Why it saves time
dfb at bbs.cruzio.com
Fri Apr 19 03:55:06 PDT 1996
To show why it saves time to admit an alternative to the Smith set if
it isn't beaten by more alternatives than some member of the Smith set,
say you're determining the Smith set without a computer, and there are
about 30 alternatives in the election.
Admmittedly doing the 435 pairwise comparisons isn't something that
you'd want to do without a computer, even though you might find
something that beats everything before you do all 435.
Say we already have ordered the alternatives according to how many
alternatives they're beaten by. Now, if we know that certain alternatives
are already in the Smith set, it doesn't take long to determine which of
those is beaten by the most alternatives, and admit to the Smith set
everything not beaten by more alternatives than that. That's the quick
& easy way to admit alternatives to the Smith set.
If we have to do it by finding out if a particular alternative beats
or ties a member of the Smith set, that requires separately comparing
it to each known member of the Smith set. And we have to do that with
each alternative not yet named as a Smith set member. So we save a
lot of time if the precedure in the previous paragraph admits lots
of alternatives to the Smith set.
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