This Method Never Has Subcycle Fratricide
Mike Ositoff
ntk at netcom.com
Fri Jun 12 01:53:34 PDT 1998
The main advantage of 2 methods proposed here, over
Smith//Condorcet was that they can get rid of subcycle
fratricide under certain conditions--a near clone set, or
other related conditions that were described.
But if it's important to get rid of subcycle fratricide, can
we do even better, then, and get rid of it altogether? Yes, it
seems to me.
That being the goal, this is an obvious, natural plan: let
subcycle members duke it out _after_ finding out if the subcycle
contains a winner with respect to alternatives outside the
subcycle. Oh, I suppose you'd like something more precise :-)
The Order of a Cycle:
If cycle B is a subcycle of cycle A, then B's order is greater
than that of A. B's order is 1 greater than that of A.
The Smith set is a cycle of order 1. It's subcycles are of
order 2, and their subcycles are of order 3, etc.
Smith//Condorcet(EM) with subcycle rule 2:
Confine the count to the Smith set, ignoring internal
defeats in cycles of higher order than 1.
If the winner is in a cycle of order greater than 1,
confine the count to the 2nd order cycle containing that
winner, ignoring internal defeats in cycles of order
greater than 2.
Continue in this way, confining the count to the next highest
order cycle containing the winner, ignoring internal defeats
in its contained cycles of greater order than it.
Of course as soon as there's a winner that isn't in a cycle
of order greater than that of the cycle to which the count
was confined when that winner became a winner, then that
winner wins the election.
***
I realize that, as the proponent of this method, it's my
responsibility to check it for problems, instead of asking
you to. But if getting rid of _all_ subcycle fratricide is
really an important goal, then someone else might want to
join in the task of checking this method out for problems.
So far I don't know of any.
***
Mike Ossipoff
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