[EM] scale and shift independent ratings based Condorcet method

[Ross Hyman]

Sorry about the formatting.  Second try.


Here is a ratings based Condorcet election method that uses ratings to determine how much each voter favors one candidate over another.  But it does not use the ratings to compare candidates across ballots, as their ratings scales might be different.  Perhaps they even used different ratings ballots.  I believe it is the second simplest way to use a ratings ballot that gives the same  results if each individual ballot undergoes an arbitrary rating shift or rescaling. (The simplist way is direct conversion of ratings to ranks.  But this method includes more ratings information.)  There is no need to ever shift or rescale any ballots as this can never change the results.  The method uses the Tideman or Schulze method but will not always assign the same winner as those methods because it uses more ratings information than a direct conversion of ratings to rankings.  The method uses more majority rule information than rankings based Condorcet.  

1.Voters rate candidates on ratings ballots of any type.
Example:
7  A = 1, B = 0.9, C=0
6 B=1,000,000,000  C = 400,000,000, A =1
5 C =1,  A= - 0.7, B  = -1
 
2. Each ratings ballot is turned into an individual ranked pair ballot.  Each pair A>B is given the score Rating(A)-Rating(B) on a ballot.  The pairs are ranked on each ballot from largest score to smallest score.  From here on, the ratings ballots are dispensed with and only the ranked pair ballots are used.
Example:
7 A>C, B>C, A>B, B>A, C>B, C>A
6 B>A, B>C, C>A, A>C, C>B, A>B
5 C>B, C>A, A>B, B>A, A>C, B>C
 
3.For each pair of candidates, A,B if more voters rank A>B higher than B>A, then B>A is removed from each ballot.  Steps 2 and 3 could easily be combined.
Example:
7  B>C, A>B, C>A
6 B>C, C>A,  A>B
5 C>A, A>B, B>C


4. Now a societal ranking of pairs of ordered pairs is produced.  This is done exactly as is done for Tideman or Schulze, except that the candidates are ordered pairs of candidates of the form (A>B) so the societal ordering will include entries like (A>B)>(C>D) if more voters
rank A>B higher than C>D.  This is the step that uses more majority rule information than rankings based Condorcet.  
Example:
(B>C)>(A>B) and (B>C)> (C>A) tied at 13, 5
(C>A)> (A>B) 11,7
 
5. Now the Tideman or Schulze method is used to turn the societal ranking of pairs of ordered pairs into a list of ranked pairs. 
Example:
B>C
C>A
A>B


6.The Tideman or Schulze method is then used a second time to turn the ranked pairs list into an ordered list of candidates.  
Example
B
C
A
 
7.The winner is the highest ranked on the candidate list.
Example 
B wins
 
Using a direct conversion of ratings to rankings with just one Tideman/Schulze step, A.