At 01.09.17 01:03 -0700 Monday, Rob LeGrand wrote: >Well, it's a good thing Craig doesn't define his IFPP method for more than >three candidates! First sentence botched. A definition can be implicit. It seems to be rather definitely defined. implicitly, now that I have a definition of P4 at http://www.ijs.co.nz/one-man-one-vote.htm (the definition is worded with a scratchiness that could hinder others' comprehending of it). > >Suppose there's an election among A, B and C: > >10:A>B>C >15:B>A>C >23:C>A>B > >C wins in IFPP after A and B are eliminated in the first round (quota 16). But >say universally despised candidate D runs: > >10:A>B>C>D >15:B>A>C>D >23:C>A>B>D > >If IFPP is generalized for four candidates, the quota becomes 12; A and D are It is a generalising of the Alternative Vote. Proving that 1/n quota without solving IFPP explicitly presumably can be done. ... >in the first round if they all had the same first-place totals. Looks like the >quota fix to IRV only "works" for three candidates, making it all but useless. > Just how useless?. It could be that the 'Q' method is overall improvement on the Alternative Vote method. >On his page http://www.ijs.co.nz/irv-wrong-winners.htm Craig calls this IFPP >generalization the 'Q' method. > The Q method certainly can be criticised a lot. At the moment I don't see how to improve it. Here is a quick line of reasoning that ends in a dead end. I could say that it just a matter of casting shadows, starting with votes being about equal and the region small and centred around the simplex-centre. However there are problems with corners of rectangular faces casting shadows with 3 or surfaces. Also the attempt can't be completed without a definition of all the rules. A problem ought occur if the "power<=1" rule isn't defined, and when I got that defined, then the shadow [of the infinitesimally applying 'P4' rule] was umbral and casting 'reducing in size' shadows which could be reverted. The rejecting of consideration of pairs can be retained but unlike with monotonicity with its concern for a single candidate, keeping the powers of factions (of papers) constrained can involve a consideration of more than one candidate. The presumption of having k stages (or <=k stages) in an election with k candidates is so unsound that it might even favour with the CVD crabs scuttling to produce a spirit of reform in others. My method below is the use of guessing, and the aim is to find the H terms. Ma = (a<1/4) : Mb = (b<1/4) : Mc = (c<1/4) : Md = (d<1/4) Aw = (1/4<a)[(b<1/4) or Hba][(c<1/4) or Hca][(d<1/4) or Hda] Assume solution is of this form, which is in the style of 3 candidate 1 winner IFPP: Aw = -Ma[Mb or Hba][Mc or Hca][Md or Hda] : Aw = (A wins), etc. The terms Hba, etc., are unknown. 3 candidate IFPP: Aw' = (1/3<a')[(b'<1/3)or(b'+cb'<a'+ca')][(c'<1/3)or(c'+bc'<a'+ca')] Aw = -Ma[Mb or Hba][Mc or Hca][Md or Hda] Bw = -Mb[Mc or Hcb][Md or Hdb][Ma or Hab] Cw = -Mc[Md or Hdc][Ma or Hac][Mb or Hbc] Dw = -Md[Ma or Had][Mb or Hbd][Mc or Hcd] CASE d<c<1/4<b<a : True = Md = Mc, False = Mb = Ma Aw = Hba Bw = Hab Cw = Dw = False Maybe replace Hba with Hba = (0 < Tba), etc. CASE d<1/4<c<b<a : True = Md, False = Mc = Mb = Ma Aw = Hba.Hca Bw = Hcb.Hab Cw = Hac.Hbc Dw = False That does not suggest rejecting Hba=(0<Tba) idea CASE d<c<b<1/4<a : True = Md = Mc = Mb, False = Ma Aw = True Bw = Cw = Dw = False But what to do now is not obvious: the 3 candidate Aw IFPP formula is not in a form that appears to factorize into Hba.Hca, = (0<Tba)(0<Tca). That does not seem to lead anywhere obvious. Defining the T values looks like something that will not happen So that's a weak attempt to justify the absence of an improvement to the Q method. A fix to Q might involve regarding the 1st stage as being 4-fold. There is the option of truncating, in addition to the known method of eliminating and transferring papers. It would be nice to hear from the CVD so called "I.R.V." experts provide the mathematical arguments that led them to see the obviously obvious Q method as being inferior. Fixing Q might take years of research, but getting intelligence from the CVD could take decades, if ever achievable. I fear they might one day say that they want to know what IRV is, but so far no sign of such a threat against experts.
