1 more thing about subcycles & Copeland

[Mike Ossipoff]

I should add that the kind of subcycle that needs to be considered
by the subcycle rule is one in which every alternative is beaten
by another member of the subcycle. Sure, a more general definition
of a subcycle could be used, but I'm just saying that the definition
could be narrowed to the one stated above, and the subcycle rule
would still make Condorcet comply with LO2E-2.

The result, with that narrower definition of a subcycle, would
be that the subcycle rule would no longer help Copeland meet
ITC.

If this seems like contriving the rules to exclude Copeland,
that's ok, if it shows that what's needed to make Condorcet
meet LO2E-2 won't help Copeland meet ITC.

Maybe I should say that definition less circularly:

For the purpose of making Condorcet meet LO2E-2, the following
narrower definition of a subcycle could be used:

 A subcycle is a set of alternatives all of whose elements
are members of another cycle, all occuping the same position in
that cycle, and all of whom are beaten by another member of the
set in question.

By "occupying the same position in that cycle", I mean that
all members of the set beat & are beaten by the same alternatives
outside that set, in a different cycle of which those alternatives
are all members.

So it could be said that the set is an element of that other
cycle, though my wording in the paragraph before this is
probably more precise, because I haven't specifically
defined elsewhere what I mean by a set of alternatives being
an element of a cycle.

***

Mike





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