[EM] Intermediate RV rating is never optimal

[Michael Ossipoff]

Lomax says:

But then I noted that the optimum vote for B in the zero-knowledge case 
(where we must assume equal probability of election of all the candidates) 
was 50%

I reply:

That’s only because, in Approval it wouldn’t make any difference, 
expectation-wise, whether or not you vote for B. In Approval, flipping a 
coin would be a good way to decide. That’s the  only reason why an RV voter 
wouldn’t be voting suboptimally if s/he gives B middle rating instead of one 
of the extremes. In RV, in your example, giving B top rating or bottom 
rating would be just as good as giving hir a middle rating. You might  
choose middle rating simply because it’s like flipping a coin in Approval, 
and because, in this instance, it isn’t suboptimal to rate sincerely.

Let me say it in more general terms: When a candidate is exactly at your 
Approval cutoff, then, whether the method is Approval or RV, it makes no 
difference what rating you give hir. In Approval the choices are top and 
bottom. It doesn’t matter which you give, but I’d flip a coin.

In RV, when a candidate is at your Approval cutoff, so that it makes no 
difference how you rate hir, obviously it doesn’t matter whether you give 
hir top rating, bottom rating, or anything in between. Of course that means 
that you can rate hir sincerely if you want to.

So yes, a candidate exactly at your Approval cutoff is the one exception, in 
a public election, to the statement that it’s always suboptimal to give an 
intermediate rating in RV.
And, since it doesn’t matter how you rate hir, you could give hir a sincere 
rating. I would.

But Warren Schude’s statement was correct: When a candidate is at your 
Approval cutoff, so that it makes no difference how you rate hir, then there 
is no such thing as an optimal (or sub optimal) rating. Therefore it’s 
correct to say that, in public elections with RV, it’s never optimal to give 
an intermediate rating.


Lomax says:

Now, to the core of Schudy's claim: He uses the word "never," which is an 
absolute, making it trivial to refute his claim, all I have to show is a 
simple counterexample, and I already did that.

I reply:

No. You didn’t. As I said, in your example, B is at your Approval cutoff, so 
that it makes no difference how you rate B. So there’s no such thing as an 
optimal way to rate B. You might want to then say that _all_ possible 
ratings for B are optimal, but then the word pretty much loses its meaning.




Lomax continues:

And with Range, we are doing the same, counting all the votes, only every 
voter can cast up to N votes for each candidate.) Now, in the Approval 
example, we have a crisis point. If I am considering which candidate is the 
frontrunner, between A and C, on which my choice turns, and as the relative 
probability of the election of C increases, there is a point where my vote 
for B suddenly flips from disapproval to approval. The discontinuity is a 
sign that there is something amiss. If we look instead at this same context 
for a Range election, there would be no discontinuity. As the relative 
probability of the election of C increased, the optimum rating of B would 
increase, until, at some point, the rating of B would become maximum.

I reply:

That’s incorrect. It’s exactly the same in RV as in Approval. In your 
example, with B at your Approval cutoff, it doesn’t matter how you rate B. 
But, when you make C more likely to outpoll A than vice-versa, that lowers 
the Approval cutoff. Now B is above the Approval cutoff. There is then one 
optimal way to vote: Give B a top rating. As soon as the Approval cutoff 
goes below where B is, you abruptly must give B a top rating, for 
optimality, whether the method is Approval or RV.

This is a good example of why a newcomer should speak not so assertively.

Of course, likewise, if the A were more likely to outpoll C than vice-versa, 
raising the Approval cutoff, that would put B below the Approval cutoff, and 
it would be necessary to bottom-rate B, for optimality.

Lomax repeats:

If A and C are equally likely to be elected, or we don't know which of them 
is equally likely, so we must assume equality, and given the initial 
condition that the preference strengths are balanced, it's clear that game 
theory would optimize our vote as 50% for B.

I reply:

As I said, with B at your Approval cutoff, there is no such thing as an 
optimal way to rate B, because it makes no difference how you rate B. Feel 
free to rate hir sincerely, but don’t call it optimal.

Mike Ossipoff