[EM] Let's play Jenga!

[Ross Hyman]

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.  

This method is different from Tideman Ranked pairs.Consider the pair ordering B>D, B>A, C>B, D>C, C>A, A>D.
The above method produces: D>C>B>A. The Tideman order is C>B>A>D.  The Tideman order is better. The Schulze winner is also C.



 

    On Saturday, September 30, 2017 12:57 PM, Ross Hyman <rahyman at sbcglobal.net> wrote:
 

 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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