Chris Benham wrote:
Yes. I suggest that those "not rated" should be interpreted as
disapproved and bottom-most rated. Those candidates rated "zero"
should be considered to be half-approved. Candidate X's approval
opposition to Y should be X's approval score (including of course the
half-approvals) plus half X's approval score (likewise) on ballots
that rate Y zero. Y's "Approval Oppostion" score refers to Y's
maximum approval opposition score from any X.
Here it seems you would have a choice analogous to wv versus margins in
Condorcet. What you describe would be margins; wv would give no points
to A nor B in the case of a tie.
"Normalization could be used if required, with either the voter
specifying "absolutely worst" and "absolutely best" (setting the
range), or by the lowest and highest rated candidate having those
positions. So if a voter wants to say that he likes all the
candidates, but some are better than others, he could vote all
positive integers, whereas a McCain/Obama/Clinton voter could vote
McCain less than zero and the other two greater than zero. With
normalization, the contribution of
A: 1 pts. B: -1 pts.
to the raw scores would be the same as
A: 3 pts. B: 1 pt.
but would have a different effect regarding the approval component
(only A approved in the first case, both approved in the second)."
I don't think I'm that keen on "normalization", but I don't really
object to 'automating' the approval cutoff, so that ballots are
interpreted as approving the candidates they rate above the mean of
the ratings they've given (and half-approving those exactly at that
mean). I can imagine that others would object on various grounds,
and the US voting reform enthusiasts who like FBC-complying methods
like Range and Approval generally seem to prefer their voting methods
to have 'manual transmission'.
The advantage of having zero set the boundary between approved and
disapproved, instead of the mean doing so, is that you could express a
general favor (or dislike) of politicians. For instance, if you think
only one person's mostly decent and the rest are all corrupt (but some
are more corrupt than others), you could vote the favored candidate
above zero and the others below zero, whereas "above mean" would include
some of the corrupt candidates as well.
I can understand that some would prefer the ballot to have, to use your
own words, a manual transmission, but I think the concept of an explicit
approval cutoff would be confusing to most. With the boundary at 0, you
can just say, implicitly, "give those who you like points, and take
points away from those you don't like".
When Approval voting has better strategies than plain commonsense
approval, that's going to be a suboptimal strategy, but hopefully the
voters are going to be mostly honest so that that's not much of a problem.
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