Oops, it isn't Condorcet(EM)
Mike Ositoff
ntk at netcom.com
Thu Aug 6 13:38:44 PDT 1998
I've just realized that I was mistaken when I saids that
sequential dropping of defeats that conflict with stronger ones
is the same as plain Condorcet(EM).
In my recent clone-set example, Sequential Dropping picks B,
as does Petry (and my rewording of it), Schulze, TRideman
(as I now understand it), and the method I proposed yesterday,
which I call Low Order Precedence (LOP).
Maybe Petry is the same as my wording of it, and Tideman,
and maybe Sequential Dropping.
In my indecisiveness example, LOP picks B. Sequential Dropping
picks E. My version of Petry pics E. There's no Schulze winner,
and I don't know if there is a set with un-countered beat-paths
to all the rest.
It seems fairer to pick B than E in that example. It seems
important, to me, to pick something that's a winner in a
1st order cycle among the Smith set. I'd like to define
a criterion about that. (I just have). But that criterion
is incompatible with Pareto, as is LOP.
The academic criticism resulting from Pareto violation
is probably more important than what happens when there's
a subcycle, a rare problem most likely.
But I'm more interestedin the main cycle, since that's
where the need for defensive strategy is caused or not caused,
depending on the method. It's where the Condorcet winner,
and the alternatives of the order-reversers or truncators,
and the alternative that theyk cause to beat the CW are.
Sure it's important to not violate majority rule, but how
important is an important principle in an unimiportant
pairwise comparison? Especially when it can cause the same
violation in the more important main cycle?
But what I like isn't necessarily the most practrical public
proposal, because of Pareto violation, & because of wordiness.
But a somewhat less wording version is possible. But I'll
send that in a subseq ukent message, just incase the keyboard
is about to quit.
Mike
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