Hi Markus, on 29.04.2010 20:33 you asked: > is Jobst Heitzig's river method identical > to Blake Cretney's goldfish method?
I'm sorry that I have not read any list posts for months, so this caught my attention just now. I will check the differences! You probably refer to the method from Blake's Aug 12, 1998 post I cite below? Yours, Jobst On Aug 12, 1998, Blake Cretney wrote: > Here's my entry for single-winner system of the week. It was motivated > by my desire to make a method that would be easy to program. To this > end, it does not require cycles or the Smith set to be found. > I'll call it "Goldfish" until someone shows me a previous mention > under a different name. The idea of goldfish is that the candidates > seem to eat each other, becoming bigger and bigger, until > only one is left swimming in the electoral fish bowl. > > Goldfish definition: > Successively find the worst defeat and eliminate the pair-wise loser. > Any win achieved by the pair-wise loser is now scored as if it was > achieved by the pair-wise winner, provided it is larger than the > one already scored by him, or he is currently scored a loss. > > Start by making a "victory" table. For each row, enter the votes > against each column's candidate, if the row's candidate wins > pair-wise. Otherwise enter a 0. > > The best way to resolve ties is for a chairman, president, or random > voter to enter a special ballot. This ballot must not be truncated. > > Repeat until only one candidate is left: > FIND: > Find the highest value in the table. Call this cell i,j. If > more than one row share this value, choose the row that is > higher in the special ballot. > MERGE: > Here's where the big fish eats the little one. For each cell > in the i row, if there is a higher value for that column in > the j row, copy it over. For each cell in the i column, if > there is a zero for that row in the j column, copy it over. > Do not change the empty cells on the diagonal. > ELIMINATE: > Remove the j candidate and its row and column from > consideration. > > I'm going to use the word "beats" to mean "defeats pair-wise" and > "eats" to mean "is chosen to defeat and merge with". > > MIIAC -- Candidates outside the Smith set are always beaten by > members of the Smith set. When they eat them, the rows and > columns are merged, but this provides nothing of use for beating > other Smith members, because candidates outside the Smith set only > have losing scores against those inside, and the merge rule does > not copy losing scores. This is because only 0 values are copied > from column to column. > > GITC -- If someone outside a clone set eats a clone, all the > clones will be eaten on successive rounds, just as if there was > only one. If a clone eats someone outside, the merge occurs. > Because the outsider loses to the clone, it can provide no help in > defeating other clones. It does not matter which clone eats an > outsider, because eventually all clones will be eliminated, or one > will eat all the others, and merge with them. > > GMC -- Because candidates are removed in order of votes against, > and because removal does not eliminate a majority vote against > a candidate, but merely copies it, candidates with a majority against > will be removed first. > > Elimination methods frequently have the problem that it is > possible to help elect a candidate by ranking it lower. This > happens when you can reduce the amount by which a victory is > obtained, so that a candidate is not eliminated, and can carry on > to defeat your enemies. The merge step in Goldfish makes this > strategy unnecessary. The winner ends up beating the same candidates > as the loser, and by as much. Lower losing values are not copied, > but having another candidate in the race with lower losing values > is not helpful. > > This seems like a pretty good system and is fairly easy to program. > With a couple of tweaks, it can be converted to Tideman. ---- Election-Methods mailing list - see http://electorama.com/em for list info