4. Elect Y. This method, like yours, guarantees a probability proportional to faction size for those factions that choose to bullet, yet it gently encourages friendship. What do you think? Forest - Original Message - From: Jobst Heitzig Date: Friday, July 4, 2008 9:45 am Subject: Re: [Election-Methods] Challenge Problem To: [EMAIL PROTECTED] Cc: election-methods@lists.electorama.com Hi again. There is still another slight improvement which might be useful in practice: Instead of using the function 1/(5-4x), use the function (1 + 3x + 3x^7 + x^8) / 8. This is only slightly smaller than 1/(5-4x) and has the same value of 1 and slope of 4 for x=1. Therefore, it still encourages unanimous cooperation in our benchmark situation 50: A(1) C(gamma) B(0) 50: B(1) C(gamma) A(0) whenever gamma (1+1/(1+(slope at x=1)))/2 = 0.6, just as the other methods did. The advantage of using (1 + 3x + 3x^7 + x^8) / 8 is that then there is a procedure in which you don't need any calculator or random number generator, only three coins: Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Matrix voting and cloneproof MMP questions
Kristofer Munsterhjelm wrote: (On a related note, has anyone tried to use Range with LeGrand's Equilibrium Average instead of plain average?) I don't recommend using Equilibrium Average (which I usually call AAR DSV, for Average-Approval-Rating DSV) to elect winner(s) from a finite number of candidates. AAR DSV is nonmanipulable when selecting a single outcome from a one-dimensional range, just as median (if implemented carefully) is, but it is manipulable when used as a scoring function in a way similar to how Balinski and Laraki proposed using median: http://rangevoting.org/MedianVrange.html For more on AAR DSV, please see chapter 3 of my now-completed dissertation: http://www.cse.wustl.edu/~legrand/dissertation.pdf -- Rob LeGrand, psephologist [EMAIL PROTECTED] Citizens for Approval Voting http://www.approvalvoting.org/ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] A Monotone, Clone Proof Lottery for which Sincere Rankings = Optimal Strategy (Correction)
I'm sorry to say my original claim is not true. Counterexample: Sincere Rankings 4 ABC 3 BAC 2 CBA If (in the third faction) B is sufficiently close to C in utility, it is to that faction's advantage to reverse the order of B and C. On the other hand, as long as C has greater utility than B, and epsilon is sufficiently small, the probability distribution (1/9 - epsilon, 1/9 - .75epsilon, 1/9 - .50episilon, ... , 1/9 + epsilon) in place of my original suggestion will do the job. In this example, epsilon 2*(deltaR)/9 is sufficiently small, where deltaR is the percentage difference in utility between C and B. Forest Draw a ballot at random. Use the ranking on this ballot to rank all of the other ballots from worst to best according to their favorites. Elect the favorite indicated on the k_th ballot with probability 2*k/(n+n^2) , where n is the number of ballots. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Matrix voting and cloneproof MMP questions
On the question of whether electing a subgroup should be proportional or majoritarian...I often make a distinction on two factors: 1) Is the association voluntary (in which dissatisfied minorities can easily withdraw to join or form a different association), and 2) Is the function of the association directional or goal oriented, vs. service, maintenance or regulatory-oriented (a political party that wants to move society in a direction, vs. an alumni association). Voluntary associations that have a directional goals (such as a platform) can sometimes be best served by majoritarian or centrist internal election method, such as electing party leaders, Whereas compulsory associations that are engaged in maintenance (a government) are best served by proportional methods. Terry - Original Message - From: Kristofer Munsterhjelm [EMAIL PROTECTED] To: EM election-methods@lists.electorama.com Sent: Saturday, July 05, 2008 7:09 PM Subject: [Election-Methods] Matrix voting and cloneproof MMP questions I thought I could ask a few questions while otherwise being busy making my next simulator version :-) So here goes.. First, when a group elects a smaller group (as a parliament might do with a government, although real parliaments don't do it this way), should the method used to elect the smaller group be proportional? I think one could make a majoritarian version with cardinal ratings/Range. It'd work this way: for n positions, each voter submits n rated ballots. Then, with k candidates, make a k*n matrix, where position (a,b) is the sum of the ratings the voter assigned candidate a in the ballot for position b. We've now reduced the problem of picking (candidate, position) values so that the sum is maximized. The constraints on the problem are: only one value can be selected from each row (can't have the same candidate for two positions), and only one value can be selected from each column (can't have two candidates for the same position). I think that's solvable in polynomial time, but I haven't worked out the details. That's for majoritarian matrix votes with cardinal ratings (or Range - could also be median or whatever as long as the scores are commensurable). (On a related note, has anyone tried to use Range with LeGrand's Equilibrium Average instead of plain average?) Perhaps the same pick-the-best-sum reasoning could be extended to a Condorcetian matrix vote, using Kemeny score for the Condorcet matrix for the position in question instead of ratings sums/averages. But as far as I remember, Kemeny scores relate to social orderings, not just candidate choices, so maybe the Dodgson score instead -- but that may not be comparable in cases where different candidates are Condorcet winners in different elections, since those would all have Dodgson scores of 0 (no swapping required). In any case, the reduction above won't work if matrix voting methods ought to be proportional. I'm not sure whether it should be majoritarian or proportional, and one could argue for either - majoritarianism in that that's how real world parliamentary governments are formed (negotiations notwithstanding), and proportionality because some group may be very good at distinguishing suitable foreign ministers while some other, slightly larger group, might not do very well at that task but be good at distinguish suitable ministers of interior. Second, I've been reading about the decoy list problem in mixed member proportionality. The strategy exists because the method can't do anything when a party doesn't have any list votes to compensate for constituency disproportionality. Thus, cloning (or should it be called splitting?) a party into two parties, one for the constituency candidates, and one for the list, pays off. But is it possible to make a sort of MMP where that strategy doesn't work? That MMP method would have to use some kind of reweighting for those voters who got their way with regards to the constituency members, I think, because if the method just tries to find correlated parties, the party could theoretically execute the strategy by running all the constituency candidates as independents. What kind of reweighting would that be? One idea would be to have a rule that says those with say x about the constituency vote gets 1-x in the list vote. Then vary x until the point of party proportionality is found. No matter what party someone who makes a difference with regards to the constituency candidate chooses, his vote loses power proportionally, and thus decoy lists wouldn't work. No concrete methods here, but maybe someone else will add to them... or find flaws in my reasoning and correct them :-) Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
