I made a copy paste error. > A will be eliminated. B wins. should be "L will be eliminated. R wins."
Juho On Nov 17, 2006, at 18:58 , Juho wrote: > Earlier I mentioned that the Ranked Preferences Method may need some > fine tuning to avoid situation where votes of some voters may work > against their interests. Now I found the time to do that. > > The Ranked Preferences Method could be characterized by saying that > during the process of eliminating the candidates the votes are > treated at each round in a way that we suppose to be in the best > interest of the voters (no such strategic changes though that would > depend on the progress of the calculation). This means that > situations where the vote works against the voter's interests should > be eliminated - also to avoid generating any need to change the > sincere vote to a strategic one. > > I'll explain the new variant of the method starting from how the > individual votes are handled. Capital letters indicate candidates > that are still in the race. > > Vote a>>>B>c>>D>>e>F will be handled at this round (A, C and E have > already been eliminated) as if it was a=B=c>D>e=F since >> is the > highest preference relation that still has non-eliminated candidates > at both sides. > > Relation >>> will be handled as = since after A has been eliminated B > and C are now her favourites and she has no interest to push them > down. This feature was not included in my previous description of the > method. > > In addition to all this "dynamic interpretation" of the ranking based > votes the method also has the tied at top and tied at bottom rules. > Tied at top candidates are all considered to win each others but > never lose to each others (+1 point in all comparisons). Tied at > bottom candidates all lose to each others and never win each others > (-1 point in all comparisons). (These rules are included to eliminate > the need to put the top and bottom candidates in some preference > order for strategic reasons.) > > Note that votes that use only one preference strength are calculated > just like in the regular Condorcet methods. Tied at top/bottom rules > however apply if = is used in addition to >. > > At each round each vote is thus processed so that first the strongest > preference relation with non-eliminated candidates at both sides is > sought. Then all other preference relations (than preferences of this > strength that have non-eliminated candidates at both sides) are > considered to be =. After this the matrix is calculated as usual in > the Condorcet methods except that also tied at top and tied at bottom > rules apply. Also the already eliminated candidates are included when > counting the comparison results (remaining candidates may thus be > beaten by them). > > After this the described method uses simply minmax(margins) to > eliminate the weakest non-eliminated candidate. And sequentially > drops candidates one after another until only the winner is left > (dropping weakest groups would be an option, but a complex one with > no very clear benefits). > > The result of the following example changes as a result of the > changed rules. > > 45: L>>C>R > 20: C>>R>L > 35: R>>C>L > > I use * to mark the use of the tied at top/bottom rules. > > L-C = +45 -20 -35* = -10 > L-R = +45 -20* -35 = -10 > C-L = -45 +20 -35* = -60 > C-R = -45* +20 -35 = -60 > R-L = -45 -20* +35 = -30 > R-C = -45* -20 +35 = -30 > > C will be eliminated. C would be the Condorcet winner in regular > Condorcet elections where preference strengths are not taken into > account. Top strength of the 20 C supporter votes is now ">". > > L-C = +45 -20 -35* = -10 > L-R = +45 -20 -35 = -10 > R-L = -45 +20 +35 = +10 > R-C = -45* +20* +35 = +10 (this value changed in the new variant) > > A will be eliminated. B wins. > > Juho Laatu > > > > P.S. > In my first description from October 24th two lines should be changed > to get this new version. > - Add one point if x is ranked higher than y (top strength or higher) > and > - Subtract one point if x is ranked lower than y (top strength or > higher) > become > - Add one point if x is ranked higher than y (top strength > preferences with non-eliminated candidates at both sides) > and > - Subtract one point if x is ranked lower than y (top strength > preferences with non-eliminated candidates at both sides) > (Higher strengths need not be mentioned in the new version.) > > Send instant messages to your online friends http:// > uk.messenger.yahoo.com > ---- > election-methods mailing list - see http://electorama.com/em for > list info Send instant messages to your online friends http://uk.messenger.yahoo.com ---- election-methods mailing list - see http://electorama.com/em for list info
