[EM] Let's play Jenga!
Ross Hyman
rahyman at sbcglobal.net
Sat Sep 30 10:57:04 PDT 2017
Let’s play Jenga!
I think that Schulze has pointed out in earlier posts that his method is equivalent to the following:
Repeatedly remove the weakest link whose removal leaves at least one candidate with a beat path to every other candidate. When only one such candidate has a beat path to every other candidate, elect that candidate.
This way of looking at the Schulze method resembles the game Jenga, where one repeatedly removes blocks from a tower, attempted to preserve some structure in the tower to hold it up. (Ok, I know that in real Jenga you put the blocks back at the top but it’s the best analogy I can think of.)
The Schulze method preserves the simplest possible structure for which there is one winner. But one can imagine more complicated structures, each resulting in a different method.
For example: Repeatedly remove the weakest link whose removal leaves at least one ranking of all of the candidates in which there is a direct win for the higher candidate over the next lower candidate. When only one such ranking exists, elect that ranking of candidates.
Schulze’s method produces a tree structure like Jobst Heitzig’s River method but I believe the two methods in general produce different results. The method I just proposed above produces a ranking like Tideman’s Ranked Pairs method. Will it in general produce a different ranking than Tideman?
Let’s say you wanted to elect two candidates. Perhaps you would want to preserve that structure that produces a unique winner and a unique runner up by preserving a structure that is a combination of Ranking and River.
Repeatedly remove the weakest link whose removal leaves at least one pair of candidates with the property that the first one has a direct win over the second candidate and the second candidate has a beat path to every other candidate. When only one such pair of candidates exist, elect them to the first and second position.
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