On Tue, Sep 4, 2012 at 10:15 PM, Kristofer Munsterhjelm <[email protected]> wrote: > So here's the system. Say you have k different legislative bodies (n doesn't > matter, but should probably be small, and if possible highly composite, so > something like 2, 3, or if you're really pushing it, 6).
3 isn't technically highly composite :). > Furthermore, say > there are n voters. After the election, associate to each body, n/k voters > so that the difference between the seat allocation to each were one to run a > majoritarian election for that body accordng to the associated voters, and > were one to run a proportional election for that body, is minimized. Then > run the actual elections - one PR election for each body - and you're done. So, assuming rankings, you fill the body based on condorcet ordering and PR and pick the sets of voters so as to try to match the 2 assemblies. It isn't clear how to do that in a systematic way. Find the maximum can often be NP-complete. You could also take into account rankings directly. For example, pick the distribution that minimise the sum of the condorcet rankings over all PR-assemblies. A PR assembly containing candidates ranked at 1-34 and 36 is better than one that has candidates 1-34 and candidate 100, even though there are 34 matches. > If society is divided, then the proportional result becomes like the > majoritarian one (or less different) if each group gets its own body -- and > we don't have to set ahead of time or have any preconception about what > those groups actually are. However, it does create an incentive to lie in the first stage and try to infiltrate other assemblies. It also breaks the secret ballot. > The system is not perfect, of course. By enshrining a division into n > groups, it may polarize those groups. One possible option would be to have the number of assemblies decided based on social polarisation. There could be a formal clustering algorithm of some kind. Some of them allow you to estimate the number of clusters. If the public can be modeled as a single Gaussian, then you would only have 1 assembly. > Mutual veto or double majority rules > could help counter this, but that doesn't make the system elect more > compromise candidates. In Northern Ireland, they have a mandatory coalition system. Basically, the leader of the largest party becomes First Minister and leader of the largest party from the other community becomes deputy First Minister. The remaining seats at cabinet are then divided using the d'Hondt method between the parties. When a party is assigned a seat, the leader of the party gets to pick which department the cabinet member will be responsible for (of the ones remaining). This gives an added bias towards the larger parties, since they get to pick first. It also means that each assembly member has to declare which community they are from (there are cross-community rules for certain bills). This means that assembly members who refuse to do that have reduced power. Non-sectarian parties should at minimum have equal power to the sectarian parties. There was a situation where some non-aligned tactically declared in order to get a bill passed and break a deadlock. Majority based democracy doesn't work very well when you have a divided society that is near 50-50. Voters in the larger faction can be convinced of the need to vote as a bloc, so both communities end up with less democracy (though the minority ends up with none). If the larger faction had a more solid majority, then that fear would be reduced and wouldn't end up being the main basis on which voters vote. I think if a society was made up of many sub-groups, with none near a majority on its own, then standard PR should work reasonably well, since each sub-group can negotiate. That assumes that you don't end up with a de-facto bloc of voters with slightly above 50%. You really need to deal with the case where the minority is large enough to be a threat, so that the majority feels the need to vote as a bloc. ---- Election-Methods mailing list - see http://electorama.com/em for list info
