wms, for me the first question is always what does the tiebreaker mean. When SODOS starts giving a different answer if different origins are used I get confused as to what it means. Is the godraw origin invalid, is the macmahon origin valid? What origin should I be using for a tournament?
With SOS I don't have to worry about origin, the result is invariant about any origin.
It's very hard to work out who had the toughest opponents in a tournament. :)
This seems to be an obvious result of any aggregation method a la Arrow's Impossibility Theorem.
What are the differences in godraw origin and mcmahon origin?
You say that with SOS you don't have to worry about the origin, but that's a silly argument. I pick my origins well to give the SODOS I want. If I just give everybody ties, with no tiebreaker, then I don't have to worry about who played who at all, but does that make it better?
So far nobody has challenged that, when the origin is picked to give those at or below the lower bar 0 points, SODOS is a good tiebreaker.