[EM] two bit ratings

[Richard Moore]

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