[EM] Let's play Jenga!

[Ross Hyman]

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.