[EM] Simulating multiwinner goodness
There was a question on the list a while ago, and skimming to catch up I didn't see a resolution, about what the right way to measure multiwinner result goodness is. Here's a simple way to do it in simulator: Each voter has a preference [0.0 ... 1.0] for each candidate. Measuring the desirability of a winning set of candidates is simply summing up those preferences, but capping each voter at a maximum of 1.0 satisfaction. Unfortunately, this won't show proportionality. If 3/4 of the population have a 1.0 preference for a slate of 3/4 of the choices, we would measure electing one of them as being just as good as electing the whole set. So, we could apply the quota. If a candidate is elected by 3 times the quota, only apply 1/3 of each voter's preference for that candidate to their happiness sum. Now the huge coalition with their slate elected should each add up to about 1.0 happiness, and smaller coalitions should get theirs too. This is sounding a bit like an election method definition, and I expect that this definition of 'what is a good result' does pretty much imply a method of election. At worst, given ratings ballots that we can treat as the simulator preferences, for not too large a set of winning sets of candidates, get a fast computer and run all the combinatoric possibilities and elect the set with the highest measured sum happiness. Another thing we could measure in multiwinner elections (and possibly single winner) is the Gini inequality measure. If we have a result with both pretty high average happiness and low inequality, that's a good result. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Simulating multiwinner goodness
Brian, But obviously, real world satisfaction with an election outcome is not so straight forward. I may favor a certain slate of candidates, but feel huge dissatisfaction if they all win, such that there is no opposition in the legislative body to keep them honest. This is what happened for many in British Columbia in 2001, when the Liberal Party won 77 out of 79 seats in the Provincial legislature. The utility, or hoped for happiness measurement before the election may be changed BY the election results themselves. While this is especially true of multi-seat elections, it is even true of single seat elections. I may want my candidate to win, but be disappointed if she wins despite the fact that a majority of voters preferred another candidate (due to a feature of the voting method)...My preference for majority rule may trump my candidate preference. Terry Bouricius - Original Message - From: Brian Olson b...@bolson.org To: Election Methods Mailing List election-meth...@electorama.com Sent: Thursday, March 11, 2010 7:35 AM Subject: [EM] Simulating multiwinner goodness There was a question on the list a while ago, and skimming to catch up I didn't see a resolution, about what the right way to measure multiwinner result goodness is. Here's a simple way to do it in simulator: Each voter has a preference [0.0 ... 1.0] for each candidate. Measuring the desirability of a winning set of candidates is simply summing up those preferences, but capping each voter at a maximum of 1.0 satisfaction. Unfortunately, this won't show proportionality. If 3/4 of the population have a 1.0 preference for a slate of 3/4 of the choices, we would measure electing one of them as being just as good as electing the whole set. So, we could apply the quota. If a candidate is elected by 3 times the quota, only apply 1/3 of each voter's preference for that candidate to their happiness sum. Now the huge coalition with their slate elected should each add up to about 1.0 happiness, and smaller coalitions should get theirs too. This is sounding a bit like an election method definition, and I expect that this definition of 'what is a good result' does pretty much imply a method of election. At worst, given ratings ballots that we can treat as the simulator preferences, for not too large a set of winning sets of candidates, get a fast computer and run all the combinatoric possibilities and elect the set with the highest measured sum happiness. Another thing we could measure in multiwinner elections (and possibly single winner) is the Gini inequality measure. If we have a result with both pretty high average happiness and low inequality, that's a good result. 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] Simulating multiwinner goodness
On Mar 11, 2010, at 4:35 AM, Brian Olson wrote: There was a question on the list a while ago, and skimming to catch up I didn't see a resolution, about what the right way to measure multiwinner result goodness is. Here's a simple way to do it in simulator: Each voter has a preference [0.0 ... 1.0] for each candidate. Measuring the desirability of a winning set of candidates is simply summing up those preferences, but capping each voter at a maximum of 1.0 satisfaction. Unfortunately, this won't show proportionality. If 3/4 of the population have a 1.0 preference for a slate of 3/4 of the choices, we would measure electing one of them as being just as good as electing the whole set. So, we could apply the quota. If a candidate is elected by 3 times the quota, only apply 1/3 of each voter's preference for that candidate to their happiness sum. Now the huge coalition with their slate elected should each add up to about 1.0 happiness, and smaller coalitions should get theirs too. This is sounding a bit like an election method definition, and I expect that this definition of 'what is a good result' does pretty much imply a method of election. At worst, given ratings ballots that we can treat as the simulator preferences, for not too large a set of winning sets of candidates, get a fast computer and run all the combinatoric possibilities and elect the set with the highest measured sum happiness. Another thing we could measure in multiwinner elections (and possibly single winner) is the Gini inequality measure. If we have a result with both pretty high average happiness and low inequality, that's a good result. As with any choice system based on cardinal utility, there end up being two problems that are not, I think, amenable to solution. One is the incomparability of individual utility measures from voter to voter (and here we're talking about utility deltas, since the utilities are normalized to max=1.0). The other is that, even if comparability were solved, we don't have a means of, in the individual case, determining what they are. In particular, reported utility isn't very useful, since for the system to work, we need sincere utility, and a utility-based system provides every incentive to strategize. And, as Terry suggests, it's not clear what we *mean* by utility here. Happiness with what? The outcome of the individual election? The makeup of the resulting legislature? The legislation resulting from that legislature? And even if we could somehow measure the voter's ultimate happiness as a function of legislative outcome and come back in time and cast a vote, we don't have utilities for the counterfactual alternatives. However attractive it might be to fantasize about functions from cardinal utility to social choice, it comes down to an attempt to square a circle or invent a perpetual motion machine. The attemp might be fun, but we know a priori that it will fail. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Simulating multiwinner goodness
A couple years ago I moved from the California Democratic Party Machine to the Massachusetts Democratic Party Machine. I'm not sad when my party wins, I'm sad when they run boring stick-in-the-mud establishmentarian candidates. I'd love pressure from other parties to keep them honest, and that's what a lot of this whole election method reform thing is about. Anyway, an election method can't (directly) give me better choices, but just help me and the rest of society choose from the options available at the time. I posit that a better choice method will (eventually) encourage the availability of better choices. The current pick-one-primary and pick-one-general favors the boring old establishment too much. If I can safely vote for the obscure but awesome candidate as my first choice, and the safe establishment choice as second or third, I think we'll se more interesting little guys, and sometimes they'll win. But we knew all that. /advocacy On Mar 11, 2010, at 9:42 AM, Terry Bouricius wrote: But obviously, real world satisfaction with an election outcome is not so straight forward. I may favor a certain slate of candidates, but feel huge dissatisfaction if they all win, such that there is no opposition in the legislative body to keep them honest. This is what happened for many in British Columbia in 2001, when the Liberal Party won 77 out of 79 seats in the Provincial legislature. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Simulating multiwinner goodness
On Mar 11, 2010, at 11:29 AM, Jonathan Lundell wrote: As with any choice system based on cardinal utility, there end up being two problems that are not, I think, amenable to solution. One is the incomparability of individual utility measures from voter to voter (and here we're talking about utility deltas, since the utilities are normalized to max=1.0). The other is that, even if comparability were solved, we don't have a means of, in the individual case, determining what they are. Arrow made the same mistake. We can't compare interpersonal utility, but in practice we do. We set everyone's utility to One. One person one vote. That's how much you get. In particular, reported utility isn't very useful, since for the system to work, we need sincere utility, and a utility-based system provides every incentive to strategize. And, as Terry suggests, it's not clear what we *mean* by utility here. Happiness with what? The outcome of the individual election? The makeup of the resulting legislature? The legislation resulting from that legislature? Reported utility is vulnerable to all kinds of noise, imperfect reporting, imperfect introspection, and so on. And yet this can be simulated. We can make sim people who are perfectly knowable, add that noise, run the election, and see what happens both compared to the noisy utility and true utility. When I did this it turns out there are some methods less vulnerable to noise! (Condorcet better, IRV, with it's non-monotonic threshold swing regions is more vulnerable to noise.) And even if we could somehow measure the voter's ultimate happiness as a function of legislative outcome and come back in time and cast a vote, we don't have utilities for the counterfactual alternatives. However attractive it might be to fantasize about functions from cardinal utility to social choice, it comes down to an attempt to square a circle or invent a perpetual motion machine. The attemp might be fun, but we know a priori that it will fail. Are we talking about real people or sim people? I think we can make simulations and models that are useful. Lots of people keep trying, including me. Or are you sayng that we can't reasonably make sim people whose knowable sim qualities bear any useful resemblance to the real world? We're talking about all kinds of mathematical properties of election methods, why not various measures under stochastic test? What would be a good measure? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Simulating multiwinner goodness
On Mar 11, 2010, at 8:50 AM, Brian Olson wrote: On Mar 11, 2010, at 11:29 AM, Jonathan Lundell wrote: As with any choice system based on cardinal utility, there end up being two problems that are not, I think, amenable to solution. One is the incomparability of individual utility measures from voter to voter (and here we're talking about utility deltas, since the utilities are normalized to max=1.0). The other is that, even if comparability were solved, we don't have a means of, in the individual case, determining what they are. Arrow made the same mistake. We can't compare interpersonal utility, but in practice we do. We set everyone's utility to One. One person one vote. That's how much you get. In particular, reported utility isn't very useful, since for the system to work, we need sincere utility, and a utility-based system provides every incentive to strategize. And, as Terry suggests, it's not clear what we *mean* by utility here. Happiness with what? The outcome of the individual election? The makeup of the resulting legislature? The legislation resulting from that legislature? Reported utility is vulnerable to all kinds of noise, imperfect reporting, imperfect introspection, and so on. And yet this can be simulated. We can make sim people who are perfectly knowable, add that noise, run the election, and see what happens both compared to the noisy utility and true utility. When I did this it turns out there are some methods less vulnerable to noise! (Condorcet better, IRV, with it's non-monotonic threshold swing regions is more vulnerable to noise.) And even if we could somehow measure the voter's ultimate happiness as a function of legislative outcome and come back in time and cast a vote, we don't have utilities for the counterfactual alternatives. However attractive it might be to fantasize about functions from cardinal utility to social choice, it comes down to an attempt to square a circle or invent a perpetual motion machine. The attemp might be fun, but we know a priori that it will fail. Are we talking about real people or sim people? I think we can make simulations and models that are useful. Lots of people keep trying, including me. Or are you sayng that we can't reasonably make sim people whose knowable sim qualities bear any useful resemblance to the real world? We're talking about all kinds of mathematical properties of election methods, why not various measures under stochastic test? What would be a good measure? I agree that simulations can give us insight into the nature of voting system. It's the translation of those result to real elections that I object to. The sim voter can be interesting in the model without remotely resembling any real voter. (And I don't believe Arrow was mistaken. He was talking about real-world social choices, not models.) Election-Methods mailing list - see http://electorama.com/em for list info
[EM] A monotonic proportional multiwinner method
I think I have found a multiwinner method that is both monotonic and
proportional. I have, at least, found no counterexample.
The method achieves monotonicity by cheating about proportionality:
instead of strictly adhering to the quota, it determines a divisor and
sets up a number of constraints on the output. The idea is similar to
how Webster's method (and other divisor methods) maintain monotonicity
by, in certain cases, violating quota.
Note that I although I think it is likely that one can't have both Droop
proportionality and monotonicity, I have no proof of this.
How does the method work? It has two phases, which I'll call the
constraint phase and the margins phase.
For both phases, we'll need to transform the input set of ballots into a
list of solid coalitions. This list gives all the sets for which at
least one vote preferred the members of the set (in any order) to those
not in the set, and is the same data as is used to determine the outcome
in Descending Acquiescing/Solid Coalitions.
For example, consider the ballot set
13: ABC
1: ACB
11: BAC
10: BCA
17: CAB
18: CBA
The solid coalition list is
Coalitionvoters
ABC 70
AB 24
AC 18
BC 28
A14
B12
C27
because 24 voters prefers A and B to everything else (thus voted either
ABC or BAC), 18 voters prefer A and C to everything else, and so on.
The first phase consists of setting up constraints to narrow down which
group of winners we are going to elect. The constraints on each
coalition is:
at least round(V_i / q) candidates from this coalition must be in
the outcome[1],
where round is the rounding-off function, V_i is the number of
voters supporting coalition i, and q is determined to be the least value
that doesn't lead to a contradiction. A particular choice for the value
of q leads to a contradiction if it's impossible to construct an
outcome that passes all the constraints.
In other words, determine the value of q so that at least one set can
pass the combined set of constraints (at least round(V_i / q) of the
candidates from coalition i must be in the outcome). Call this value,
the divisor. It can be found using binary search in conjunction with
trying all possible outcomes to find out how many pass the constraints,
or (probably) in some more sophisticated manner.
Returning to our example, let's say we're going to elect a council of
size 2.
Our initial options are: elect {AB}, {AC}, or {BC}. The value of q that
satisfies our desiderata is slightly greater than 28, let's say 28.0034.
That value gives the following constraints:
Coalitionvoters ===elect at least
ABC 70 round(70/28.0034) = 2
AB 24 round(24/28.0034) = 1
AC 18 round(18/28.0034) = 1
BC 28 round(28/28.0034) = 1
A14 round(14/28.0034) = 0
B12 round(12/28.0034) = 0
C27 round(27/28.0034) = 1
(Note here that A is *very* close to getting a seat, as 14/28.0034 =
0.49994. That will become important later.)
Can AB pass? No, because it violates the must have at least 1 of the
{C} coalition criterion. Can AC pass? Yes. Can BC pass? Yes.
So in this example, the constraint phase has narrowed down our choice of
outcomes to AC and BC. But which should we pick? That's where the
margins phase comes into play, and herein lies the trick that makes the
method monotonic:
For some coalition i, define i's /margin/ equal to:
floor(V_i / q) + 0.5 - V_i / q.
Calculate these. For our example:
Coalitionvoters margin
ABC 700.000307
AB 24 -0.357038
AC 18 -0.142778
BC 28 -0.499877
A140.60
B120.071481
C27 -0.464167
Assign to each possible outcome, the margins of those coalitions with
which it shares at least one candidate, then sort the margins, lesser
first. Negative margins have to be altered somehow, but it usually
doesn't matter how you do it - I just add one to them as that seems to
be the most natural. Margins for coalitions that don't match are set to
infinity, so that any margin against a coalition that actually matches
(shares at least a candidate in common) is better than no match, which
makes sense.
AC shares at least one candidate with {ABC, AB, AC, BC, A, C}.
BC shares at least one candidate with {ABC, AB, AC, BC, B, C}.
Thus the sorted margins lists are:
positive margins negative margins, adjustedn/a
AC: 0.607 0.000307 | 0.500123 0.535833 0.642962 0.857222 | infinity
BC: 0.0003066 0.071481 | 0.500123 0.535833 0.642962 0.857222 | infinity
Re: [EM] Simulating multiwinner goodness
Brian Olson wrote: There was a question on the list a while ago, and skimming to catch up I didn't see a resolution, about what the right way to measure multiwinner result goodness is. [snip] This is sounding a bit like an election method definition, and I expect that this definition of 'what is a good result' does pretty much imply a method of election. At worst, given ratings ballots that we can treat as the simulator preferences, for not too large a set of winning sets of candidates, get a fast computer and run all the combinatoric possibilities and elect the set with the highest measured sum happiness. The details of proportional representation isn't well known. Proportional representation itself appears to involve a tradeoff between accuracy - proportionality of what counts - and quality - how highly the individual voters rank a given candidate. There is something similar for single-winner methods: the question of how much to value what few rank very highly in comparison to what some rank in the middle; but for single-winner methods, we at least have concepts like the median voter and desirable-sounding criteria like clone independence and the Condorcet criterion. What I'm trying to say is that before we can optimize, we must know what it is we're going to optimize -- or proceed in a vague direction using feedback (as is part of my reason for experimenting with multiwinner methods). What would be analogous to the median voter concept for multiwinner elections - accurate reproduction of opinion space? According to what measure? And so on... Another thing we could measure in multiwinner elections (and possibly single winner) is the Gini inequality measure. If we have a result with both pretty high average happiness and low inequality, that's a good result. The proportionality scoring part of my election methods program works somewhat like this, according to a very simple model. Every candidate and voter has a binary n-vector of ayes/nays (representing binary opinions). Voters prefer candidates closer to them (Hamming distance wise). Then the proportion of each bit being a yes can be measured both for the elected council and for the people in general, and the closer the better. I use either root mean squared error or the Sainte-Lague index for measuring error, though my program can also use the Gini (or the Loosemore-Hamby index for that matter). Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Smith, FPP fails Minimal Defense and Clone-Winner
Juho wrote: On Mar 10, 2010, at 7:26 PM, Kristofer Munsterhjelm wrote: Juho wrote: I'm not aware of any sequential candidate elimination based method that I'd be happy to recommend. One can however describe e.g. minmax(margins) in that way. Eliminate the candidate that is worst in the sense that it would need most additional votes to win others, then the next etc. In the elimination process one would consider also losses to candidates that have already been eliminated (I wonder if this approach makes it less natural looking than the elimination process of IRV). To my knowledge, Schulze-elimination is the same as basic Schulze. In other words, if you run Schulze, eliminate the loser, run it again, etc, you end up with the original result. That's not very useful, but still... It might also be that any full-blown candidate elimination method (you run the election as if the one that was eliminated never stood) with a weighted positional base method (Borda, Plurality, ...) is nonmonotonic. I can't prove it though! One more addition to this elimination discussion. Maybe ability to give an ordering of the candidates is more important (and more generic) than using an elimination process. The preference graphs that many Condorcet methods use may not be as easy to understand to the voters as plain ordering is. In principle single winner methods need not be able to produce any ordering of the candidates. It is enough to pick the single winner. But in order to make it easy to the voters and candidates to understand the results (and to explain e.g. how close some candidate was to winning the election) good and simple graphical and numeric information may be valuable in practical elections. Both of the advanced methods give an ordering, as do the obvious ones (Minmax, least reversal, Copeland, second order 2-1-Copeland...). They don't provide numerical information (this close to winning), but that is hard: I read a paper about extending Schulze to do so, and it used some rather complicated use of linear programming. Could you sell that to the public? Not very likely, unless they happened to be of the same kind that voted for the use of Meek in local New Zealand elections. (I have to add that if people want to keep the USA as it mostly is, a two party based system, then I must recommend FPTP :-). And if not, then maybe also some additional (maybe proportionality related) reforms are needed.) Wouldn't something like Condorcet multiwinner districts be better? Pick a good Condorcet method and send the 5 first ranked on its social ordering to the legislature. That would pick a bunch of centrists (thus have stability), but it would pick the centrists people actually wanted. Hm, that might not provide a true two-party system, though. One could also have a PR system where the number of votes is weighted so that parties with broad support gain superproportional power, but then the question becomes why one should bother with the PR at all. Maybe Condorcet + single winner districts is a more stable approach. That combination makes a two-party system just somewhat softer, and allows the party structure (in individual districts) to evolve in time. Another approach to systems between proportional representation and the two-party approach could be to have a proportional method but use districts with only very few representatives (2, 3,...). That would provide rough but in principle accurate proportionality and still give space only to few major parties. (Obviously my definition of full proportionality must be with 1/n of the votes you will get one seat (where n = number of representatives).) An interesting hybrid, I think (and I've mentioned it before), would be to have a bicameral system where senators are elected according to a statewide Condorcet method (pick a good centrist for each state), and the House representatives are elected according to PR. Having just a single from each state may be /too/ centrist, but to pick two senators from each using a proportional ordering might work - as long as it doesn't introduce partisan division. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Smith, FPP fails Minimal Defense and Clone-Winner
On Mar 11, 2010, at 11:41 PM, Kristofer Munsterhjelm wrote: Juho wrote: On Mar 10, 2010, at 7:26 PM, Kristofer Munsterhjelm wrote: Juho wrote: I'm not aware of any sequential candidate elimination based method that I'd be happy to recommend. One can however describe e.g. minmax(margins) in that way. Eliminate the candidate that is worst in the sense that it would need most additional votes to win others, then the next etc. In the elimination process one would consider also losses to candidates that have already been eliminated (I wonder if this approach makes it less natural looking than the elimination process of IRV). To my knowledge, Schulze-elimination is the same as basic Schulze. In other words, if you run Schulze, eliminate the loser, run it again, etc, you end up with the original result. That's not very useful, but still... It might also be that any full-blown candidate elimination method (you run the election as if the one that was eliminated never stood) with a weighted positional base method (Borda, Plurality, ...) is nonmonotonic. I can't prove it though! One more addition to this elimination discussion. Maybe ability to give an ordering of the candidates is more important (and more generic) than using an elimination process. The preference graphs that many Condorcet methods use may not be as easy to understand to the voters as plain ordering is. In principle single winner methods need not be able to produce any ordering of the candidates. It is enough to pick the single winner. But in order to make it easy to the voters and candidates to understand the results (and to explain e.g. how close some candidate was to winning the election) good and simple graphical and numeric information may be valuable in practical elections. Both of the advanced methods give an ordering, as do the obvious ones (Minmax, least reversal, Copeland, second order 2-1- Copeland...). They don't provide numerical information (this close to winning) At least minmax(margins) does. It gives each candidate the number of additional votes that would guarantee victory to them. That is quite simple and could be used to e.g. provide information to the voters while the counting is in progress (1000 votes still not counted, 100 first preference votes would be enough to win). Also a simple histogram would tell how each candidate is doing at the moment. , but that is hard: I read a paper about extending Schulze to do so, and it used some rather complicated use of linear programming. Could you sell that to the public? Not very likely, unless they happened to be of the same kind that voted for the use of Meek in local New Zealand elections. (I have to add that if people want to keep the USA as it mostly is, a two party based system, then I must recommend FPTP :-). And if not, then maybe also some additional (maybe proportionality related) reforms are needed.) Wouldn't something like Condorcet multiwinner districts be better? Pick a good Condorcet method and send the 5 first ranked on its social ordering to the legislature. That would pick a bunch of centrists (thus have stability), but it would pick the centrists people actually wanted. Hm, that might not provide a true two-party system, though. One could also have a PR system where the number of votes is weighted so that parties with broad support gain superproportional power, but then the question becomes why one should bother with the PR at all. Maybe Condorcet + single winner districts is a more stable approach. That combination makes a two-party system just somewhat softer, and allows the party structure (in individual districts) to evolve in time. Another approach to systems between proportional representation and the two-party approach could be to have a proportional method but use districts with only very few representatives (2, 3,...). That would provide rough but in principle accurate proportionality and still give space only to few major parties. (Obviously my definition of full proportionality must be with 1/n of the votes you will get one seat (where n = number of representatives).) An interesting hybrid, I think (and I've mentioned it before), would be to have a bicameral system where senators are elected according to a statewide Condorcet method (pick a good centrist for each state), and the House representatives are elected according to PR. Yes, having also representatives that are non-partisan by nature could add something interesting and useful to an otherwise very party oriented and divided community. (One could btw call this kind of representatives widists instead of centrists since Condorcet would pick a candidate with wide support instead of a candidate that is supported specifically by the centrist parties. Or maybe also term centrist has some similar meaning in addition to referring to the parties in the
Re: [EM] Smith, FPP fails Minimal Defense and Clone-Winner
On Thu, Mar 11, 2010 at 9:41 PM, Kristofer Munsterhjelm km-el...@broadpark.no wrote: Having just a single from each state may be /too/ centrist, but to pick two senators from each using a proportional ordering might work - as long as it doesn't introduce partisan division. You would probably end up getting the centre of each of the 2 parties if you did that, so it defeats the idea of finding centerists to cancel out the 2 party system. You could split states into districts, if you wanted more than 1 senator elected at the same time. Ofc, districting runs in gerrymandering problems. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] A monotonic proportional multiwinner method
Kristofer Munsterhjelm's monotonic proportional multiwinner method -- a few comments (1) wow, very complicated. Interesting, but I certainly do not feel at present that I fully understand it. (2) RRV obeys a monotonicity property and a proportionality property http://rangevoting.org/RRV.html (3) assuming we're willing to spend exponential(C) computer time to handle elections with C candidates, then KM's constraints form a linear program which in fact would be an 01 integer program if candidates get elected or not (cannot be 37% elected). Program has exponential(C) number of constraints. -- Warren D. Smith http://RangeVoting.org -- add your endorsement (by clicking endorse as 1st step) and math.temple.edu/~wds/homepage/works.html Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Smith, FPP fails Minimal Defense and Clone-Winner
Raph Frank wrote: On Thu, Mar 11, 2010 at 9:41 PM, Kristofer Munsterhjelm km-el...@broadpark.no wrote: Having just a single from each state may be /too/ centrist, but to pick two senators from each using a proportional ordering might work - as long as it doesn't introduce partisan division. You would probably end up getting the centre of each of the 2 parties if you did that, so it defeats the idea of finding centerists to cancel out the 2 party system. You could split states into districts, if you wanted more than 1 senator elected at the same time. Ofc, districting runs in gerrymandering problems. I've thought about this, and it makes sense. Any argument I could use against having a division inside states could also be used to argue against a division among states (e.g. why have one from each state? why not one from a block of states? Thus you should have one from a region of each state if you have more than one). Districting runs into gerrymandering. I think the solution there is to let some independent body do the redistricting -- it works in Canada. That raises the question of why such hasn't been done already, but I think the parties are just too strong. The initial cancelling-out done by Condorcet might be enough to pull the system away from that kind of entrenchment. More exotic systems might be possible - for instance, some sort of supermajority requirement for councils of two, or a weighted kind of PR that pulls the centrists towards the center, or something, but that lacks the simplicity of the ideas above. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] A monotonic proportional multiwinner method
Warren Smith wrote: Kristofer Munsterhjelm's monotonic proportional multiwinner method -- a few comments (1) wow, very complicated. Interesting, but I certainly do not feel at present that I fully understand it. Alright. If you have any questions, feel free to ask. (2) RRV obeys a monotonicity property and a proportionality property http://rangevoting.org/RRV.html My experiments with multiwinner methods seem to indicate that you need proportionality not just of single candidates but also of groups of them, like satisfied by the DPC or by this. (3) assuming we're willing to spend exponential(C) computer time to handle elections with C candidates, then KM's constraints form a linear program which in fact would be an 01 integer program if candidates get elected or not (cannot be 37% elected). Program has exponential(C) number of constraints. So do methods like Schulze STV. In any case, I wonder if it's possible to make some sort of polytime algorithm for my method, but it would probably be quite difficult. One would have to understand the nature of the shifting of constraints as the divisor changes to find the best-margin council that doesn't contradict, implicitly. If it's possible, a comparison would be that a method like STV satisfies the Droop proportionality criterion even though this is also, mathematically speaking, an integer program (every coalition supported by more than k Droop quotas should have at least k members in the outcome, unless the size of the coalition is less than that). Election-Methods mailing list - see http://electorama.com/em for list info
