Re: [EM] What does proportional representation MEAN? And list of known PR methods (know any more?)
Here's another idea for PR: First use MCA ballots (Majority Choice Approval, where favorites and also approved are indicated) to get a distance between pairs of candidates. The distance between two candidates is the number of ballots on which just one of the two is neither favorite nor also approved. Next do a cluster analysis of the candidates by one of the standard methods that yields a binary tree as output. Initialize a system for labeling each node of the tree by labeling each branch with both the number of candidates that it (the branch) leads to and the total number of favorites garnered by all of those candidates. One by one send each seat down the tree until it reaches a candidate. At each node a decision must be made. Which of the two branches will get the seat? Send the seat down the branch with the greatest favorite label. Then make the following label adjustments: We decrement (i.e. subtract one from) the number of candidates label, and then reduce the number of favorites label by the number of voters a seat is supposed to represent. If this last number is still positive when the candidate number reaches zero, then the remainder is transferred proportionately to the favorite totals of the branches of the sub-tree beginning at the other branch. If there is only one seat, then at each node it goes according to the majority in the sub-tree for which that node is the root. If any candidate is majority favorite, then that candidate will win the one seat. If the clusters are arranged along a line without overlapping, then the median voter candidate on that line will get the seat. So the method picks the Condorcet winner for one dimensional issue spaces. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] What does proportional representation MEAN? And list of known PR methods (know any more?) correction
If the clusters are arranged along a line without overlapping, then the median voter candidate on that line will get the seat. So the method picks the Condorcet winner for one dimensional issue spaces. Sorry, This last statement is wrong! Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] What does proportional representation MEAN? And list of known PR methods (know any more?)
Warren Smith wrote: Kristofer Munsterhjelm asked me what proportional representation (PR) means. At this time it is probably unwise to make a too-precise definition since every PR voting method seems to obey a different proportionality theorem. I say you should just assess each theorem on a case by case basis to see if you like it. But a somewhat imprecise definition is: ... HERE'S MY LIST OF KNOWN PR VOTING METHODS: ... That's my list. Is anybody aware of any other PR methods? Yes, the CIVS voting system implements a Condorcet PR method that I came up with. It seems to work well in practice, having been used for dozens if not hundreds of elections/polls. In the k=1 case it devolves to regular Condorcet. There is a description of it on the CIVS web site: http://www.cs.cornell.edu/w8/~andru/civs/proportional.html -- Andrew Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] What does proportional representation MEAN? And list of known PR methods (know any more?)
On Tue, Nov 17, 2009 at 5:02 PM, Warren Smith warren@gmail.com wrote: Kristofer Munsterhjelm asked me what proportional representation (PR) means. At this time it is probably unwise to make a too-precise definition since every PR voting method seems to obey a different proportionality theorem. I say you should just assess each theorem on a case by case basis to see if you like it. But a somewhat imprecise definition is: I would say that any voting method which elects W winers from N candidates (arbitrary 0WN) with the property that under an assumption of 'standard racist' voter behavior, it always elects the same proportions of different-'color' candidates as the voters (provided enough candidates of each color run) up to some reasonable error bound is PR. However * what is the 'standard racist' voter behavior? * what are the 'error bounds'? (Once they get poor enough, they would no longer be acceptable, but I propose no precise threshhold) I am not sure referring to racism is a good plan :). Something like Any group representing more than N/M of the voters, where M is the number of seats to be filled, must be able to guarantee that N of their candidates are elected (assuming they run enough candidates). I think all PR methods meet this (as it is the Hare quota). Also, a reasonable definition for ranked methods is: http://en.wikipedia.org/wiki/Proportionality_for_Solid_Coalitions Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] What does proportional representation MEAN? And list of known PR methods (know any more?)
Warren Smith wrote: Kristofer Munsterhjelm asked me what proportional representation (PR) means. At this time it is probably unwise to make a too-precise definition since every PR voting method seems to obey a different proportionality theorem. I say you should just assess each theorem on a case by case basis to see if you like it. But a somewhat imprecise definition is: I would say that any voting method which elects W winers from N candidates (arbitrary 0WN) with the property that under an assumption of 'standard racist' voter behavior, it always elects the same proportions of different-'color' candidates as the voters (provided enough candidates of each color run) up to some reasonable error bound is PR. However * what is the 'standard racist' voter behavior? * what are the 'error bounds'? (Once they get poor enough, they would no longer be acceptable, but I propose no precise threshhold) These differ from theorem to theorem. And for Asset Voting standard racism assumptions also are needed about the candidate-behavior. I think that the measure of proportionality should be on sets, not just candidates, because I'd like the method to be better than open party list. Because of that, I like the Droop proportionality criterion, and hope something analogous to it can be constructed for Webster, because it seems that when people *do* vote party list style, Webster beats Droop in the proportionality department (as you yourself have shown on your apportionment pages). A proportionality based on sets would also permit voters to vote for some semi-popular candidate first and a less-known independent second, and have the vote support both. Even that does have limits, though, because it would not guarantee that a vote of independent first, then semi-popular would support semi-popular if independent didn't make it, a property which I'd also like. If I can have a pony, metaphorically speaking, the method should capture people's preferences in orders of sets as well. E.g. if there are n% libertarian socialists, then the method should pick n% that are both, not just ensure n% libertarian, n% socialist. This might not be possible, and might reduce to a set covering problem even if technically possible. In any case, this is all informal. HERE'S MY LIST OF KNOWN PR VOTING METHODS: Webster, and certainly all divisor methods for party-list (it is one) already are known to obey such criteria. (The very definition of divisor method is a PR theorem.) This should include my new notion of generalized divisor methods where both multiplicative and/or additive parameters are involved. Hamilton-Vinton is one. See http://rangevoting.org/Apportion.html http://www.RangeVoting.org/NewAppo.html http://www.RangeVoting.org/BishopSim.html M.L. Balinski H. Peyton Young: Fair Representation: Meeting the Ideal of One Person, One Vote (2nd edition), Brookings Institution Press 2001 Asset voting also obeys a PR theorem. http://rangevoting.org/Asset.html paper #77 at http://www.math.temple.edu/~wds/homepage/works.html RRV also (RRV is kind of based on stealing the divisor-method idea, inside). paper #78 at http://www.math.temple.edu/~wds/homepage/works.html http://rangevoting.org/RRV.html Hare/Droop STV also. Nicolaus Tideman: The Single transferable Vote, J. Economic Perspectives 9,1 (1995) 27-38. And LPV(kappa) (logarithmic penalty voting) also. Invented by F.Simmons. Described in paper #91 at http://www.math.temple.edu/~wds/homepage/works.html Also certain PR methods which are precinct countable invented by Forest Simmons, see puzzle#15 at http://rangevoting.org/PuzzlePage.html . Finally, there was also a simple one invented by a student at University of Michigan named Tim Hull. See http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2007-April/020194.html http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2007-April/020195.html That's my list. Is anybody aware of any other PR methods? Non-divisor party list PR (closed and open, though neither is proportional within each list). Party list PR in general might be a good place to consider how much PR is PR. For instance, is Jefferson party list PR? Imperiali? Using party list gets rid of the question of proportionality of *what*, because there can only be proportionality of two things, and these two don't interfere: of party lists, and of candidates within those lists (if open list PR). I have also constructed some proportional and semiproportional methods. One simple method is multiwinner Bucklin, which goes like this: do ordinary Bucklin until some candidate has the support of at least a Droop quota. Elect him and remove from all ballots, reweighting the ballots who contributed to his victory, then restart. I also tried to make a Droop proportional summable version of Bucklin, but it failed because of an ambiguity problem I called shadowing. See
Re: [EM] What does proportional representation MEAN? And list of known PR methods (know any more?)
At 01:03 PM 11/17/2009, Raph Frank wrote: I am not sure referring to racism is a good plan :). The word racist was used. A more politically correct term would be factionally affiliated or factionally dedicated. Something like Any group representing more than N/M of the voters, where M is the number of seats to be filled, must be able to guarantee that N of their candidates are elected (assuming they run enough candidates). I think all PR methods meet this (as it is the Hare quota). Because Asset Voting is a system which can create an electoral college that elects the assembly, I prefer the Hare quota, but, of course, this leaves the question of dregs: after all the seats are assigned from candidates who are elected and the easy vote transfers are done, there may be votes which belong to candidates not elected and they are having difficulty finding a suitable compromise. If any votes are left unused, of course, there is then a vacant seat, and, less likely, more than one vacant seat. Is it necessary to fill this seat? The importance of it is not necessarily clear. The Election Science Foundation is currently used Asset Voting, experimentally, to select a steering committee of three members. It's pretty unlikely that more than one seat would remain unallocated if the Hare quota is used, but one empty seat is reasonably possible. That represents what could be approaching one-third of members who aren't represented. Now, if direct voting on issues is allowed -- if this is to become a board of a corporation, there could be some legal problems with both direct voting and the possibility of unequal voting powers, but decision-making is a separate issue from voting and voting method, per se -- and if the members of the unrepresented group still have a means to bring some matter to the attention of the short committee, it's not particularly harmful. Decisions could require, I believe, a majority of the board, which with two members requires unanimity. That, again, might not be harmful. The organization is proposing to have a separate presiding officer who would be elected by the committee, and who could vote to break ties. So, again, it would take unanimity to elect this officer, so the officer is likely to represent a compromise who would satisfy at least two-thirds of the members. Not bad. But it would be better if the remaining voters are represented. So what happens if we use the Droop quota? We end up with a single-winner election for that last seat, with the voters being those who are unrepresented plus excess votes from those elected. This member of the board might represent a fairly small number of voters, but gets equal voting power (normally). This is the reason I prefer the Hare quota, it's exact, every member elected does represent a specific group of voters, the same as the quota, with the same percentage of voting power in the committee. And then the elected board can make whatever special rules it finds appropriate to secure representation for the remaining voters. It can even, as I'd implement Asset, pick an entirely new candidate, who was not on the ballot. Ideally, for that last seat, it would maximize representation, encouraging a broad compromise among the remaining voters, and it could be flexible. The quota could be adjusted down for the last seat, but that lowering could also be restricted so that disparity of representation doesn't exceed a limit. There is little harm if a small faction has a slightly higher voting power; by definition in our problem here, it is a small faction that can only exercise power through coalition, and if the disparity is limited, it would, in a practical sense, not have true excess power, because actual voting is limited. The goal in an elected committee or assembly, as I see it, is to fairly represent as much of the electorate as possible. When the number of seats is small, that becomes quite important, how that last seat is chosen. With a hundred seats, it wouldn't be so important but, on the other hand, an assembly with a hundred seats is pretty large, it really needs to function through a (sub)committee system, direct meeting for most business becomes too cumbersome. Normally, supermajority of a deliberative body can change or suspend the rules. So ... rules could provide that, say, two-thirds of the assembly (full size, so this is an absolute supermajority based on the full assembly assuming all seats had been elected) can determine how the last seat is chosen, within certain simple parameters designed to prevent serious abuse. Note, however, that if two-thirds of any body with power wants to abuse, it can. Period. An absolute majority can, not merely a supermajority, that's the Nuclear Option in the U.S. Senate. And the nuclear option has never been exercised, to my knowledge, because of the recognized damage to the traditions of the Senate. It was bad enough that the Senate
