[EM] Change in definition of defensive strategy
nkklrp at hotmail.com
Fri Aug 30 20:28:45 PDT 2002
Because I've let some committments get way out of hand, I haven't
had a chance to check or write to EM for a few days. Right after I
posted my most recent message, it occurred to me that defensive strategy
needed to be defined slightly differently from the way that I'd written it
in that posting.
Though I'm not changing my definitions of majority rule and
offensive stratety, I'm changing my definition of defensive strategy
as follows: Substitute "majority wishes" for "majority rule".
Here's how I define majority wishes:
Electing candidate Y would violate majority wishes if another candidate
is preferred to him by a majority of all the voters, and that
majority pairwise preference isn't the smallest majority pairwise
preference in a cycle of majority pairwise preferences.
A majority pairwise preference is an instance of a majority of the
voters preferring one candidate to another.
The strength of a majority pairwise for X over Y is measured by
the number of people who prefer X to Y.
[end of majority wishes definition]
Now, it might seem as if the mention of cycles in a definition of
majority rule or majority wishes sounds arbitrary or artificial,
rather than natural or obvious. But what could nullify a majority
defeat or a majority pairwise preference, if not a cycle of stronger
majority defeats or majority pairwise preferences? A defeat or
a majority pairwise preference that's the weakest in a cycle of
similar ones loses its significance thereby.
It could also be claimed that since my definitions of majority rule
and majority wishes, and therefore my definition of defensive
strategy, specify winning-votes, it could seem that the margins methods
and IRV fail in those regards merely because of how I've chosen
to define those majority terms. Actually, though, IRV & margins methods
fail the defensive strategy and majority rule standards without there
being a cycle of majority defeats or a cycle of majority pairwise
You can't really speak of a majority preference or defeat unless
you mean that a majority votes or prefers X over Y. Talking about
majority means that we're talking about defeat-support, winning-votes,
rather than the difference between two opposing sets of voters. It's
inherent in discussing majority.
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