Michael, you are stepping naively into an area that has been very well studied. I include a couple of points below you may want to consider.
On 04 Jun 2012 22:18:06 -0700, Michael Ossipoff wrote: > > About gerrymanmdering; > > PR would be a solution to gerrymandering, but certainly not the only one: > > 1. Proxy Direct Democracy wouldn't have a gerrymandering problem either. If > Proxy DD can be made count-fraud-secure, then it would make PR obsolete. > > 2. Whatever can be accomplished by PR can be accomplished by an > at-large single winner election, because every single winner method > can output a ranking of candidates instead of just one winner: Elect > the winner. Then delete the winner from the ballots and count them > again. That will elect the rank 2 winner. Then eliminate the rank 2 > winner too, and count the ballots again. Each time, delete every > previous winner before counting to determine the next winner. So you > can elect N winners at large in a state, or nationally, for a body > such as Congress (or its separate houses, if you want to keep them) > or a state legislature. Of course, with Approval, it only requires > one count, and you elect the N candidates with the most approvals. Can you prove that the ranking from a single-winner election is proportional? I think not. At the very least, you should remove ballots, in some fractional way, when a ballot has achieved some portion of its preference. Single Transferable Vote (STV) is one way, of course, but there is also Reweighted Range Voting, and a Bucklin variant proposed by Jameson Quinn as AT-TV a year ago. My simplified version of JQ's method is Graded Approval Transferable Vote (GATV) and can be found here: https://github.com/dodecatheon/graded-approval-transferable-vote > > 3. But districting needn't have a gerrymandering problem, even if > single-member districts are kept. Who said that districts have to be > arbitrary and freehand-drawn?? Where did we get that silly > assumption? > > Draw the district lines by some simple rule that doesn't leave any > human discretion or choice. It would be completely automated, but it > would be so simple that it would be very easy for anyone to check. > > For example: You could divide the country (or state) into N1 > latitudinal bands such that each has the same population/average > longitudinal width. Then divide each latitudinal band into > longitudinal sections, in such a way as to give each section the > same population, and so that there are the right number of such > sections overall. > > But of course you wouldn't have to use latitude and longitude if you > don't want to. On a map, on any projection, that you choose, use a > rectangular grid of lines, drawn similarly to the way described > above. If you use a gnomonic projection, then all of your district > lines will be straight lines on the Earth (great circles). If you > use a cylindrical projection, then it will be as described in the > previous paragraph. But it could be any projection you like. I'd > suggest that gnomonic and cylindrical (using parallels and meridians > as described in the previous paragraph) would be the main two > choices. Districts divided by parallels and meridians, or by > straight lines (great circles). > > The point is that it could be done by a simple rule that would have > no human input, no human choice. What if it divides a county or a > city? So what? No problem. The rule could be that houses would be > all counted on whichever side of a line most of the house's area > lies. > > It could be automated of course, but the result could easily be > checked by anyone. > Brian Olson has one automated method, with examples from the 2010 census, located here: http://bdistricting.com/2010/ There is also the shortest splitline algorithm, discussed here: http://rangevoting.org/GerryExamples.html http://rangevoting.org/GerryExec.html http://www.youtube.com/watch?v=kUS9uvYyn3A Ted -- araucaria dot araucana at gmail dot com > To change the subject a little, I'd like to bring up another > geographical government suggestion, while I'm at it: Partition. > > It doesn't make any sense for people to have to live under a > government that they don't like, with people whom they don't agree > with or don't like. So why not just divide the country up into > separate countries, according to what kind of government people > like? It's ridiculous to make everyone share the same county, when > they want different kinds of country. > > It would be like a PR election, except that it would be for square > miles instead of for seats. > > Though, like districting, the partitioning of the country could be > (1) by an automatic rule, with those same rectangles (I like that), > or (2) it could also be done by national negotiation in a PR > negotiating body, or maybe by a proxy DD negotiation. > > I like the quick simplicity of (1). But (2) could _maybe_ be done in > such a way as to ensure that each new partition-country has, to the > best extent possible by negotiation, equally good land, by whatever > standards its people want to bargain for. > > Of course an overall census could be taken periodically, and the > process repeated, to take into account people who have "voted with > their feet". But those adjustments wouldn't be necessary, because > the initial partition would let everyone live in the govt they like > best. But, though I don't watch tv, I used to watch it along with > the family I was part of, so what about a family like the one in > "All in the Family"? Should Archie Bunker's daughter have to remain > in his country? Likewise the family in "A family Affair" (if I've > got the show-name right). It is not your fault what country you're > born in. So there would be a strong case for letting people continue > to choose what country they want to live in, even after partition. > > Of course then it would be necessary to repeat the initial partition > process to adjust the national borders to the new populations. Maybe > migration should only affect borders when it's by people who were > born in the country that they're in, as opposed to people who chose > that country at partition time. > > But migration must be distinguished from fecundity, for this purpose. A > country shouldn't be able to expand over its neighbors just because it > doesn't like birth-control. > > Mike Ossipoff > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info