Kevin, thanks for doing the simulations. The offending example below led me to the improvement in my previous message. I simplified the faction sizes from 56, 92, 100 to
9 C D B A 10 C A B D 13 B D A C which gives the same results. Forest On Fri, 1 Aug 2003, [iso-8859-1] Kevin Venzke wrote: > 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 fran�ais ! > Yahoo! Mail : http://fr.mail.yahoo.com > ---- > Election-methods mailing list - see http://electorama.com/em for list info > ---- Election-methods mailing list - see http://electorama.com/em for list info
