[EM] Decisiveness of MTM & Schulze

[Markus Schulze]

Dear Steve,

you wrote (3 Jun 2000):
> 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 when I originally made that claim.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.

But when you slightly modify your example then the Schulze
winner is unique while the Tideman method is indecisive.

Example: AB51,BC51,CA51,AD60,BD60,CD60,DE61,EA52,EB53,EC54.
Now candidate A is the unique Schulze winner while the
Tideman method is indecisive between A, B and C.

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de