[EM] Automated Approval methods (was Single Contest)

[Rob LeGrand]

Kevin wrote:
> Yes, but if it were strategy-free somehow, I think it would be worth
> it. Real life isn't monotone. I don't imagine that all the prettier Yee
> diagrams would really look like that if voters were using information
> and strategy!

I may be missing something, but I don't see how you can have a
nonmonotonic method that is strategy-free.  For any example of
nonmonotonicity, you should be able to find a single voter that triggers
it--say, if that focal voter votes A>B>X>C, then X wins, but if they vote
A>X>B>C, then X loses.  Whoever wins when X loses, manipulability pops
up:

Case 1: A wins.  Then imagine that the focal voter sincerely thinks
A>B>X>C.  Insincerely voting A>X>B>C moves the winner from X to A, which
is a successful manipulation.

Case 2: B wins.  Then imagine that the focal voter sincerely thinks
A>B>X>C.  Insincerely voting A>X>B>C moves the winner from X to B, which
is a successful manipulation.

Case 3: C wins.  Then imagine that the focal voter sincerely thinks
A>X>B>C.  Insincerely voting A>B>X>C moves the winner from C to X, which
is a successful manipulation.

This "proof" may be either flawed or needlessly complex, but it's what
came to mind.

--
Rob LeGrand
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/