> Date: Sat, 03 Apr 2010 22:52:08 +0000 (GMT) > From: [email protected] > To: [email protected] > Subject: [EM] Approximating Non-Summable Methods with Summable Methods > Message-ID: <[email protected]> > Content-Type: text/plain; charset=us-ascii > > Recently Kathy Dopp initiated a thread rerquesting the best summable, > monotone, PR method ideas. > > In general non-summable methods can be approximated by summable methods if > range ballots are used > in the following way: > > At each precinct, for each candidate C take a weighted average of the ballots > that rate candidate C at > the top where the weight of a ballot is one over the number of candidates > rated at the top on that ballot. > Then the weighted averages (together with the total weights for each average) > are passed along to the > central location where they can be averaged together using their respective > weights, to get one weighted > ballot for each candidate. The method you had in mind can be applied to > these ballots. > > In particular, if you have a monotone PR method based on Range Ballots, you > can apply that method. If > you don't have a monotone PR method based on Range Ballots, you can go to > Warren Smith and get > one; he collects them. > > Of course, after the averaging, you can convert the range ballots into > ordinal rankings, and then use your > favorite method based on rankings if you don't like range ballots. > > Note that if the original ratings are zero/one only, i.e. approval ballots, > then the method still works. > > In summary, you can get a summable version of your favorite method. And if > you want, no matter what > kind of ballots you method uses, you can get the required information via > approval ballots. > >
I apologize for not having enough time to really reply or to spend studying the great responses to this question. Just briefly, I think James that your method above at least at the precinct stage is exactly equivalent to a method I proposed earlier that has the feature of ensuring that each voters' vote is worth 1 no matter how many candidates they rank or rate, the same value as every other voter. This may or may not be considered a desirable feature, but some US courts have declared it to be a vital feature for an electoral method. As far as reweighting the ballots from the precinct, I think you've only got weights for each individual voter, 1 divided by the number of candidates they ranked or 1 divided by the total number of points they assigned candidates, so what process are you using to obtain weights for a precinct, the number of voters voted in that precinct? As long as the method used to combine the tallies from each precinct at the central office was also monotonic (not IRV/STV or other nonmonotonic methods), I see no problem at all with this approach and would probably support it as far as I can tell. Thanks for thinking about it and coming up with an idea. Regards, Kathy Dopp http://electionmathematics.org Town of Colonie, NY 12304 "One of the best ways to keep any conversation civil is to support the discussion with true facts." Realities Mar Instant Runoff Voting http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf Voters Have Reason to Worry http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf View my research on my SSRN Author page: http://ssrn.com/author=1451051 ---- Election-Methods mailing list - see http://electorama.com/em for list info
