[EM] Responses to some of Forest's ideas
Richard Moore
rmoore4 at home.com
Tue Jul 24 20:14:08 PDT 2001
LAYTON Craig wrote:
> 9 A>B>C>D=E=F : 100>90>1>0=0=0 : ZI AB : St AB
> 38 B>D>A>C=E=F : 100>52>51>0=0=0 : ZI BDA : St B
I don't see why the second group would truncate to B in the
informed vote. Just given the information that clones E and
F don't have a chance, a simple informed strategy
calculation could be made by removing E and F from the
picture and doing a mean utility calculation (203/4 = 50.75)
and voting BDA. The information that C is a likely front
runner would give even more reason to vote BDA.
> 40 C>B>A>D=E=F : 100>85>70>0=0=0 : ZI CBA : St C
Discounting E and F, 255/4 = 63.75, so possible strategic
vote is CBA. Depending how confident this group is in the
information that D will lose, they might truncate to CB or
just C, but we don't know for sure. "C only" seems unlikely
to me unless these voters are reasonably sure of D's and A's
defeats.
> 9 D>C>B>A=E=F : 100>10>9>0=0=0 : ZI DC : St DC
Wrong, ZI vote here is D only (119/6 > 10). Strategic vote
could be DC or DCB, depending on how much doubt the
pre-election information casts on candidate D. If the
information is believed to be unreliable, this group might
stick with D only.
> 4 E=F>A>B>C>D : 100=100>90>12>10>0 : ZI EFA : St EFA
>
> Undefeated (definite) Condorcet Winner is B. Zero info approval winner
> (taking both mean and median into account) is A. Strategic approval winner
> is C. It seems pretty clear that I've used optimal strategy, although I
> haven't done all the math.
>
> SU scores for the top three candidates; A = 5998, B = 8148, C = 4670.
>
> Craig
For ZI I get A, also. For NZI, I see B as the most likely
winner (since I don't expect to see enough CBA voters
dropping B to make C win).
Incidentally, I've long suspected there is (in general) no
such thing as universally available "perfect information" in
Approval voting. It might be possible for one or a few
voters to have such perfect information, as for instance if
the voting is done openly by role-call and Mr. Zzyzx gets to
hear how everyone else voted before his turn comes. But
suppose everybody knows everybody else's sincere utilities
before the voting takes place, and ballots are secret. The
probability that voter X will vote for candidate Y depends
on all the other probabilities, but each of those
probabilities in turn depend on all the other probabilities,
including the "X for Y" probability we are trying to
calculate, so you can't calculate the answer if you don't
already know it. It's a system of equations with circular
dependencies and no unique solution. It is that lack of
perfect information that makes it difficult to know if the
CBA voters in the example above will truncate in the NZI case.
There are certainly special cases where there is a unique
solution. A trivial example is one where each voter has a
utility of 100 for one candidate and 0 for all others.
Richard
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