re: [EM] Strong FBC

[Alex Small]

I think I know how to state the problem better than in my previous messages:

Imagine a machine that takes as input each voter's preference order.  (I'll
argue in a moment that yes/no info isn't necessary for this result.)  Given
all of that input, as well as an election method, it assigns to each voter
a strategy that will give him or her the best outcome given everybody
else's strategies.  It might bury your favorite, it might rank him equal to
another, or it might rank him first.  It does what it needs to do, but
basically it's trying to find a Nash equilibrium.

The question is, might we get a better result if we lie to the machine?
Suppose I think A>B>C.  It takes that info, does what it needs to do, but C
is elected (presumably because a lot of other people liked C).  Could I
have brought about the election of B by ranking A second in my input, or
could I trust the machine to rank A second in my strategy if it's necessary
to bring about the election of B?

I don't know if we can in principle build a machine that we can always
trust to betray our favorite whenever doing so will improve our lot, but
otherwise always rank favorite ahead of all others (never equal to).

The idea is to build a machine that will betray favorite for us if
necessary, so we don't have to do it ourselves.  We can honestly say that
we didn't betray favorite, since we gave sincere input and got an output.

I say that yes/no votes aren't necessary for the following reason:

Suppose I personally approve only of A, but not B or C.  Suppose C is my
last choice, and he's the only one who gets a majority of yes votes in a
method which uses yes/no votes.  Although I can't say I like B, I can say
that I'd be better off with B than with C.  That's all the machine has to
know.  If it turns out that the program uses yes/no votes, and that giving
a yes to B is necessary to prevent the election of C, then so be it.  All
the machine needs to know is whether I like B better than C.

Alex

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