[EM] scale and shift independent ratings based Condorcet method

[Ross Hyman]

Here is a ratings based Condorcet election method that usesratings to determine how much each voter favors one candidate overanother.  But it does not use the ratingsto compare candidates across ballots, as their ratings scales might bedifferent.  Perhaps they even useddifferent ratings ballots.  I believe itis the second simplest way to use a ratings ballot that gives the same results if eachindividual 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 anyballots as this can never change the results. The method uses the Tideman or Schulze method but will not always assignthe same winner as those methods because it uses more ratings information thana direct conversion of ratings to rankings. The method uses more majority rule information than rankings basedCondorcet.  1.      Voters rate candidates on ratings ballots of anytype.Example:7 A = 1, B = 0.9, C=06 B=1,000,000,000  C = 400,000,000, A =15 C =1,  A= - 0.7, B = -1 2.      Each ratings ballot is turned into an individualranked pair ballot.  Each pair A>B isgiven the score Rating(A)-Rating(B) on a ballot.  The pairs are ranked on each ballot fromlargest score to smallest score.  Fromhere on, the ratings ballots are dispensed with and only the ranked pairballots are used.Example:7 A>C, B>C, A>B, B>A, C>B, C>A6 B>A, B>C, C>A, A>C, C>B,A>B5 C>B, C>A, A>B, B>A, A>C,B>C 3.      For each pair of candidates, A,B if more votersrank 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>A6 B>C, C>A,  A>B5 C>A, A>B, B>C4.       Now a societalranking of pairs of ordered pairs is produced. This is done exactly as is done for Tideman or Schulze, except that thecandidates are ordered pairs of candidates of the form (A>B) so thesocietal ordering will include entries like (A>B)>(C>D) if more votersrank A>B higher than C>D.  This isthe step that uses more majority rule information than rankings basedCondorcet.  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 toturn the societal ranking of pairs of ordered pairs into a list of rankedpairs. Example:B>CC>AA>B6.      The Tideman or Schulze method is then used asecond time to turn the ranked pairs list into an ordered list ofcandidates.  ExampleBCA 7.      The winner is the highest ranked on thecandidate list.Example B wins Using a direct conversion of ratings to rankings with just one Tideman/Schulze step, A. 
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