> Another option is to introduce weights on each party for a given region. > Say that the Northern Norway region has 6 leveling seats. Then you > calculate the desired outcome for the NN region as a whole (using > Sainte-Laguë) and compare this to the current outcome (by adding up all the > county results). Finally, you weight the votes to bring the latter closer > to the former, but never so that more than 6 seats change ownership. > By "weighting" I mean this: say Progress has too many seats. Then you > divide the number of votes they got in every county by some common x until > they get fewer seats. > I think that this can be done simultaneously for every party by using > linear programming, but I'm not sure of that. The scheme would also produce > "floating" leveling seats, because the changes of which party gets which > seat can happen in any of the counties in the region, and would happen > where the parties in question are close to getting/not getting a seat. Thus > it avoids the "where are the regional MPs going to be?" issue. >
This system was proposed by Balinski as "Fair Majority Voting"; and is probably the simplest example of a biproportional apportionment system. I believe that Zurich uses pretty much this system for municipal government. > > > As for how the party list method acts when there are few seats, this is > probably closer to the problem you're seeing (when one disregards leveling > seats). Here's an old example I often pull in similar cases: > > 46: L > C > R > 44: R > C > L > 10: C > R > L > > In the extreme case of there being only one seat, you would want C to win. > But every divisor method reduces to Plurality when there's only one seat, > so L gets elected instead. On the other hand, if you have a thousand seats, > proportional representation pretty much says you should give 46% of them to > L (were it a party), 44% to R, and 10% to C. > > So we'd like a method that is Condorcetian when there's only one seat, yet > proportional when there are loads. And such methods exist. Schulze's > proportional ordering method comes to mind. It's complex, however, and it > might be possible to make simpler methods since we can elect each > "candidate" (party) multiple times. > > A note here, though: it's often tempting to add some kind of strategy > layer. If you have a large number of seats, some voters that vote X > Y > > Z, and X "very nearly" has the number of votes needed to get another seat, > at first glance it would seem that you should somehow distribute the > X-voters' votes to Y instead so that Y can get another seat, because that's > what the voters wished. But that kind of logic, when taken to its > conclusion, leads to a quota method. Doing that sort of automatic > reallocation would turn Sainte-Laguë into something entirely different - a > quota method. And quota methods all fail population pair monotonicity as > given by the Rangevoting page I linked to. So unless you want a quota > method, that path is not the right one to take. > > > And finally, there's the threshold. In some countries, the threshold is > absolute - if the party doesn't get x% support, it gets no candidates. In > Norway it is only absolute with respect to the leveling seats. But when > dealing with thresholds, ranking is fairly simple to apply. If we permit > voters to rank the parties, then the election can be extended with a sort > of IRV-like system: > > 1. Count up the first preferences on every ballot. > 2. If no party has less than x% support, we're done. Exit. > 3. Otherwise, remove the party with the least support from every ballot, > and go to 1. > > The result is a support list where no party has less than x% support, > where x is the threshold. However, this method shares IRV's sensitivity to > initial conditions, and probably also fails monotonicity. One could > probably fix that by using a system based on DAC/DSC, but that would be > very complex. So for a leveling seat system, what comes to mind as a > suggestion is: > > 1. Count first preferences and give county seats as usual. > 2. Remove every party that has less than x% national support from every > ballot. > 3. Count again. > 4. Use the support levels thus given for the leveling seat calculation. > > That suggestion might eliminate too much: it has an "anti-Woodall free > riding" problem. If you vote "Communist > Red > Socialist Left", if the > Communist Party has no hope and the Red party is just short of the > threshold, then the IRV method above would retain Red, but this method > wouldn't. But I don't think those effects would be significant. (If you > disagree, let me know and I'll try to think of a better system!) Votes of > the type "Red > Socialist Left > Labor", however, would give support to > Socialist Left even after Red has been eliminated -- unlike the current > system that doesn't give support to any other party if you vote for a party > below the threshold. > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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