Dear Kevin!
You wrote, answering Warren:
here is another: consider the horrible DH3 pathology described at
http://math.temple.edu/~wds/crv/DH3.html
which afflicts Borda and many Condorcet methods... does it also afflict
DMC? Again answering this requires some understanding of voting strategy
Here is another question - will DMC lead to 2-party domination, or
not? To really answer this, it would help to understand optimal
voting strategy in DMC, which is probably beyond reach.
However, you may be able to just think about 3-candidate DMC elections
and thereby answer the question with