# [EM] Floyd-Warshall algorithm - variations

Markus Schulze markus.schulze at alumni.tu-berlin.de
Fri Dec 19 22:15:07 PST 2003

```Dear Ernest,

you wrote (19 Dec 2003):
> Let me put it another way.   Could you please explain in words why you
> feel it is necessary or useful to use *both* absolute votes and margins
> in the calculation?   Are the margins used simply to break a tie
> between absolute votes?  I think that's what is implied by the line:
> >            if ( p1[i,x] = d1[x,k] ) then
> >            t : = min { p2[i,x], d2[x,k] } ;

I consider the margins of defeats only when both defeats have the same
absolute number of votes for the winner. The aim is to make the method
more decisive without sacrificing any of the desired properties.

******

You wrote (19 Dec 2003):
> Also, is there a particular mathematical or anti-strategic reason for
> randomizing the tie-breaking round, rather than just automatically
> picking the candidate who would have the best chance of winning such
> a random draw?

Plurality as a tie-breaking strategy violates independence of clones.

Markus Schulze

```