I was trying to visit http://rangevoting.org/ to see if there was anything about an automated strategy to convert Range votes into Approval votes (just to move strategy from a hit-or-miss process on the part of certain savvy voters to something applied universally), and it looks like the web page is down. It resolves in an nslookup to Name: rangevoting.org Address: 128.2.209.176
and tracert'ing to it gives (after it leaves my ISP's domain): Tracing route to rangevoting.org [128.2.209.176] over a maximum of 30 hops: ... 9 90 ms 91 ms 90 ms sl-bb25-chi-5-0.sprintlink.net [144.232.20.84] 10 91 ms 90 ms 90 ms sl-bb24-chi-14-0.sprintlink.net [144.232.26.82] 11 113 ms 113 ms 113 ms sl-bb25-nyc-5-0.sprintlink.net [144.232.9.157] 12 128 ms 129 ms 129 ms 144.232.13.148 13 129 ms 129 ms 129 ms 63.160.2.10 14 130 ms 130 ms 129 ms g0-1-0-440.car1.pitc.pitbpa.e-xpedient.com [206.210.75.241] 15 131 ms 130 ms 131 ms cmu-gw.cust.e-xpedient.com [208.40.161.235] 16 130 ms 130 ms 131 ms CORE0-VL986.GW.CMU.NET [128.2.0.249] 17 130 ms 130 ms 130 ms POD-A-CYH-VL914.GW.CMU.NET [128.2.0.156] 18 131 ms 130 ms 130 ms GIGROUTER-POD-A-CYH.GW.CMU.NET [128.2.35.194] 19 130 ms 131 ms 130 ms BOOJUM.LINK.CS.CMU.EDU [128.2.209.176] I hope it's just a temporary glitch, I like reference pages like this. :) ************** Anyway, it's probably something I've asked in the past (I had a computer crash awhile back so I don't have all my notes or E-M emails), but has someone proposed a method to convert Range votes to maximal strategy Approval votes? I was just wondering what the properties of such a system might be (including cool-looking graphs, if available), and any paradoxes or problems that might arise. For example, would it be possible to convert Range ballots into the equivalent of Approval ballots where every voter has the equivalent of perfectly accurate polling data? Also, I'm curious how it would act with the Gibbard-Satterthwaite theorem where (from Wikipedia) it states: 3. The rule is susceptible to tactical voting, in the sense that there are conditions under which a voter with full knowledge of how the other voters are to vote and of the rule being used would have an incentive to vote in a manner that does not reflect his preferences. since every vote has the equivalent information. Are there weird Approval cycles -- like you have with Condorcet "rock-paper-scissors" ties -- or areas where the strategy is indeterminate? On a tangential topic, the definition for Nanson's method is given as this: Eliminate those choices from a Borda count tally that are at or below the average Borda count score, then retally the ballots as if the remaining candidates were exclusively on the ballot. Repeat the process until a single winner remains. Is this correct, or would it actually be something like the linearly-interpolated median (henceforth called LIM) score? While this may seem like a trivial distinction, since with Borda it's the same thing (well, at least if I didn't do a dumb mistake, which is entirely possible), I was thinking about a possible extension of Nanson's method to Range voting, where you drop the candidates whose LIM value is less than the LIM for all the candidates. I was also looking into making Range voting "Range-ier" for the purpose of determining the median -- if you had a single vote for a single candidate at a single value, it would just be that value, two votes for a candidate at a single value would be considered -0.25 and +0.25 from that value, three votes would be -0.333, 0, and +0.333, four would be -0.375, -0.125, +0.125, +0.375, and so on. To show the difference, let's say Candidate A has the following distribution of points: 0 1 2 3 4 (value) 2 4 5 2 3 (number of votes) Borda and Range value is: 2*0 + 4*1 + 5*2 + 2*3 + 3*4 = 32 Candidate B has the following: 0 1 2 3 4 (value) 3 2 5 4 2 (number of votes) Borda and Range value is: 3*0 + 2*1 + 5*2 + 4*3 + 2*4 = 32 The median value for both is 2. However, let's distribute the range in both: First, A: 0 1 2 3 4 2 4 5 2 3 --> (-0.25 0.25)(0.625 0.875 1.125 1.375)(1.6 1.8 2.0 2.2 2.4)(2.625 2.875 3.125 3.375)(3.75 4.25) The median value in this example is between 1.8 and 2.0, so let's take the LIM and say 1.9. Now B: 0 1 2 3 4 3 2 5 4 2 --> (-0.333 0 0.333) (0.75 1.25)(1.6 1.8 2.0 2.2 2.4)(2.625 2.875 3.125 3.375)(3.75 4.25) The media value in this example is between 2.0 and 2.2, so let's say 2.1. In a contest between A and B where the LIM is used to determine the winner, B wins over A. Since I can never seem to keep these things brief anyway, Rob Brown had something similar a couple of years ago at http://karmatics.com/stuff/median.gif He had the values for 15 elements (3,3,3,3,4,4,4,4,4,5,5,5,6,6,7) and gave an interpolated median (calculated from the midpoint of one group to the next) of 4.25, and a smoothed median of 4.248. With my method above, the interpolated median would be the eighth element in the set, or 4.2 (the "4's" are symmetrically distributed as 3.6, 3.8, 4.0, 4.2, 4.4, and the second to the highest element in that set is 4.2). It would be interesting to see what resulted from the different ways of calculating it (Rob Brown considered values immediately above and/or below the median -- between the 4's and 5's in this case -- while I just considered the 4's.) I'll leave that there, since I've drifted rather far afield from my question about what happened to rangevoting.org. :) Michael Rouse ---- Election-Methods mailing list - see http://electorama.com/em for list info
