[EM] Decisiveness of MTM & Schulze

[Steve Eppley]

In a message I posted earlier today, I retracted a claim made a 
few months ago that MTM is more decisive than Schulze.  But the 
claim may be correct.

My memory isn't adequate for me to be sure what was in my mind 
when I originally made that claim.  I wrote earlier today about 
the minor discrepancy between MTM's definition and the faster 
algorithm used by my software.  But upon further reflection, I 
probably also based the claim on a consideration of scenarios 
such as the following:

   5 alternatives.
   A & B & C are clones.
   A & B & C cycle mildly (CA51,AB52,BC53).
   A & B & C beat D solidly (60).
   D beats E solidly (61).
   E beats A & B & C moderately (55).

Schulze chooses A & B & C.  The strongest beatpaths from clone 
to clone all have a strength of 55, swamping the information 
which distinguishes between clones.

But MTM doesn't neglect the information which distinguishes 
between the clones.  MTM chooses A since the MTM-dominant 
ranking is ABCDE.  (The ABCDE ranking thwarts only the 55's and 
the 51.)

So MTM appears to be more decisive than Schulze, without 
compromising its complete independence of clones.


---Steve     (Steve Eppley    seppley at alumni.caltech.edu)