[EM] "Natural definition" correction. Very tentative alternative proposal.

[Michael Ossipoff]

I've just realized that "disregard cyclical defeats" i(where a
cyclical defeat is a defeat that's in a cycle) isn't enough to define
the Schwartz set. But (looking at this for the first time) I don't
know if it would be enough to gain MMC and Clone-Independence.

Anyway, Symmetrical-IC-Schwartz-Top would say:

Determine the Schwartz-set, by the Symmetrical IC definition of
"beat", and elect the Schwartz-set's most top-ranked member (To rank a
candidate at top is to not rank anyone over hir).

[end of

Or maybe the following slightly different method would be ok (it would
have to have a different name):

"Beats" is defined by Symmetrical IC.

Disregard any defeat that's in a cycle.

If exactly one candidate is unbeaten, s/he wins.

If all or no candidates are unbeaten, then elect the most top-ranked candidate.

If some, but not all, candidates are unbeaten, then elect the most
top-ranked unbeaten candidate.

[end of definition of un-named alternative method]

Mike Ossipoff