# [EM] two bit ratings

Richard Moore rmoore4 at home.com
Fri Sep 21 19:30:26 PDT 2001

```Craig Layton wrote:

> I expect you're right, but isn't the Condorcet Criterion phrased something
> like "if there is a sincere Condorcet winner, and all voters vote sincerely,
> then the sincere Condorcet winner must win"?

Why should the CC definition include the word "sincere" at
all? Isn't the use of "sincere CW", coupled with the
conditional "all voters vote sincerely", redundant? What
does this definition say that is different from "If there's
an expressed CW, then the expressed CW must win"?

To put this in an analogy, consider "If one car has a higher
top speed than the others, and all cars are driven at their
top speed, then the car that has the highest top speed must
win the race." If we simply guarantee that "the car that is
driven fastest wins the race", even if that car doesn't have
the highest top speed, then we would automatically guarantee
that the car with the highest top speed will win if all cars
are driven at top speed.

Besides that, I don't know if sincerity is something you can
define in a pure-mathematically useful way. Say I have a
preference A>B>C, and then mistakenly ("insincerely") vote
B>A>C. Now before the polls are closed I rethink my position
and decide I don't like A as much as I thought, and that
B>A>C is my actual preference. So did I vote sincerely or
insincerely, from the standpoint of a useful mathematical
criterion? Suppose, after some mathematician has determined
that I did in fact vote sincerely, I change my mind again?

We need to distinguish between when we are talking about the
*act* of voting sincerely and the existence of *sincere
voting incentives* that would cause a voter's ballot to
reflect a given set of static utilities. The first is
something that can only be measured psychologically, and is
likely to be a very volatile measurement. The second belongs
to the world of pure mathematics, since the static utilities
don't necessarily reflect the voter's state of mind -- they
could have been arbitrarily generated.

Richard

```