"If a majority prefers candidate x to any other candidate, then x must win".
If this test is about sincere preferences, then all methods are subject to "false positives" due to strategic voting. In theory, false negatives would also be possible if voters are misinformed about other voters' preferences:
51 A>B>C 02 B 47 C>B>A
If a few of the A voters believe that C has a chance of winning, despise C strongly enough, and are comfortable enough with B to rank B first, then it's possible for B to win in a method that meets "majority favorite".
As far as I'm concerned, Majority Favorite's main value is as a sanity check for ranked methods-- if you collect this data, you are generally obligated not to contradict it. Used in this way, only ballot information is important, not sincere preferences.
I'm generally suspicious of any criterion containing the term "majority" in the name, partly because it's so easy to come up with absurd methods that meet these criteria. Although Majority Favorite is probably more defensible than the others, which admit various kinds of "derived" or "manufactured" majorities.
Bart ---- Election-methods mailing list - see http://electorama.com/em for list info
