[Election-Methods] How does the Schulze Method and Ranking Pairs work?

[seppley at alumni.caltech.edu]

Hi,

John Wong asked:
> I was wondering, can someone can explain to me how they how work? Also,
> can someone explain what is the Smith and Schwartz sets are and how
> do we determine which? Thanks in advance.

Some people use the name Ranked Pairs to mean the Maximize Affirmed
Majorities method (MAM) and others (such as I) use it to mean the voting
method defined by T. Nicolaus Tideman in his 1987 and 1989 papers.  They
are different methods.  The most important difference is that Tideman
measured the size of each majority by subtracting the size of the opposing
minority, whereas MAM doesn't do that subtraction.  This gives MAM
superior strategic properties.

I think it's misleading to call MAM by the name Ranked Pairs, since anyone
looking up Ranked Pairs in the literature will likely find Tideman's
method.  I also think it violates convention to steal the name coined by
Tideman for his method.  I ask all of you to please use the name Ranked
Pairs only for Tideman's method, and to edit your websites accordingly.

Since John asked about the Schulze Method in the same question, he
probably means MAM, not Tideman's Ranked Pairs, since MAM & Schulze
measure the size of each majority the same way.

Here's a link to my website about MAM:
   http://www.alumni.caltech.edu/~seppley

Briefly: (First, note that regardless of the voting method, there is more
than one majority preference when there are more than two candidates.) 
Each voter ranks the candidates from top to bottom. (It's okay for the
voter to rank two or more as equals, and it's okay to leave candidates
unranked; unranked candidates will be treated as if the voter had ranked
them at the bottom, worse than all candidates explicitly ranked.)  MAM
finds the majority preference in each pairing of candidates by counting
the number of voters who ranked each candidate over each other candidate. 
Then MAM constructs the order of finish a piece at a time, by considering
the majority preferences one at a time, from largest majority to smallest
majority.  Each majority preference is included into the order of finish,
unless it's inconsistent with those already included.

Some examples are provided at my website.  There's also a link to an
online MAM engine that can be used to tally elections.

Simulations comparing MAM to the Schulze method show th