Forest, I implemented the new method (picking the least viable rank and merging it with the less viable neighbor) and did some trials.
First, I should say that the Condorcet cycle-breaker I have implemented is: "Successively drop the weakest defeats (as measured by WV) until a Smith set member is undefeated." I'm not sure what the proper name for this is, but I'll call it "SD." To my great surprise (should I have been?), I could not generate any three-candidate, three-rank scenarios where MPCR did not elect the CW when one existed: With 3 factions (random sizes) and 3 candidates and ranks: matches 10474 100% (this is total trials) sdindec 36 .34 (SD was indecisive) (I should've checked that Borda and MPCR were decisive, but I didn't.) mpcr<>cw 0 0 (was a CW, MPCR didn't pick him) mpcr=cw 9935 94.85 (was a CW, MPCR picked him) unanimous 220 2.1 (MPCR, Black, SD agreed) mpcr=borda 0 0 (MPCR and Black agreed against SD) mpcr=sd 112 1.06 (MPCR and SD agreed against Black) borda=sd 171 1.63 (Black and SD agreed against MPCR) no matches 0 0 (Black, SD, MPCR all disagreed) I got the same results with 5 and 8 factions. With 4 candidates and ranks (5 factions), some "errors" appeared: matches 4594 sdindec 5 .1 mpcr<>cw 7 .15 (.175%, excluding no-CW cases) mpcr=cw 3971 86.43 unanimous 203 4.41 mpcr=borda 23 .5 mpcr=sd 192 4.17 borda=sd 165 3.59 no matches 28 .6 Five factions and 7 candidates: matches 3563 sdindec 67 1.88 mpcr<>cw 27 .75 (1.08%) mpcr=cw 2469 69.29 unanimous 250 7.01 mpcr=borda 66 1.85 mpcr=sd 306 8.58 borda=sd 254 7.12 no matches 124 3.48 15 candidates: matches 431 sdindec 20 4.64 mpcr<>cw 6 1.39 (2.79%) mpcr=cw 209 48.49 unanimous 33 7.65 mpcr=borda 9 2.08 mpcr=sd 41 9.51 borda=sd 57 13.22 no matches 56 12.99 I went through and picked out some appalling results from the 4-rank batch. Here's one which would have been OK if the "merge the pair minimizing the sum of viability" rule had been used. This is pretty nasty because it elects the Condorcet and Borda Loser, and ignores a majority favorite: 56 22% CDBA 92 37% CABD 100 40% BDAC 248 Borda order is B>C>D>A RP order is C>B>D>A :[viability order] [new grouping as result] etc... :BCDA C,D,BA CA,B,D B,DA,C :CBAD C,DBA CA,BD BDA,C :ACBD (MPCR's result) Using the earlier rule, the MPCR part goes: :BCDA CD,B,A CA,B,D B,DA,C :BCAD CD,BA CA,BD B,DAC :CBAD But in general it doesn't seem to me that one variant is clearly better than the other. (I did 9-candidate trials on both methods and found that the new version was twice as likely to miss a CW, but it might've been a fluke.) I hope no errors crept into this message. Kevin Venzke [EMAIL PROTECTED] ___________________________________________________________ Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en français ! Yahoo! Mail : http://fr.mail.yahoo.com ---- Election-methods mailing list - see http://electorama.com/em for list info
