Eye Ball Mathematics
dfb at bbs.cruzio.com
Sat Nov 16 21:38:59 PST 1996
To answer Don's question about applying the basic democratic principle
about majority rule in multi-candidate elections:
1. It doesn't involve Approval. Approval is different, because
it allows us to merely give a vote to some & not others. We're
talking, instead, about rank-balloting, which involves _relative_
prefernces, rather than absolute votes. It's true that Approval
can be be used to express relative preferences, but it only
allows two preference levels: voted-for & not-voted-for. So no,
the implementation of that principle by rank-balloting methods
doesn't involve Approval. It uses the relative preferences expressed
in a voter's ranking, and the voter may of course express as many
of those as s/he wishes to.
2. No, the application of that principle doesn't just look
at 1st & 2nd choices. The reason it seemed that way is merely
because we were talking about a 3-candidate example, where
every ranking's 3rd choice could be ignored because it has
no effect (ranking someone last is the same as not ranking
hir). So the answer to that question is that the application
of that basic democratic principle about majority rule involves
the use of all of a voter's expressed preferences. They all
count. But in our 3-candidate examples, we only need the 1st
& 2nd choices--and that's just because they're 3-candidate
3. The mathematics? It's not complicated at all: Just take
the wording of that principle literally. That's really all there
is to it.
Sure, in a bigger example it would be more complicated to compute
the result, because there are more pairs to look at. But no
matter how many candidates there are, you still can determine
whether or not someone has a majority against hir by looking
at hir pairwise comparisons, and checking whether another
candidate is ranked over hir by a full majority of all the voters.
If so, then that candidate is the "B" referred to in the wording
of that basic democratic principle, and that candidate that
is ranked over hir by a majority is the "A" mentioned in that
wording. If one of those two wins, then it should be A.
So the goal is to avoid unnecessarily violating that principle,
and that's a reason to use Condorcet's method, or Smith//Condorcet.
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