Abd ul-Rahman Lomax wrote:
bits and pieces
At 05:33 AM 7/21/2007, Michael Ossipoff wrote:
That's incorrect. It's exactly the same in RV as in Approval. In
your example, with B at your Approval cutoff, it doesn't matter how you rate B.
In what I wrote, B was not at the voters "approval cutoff." I didn't
give an approval cutoff. Approval cutoff is an artificial insertion;
it's a device for converting range ratings to approval votes.
This is the situation described:
The voter prefers A>B>C, with the preference strength between A and B
being the same as the strength between B and C.
There is nothing here about Approval cutoff, there is nothing that
says that the voter does or does not "approve" of *any* candidate.
I think we safely say that max-rating a candidate is equivalent to
"approving" that candidate.
Ossipoff confused the fact that the candidate was intermediate
between A and C in sincere rating, i.e., being midrange, with being
"at your Approval cutoff."
If the preference strength between A and B is weaker than that between
B and C then with
the winning probabilities being equal (or unknown) then the voter's best
strategy is to max-rate
A and B. If instead the preference strength between B and C is weaker,
the voter does best to
min-rate B and C (and of course max-rate A).
Since the situation you describe is at the border of these two (max-rate
B or min-rate B), we can
say that "B is at your approval cutoff".
And, quite clearly, it *does* matter how
you rate B in some scenarios; for example, if the real pairwise
election is between A and B, then the optimum vote is to rate B at
minimum. And if it is between B and C, then the optimum vote is to
rate B at maximum.
Of course it can "matter" after the fact, but with both possible "real
pairwise elections" being
equally likely at the time of voting, in Abd's scenario it
probabilistically makes no difference what
rating the voter gives B.
Chris Benham
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