[EM] Uncovered set methods (Re: How close can we get to the IIAC)

[Jobst Heitzig]

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.