Jonathan Lundell wrote:
On Jan 17, 2009, at 4:31 PM, Juho Laatu wrote:
The mail contained quite good
definitions.
I didn't however agree with the
referenced part below. I think "sincere"
and "zero-knowledge best strategic"
ballot need not be the same. For example
in Range(0,99) my sincere ballot could
be A=50 B=51 but my best strategic vote
would be A=0 B=99. Also other methods
may have similarly small differences
between "sincere" and "zero-knowledge
best strategic" ballots.
My argument is that the Range values (as well as the Approval cutoff
point) have meaning only within the method. We know from your example
how you rank A vs B, but the actual values are uninterpreted except
within the count.
The term "sincere" is metaphorical at best, even with linear ballots.
What I'm arguing is that that metaphor breaks down with non-linear
methods, and the appropriate generalization/abstraction of a sincere
ballot is a zero-knowledge ballot.
Wouldn't it be stricter than this? Consider Range, for instance. One
would guess that the best zero info strategy is to vote Approval style
with the cutoff at some point (mean? not sure). However, it would also
be reasonable that a sincere ratings ballot would have the property that
if the sincere ranked ballot of the person in question is A > B, then
the score of B is lower than that of A; that is, unless the rounding
effect makes it impossible to give B a lower score than A, or makes it
impossible to give B a sufficiently slightly lower score than A as the
voter considers sincere (by whatever metric).
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