[EM] A?B versus A=B

Warren Smith wds at math.temple.edu
Mon Aug 29 21:02:22 PDT 2005


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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