A?B disturbed me when I first read it. As I composed the following I
found a home for it that seems consistent with your words.
When I go to count votes:
A>B Says voter prefers A over B.
A<B Says voter prefers B over A.
A=B Says voter considers them equally acceptable and, should they be
prime candidates for winning, let that be decided by other voters. Note
that the above says nothing as to why, only that this voter declares
equality as opinion.
A?B is implied by A and B both being omitted from explicit voting
via truncation by the voter. Indicates they are equally
acceptable/unacceptable, for the voter says nothing to contradict that.
DWK
On Tue, 30 Aug 2005 00:02:22 -0400 Warren Smith wrote:
I regard A=B as a declaration of knowledge on the part of the voter.
he is saying "I understand A and B and I think they have the same utility."
I regard A?B as a declaration of ignorance from the voter. he is saying
"I do not know whether A>B or B>A, I really am clueless on this matter."
In some sence A=B and A?B are not only not the same thing, they are in fact
OPPOSITE things.
This distinction can matter, and you can design your voting
system to make it matter.
Well for example, if one voter says A>B and another says A=B and
10 others say A?B, then the society-wide opinion is the same as
if the first two voters spoke and the rest were not present (or it should be).
In a voting system in which PARTIAL ORDERS are permitted as votes,
then A>B is permitted, A=B is permitted (if we permit =), and A?B arises
automatically as the absence of any stated (or inferable) relation -
absences being possible since it is a PARTIAL order. Votes containing
cycles like A>B>C>A would presumbly be disallowed as making no logical sense...
wds
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Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.
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