[EM] Strategic voting in ratings

[Roy]

> In the equality case, you can vote any rating you like for 
> B, including the sincere value, and it won't affect your 
> utility expectation.

True; I just figured that in the absence of incentive to vote 
dishonestly, one would vote honestly. (It's an assumption that 
there's some utility in honesty.)

> I'm a non-statistician but if my perception of the 
> probabilities in a CR election is clear enough I will vote
> all candidates at full-scale.

And that's the rub: how clear can those probabilities be to a voter? 
If the polls come out with these averages:

Anderson     35%
Bush         43%
Clinton, H.  40%
Dukakis      12%

What probabilities do you assign? Is there some other source of 
information than polls of this sort?

> Not sure what you're asking.

That's because I replied before I grokked what you were expressing. I 
apologize for that. Pay no attention to the multiplication of utility 
argument.

> Even if you anticipate that all like-minded 
> people will come up with the same strategy, then this would 
> be factored into the calculation of the values of the 
> deltaP's

That's another layer of complexity, though. And complexity is the 
friend of fair voting (because it stymies strategy). You might know 
that you should vote each candidate at an extreme, but if you don't 
know which extreme, you have no incentive to vote insincerely.

To complicate matters further, strategic voters would probably be 
strategic pollees. They might give a poll the inverse of their true 
ratings, to make their favored candidates look like underdogs, which 
would tend to make strategic voters push their candidates up (or at 
least would make strategic voters that much more unsure of the 
probabilities).

I will concede that with high-quality information, an electorate of 
statistically-aware voters would tend to polarize their votes. How 
significant do you think that would be in reality, if this voting 
scheme were implemented? It doesn't seem to me that the information 
about probabilities would be reliable enough, nor that a significant 
portion of the voters would know how to use it if it were.

> If you change X by some amount (say, based on a roll of 
> dice) the group dynamics won't amplify your random perturbation.

No, for two reasons: 1. you wouldn't likely be part of a large, like-
minded group; and 2. if you were, the randomness would be effectively 
self-correcting

But strategic voters need to consider that they are not acting 
independently, and that the population is going to get what it asks 
for. If a large number ask for what they don't want, they're going to 
get what they don't want. If only a small number ask for what they 
don't want, it's not going to make that much difference. So either 
way, there's a logical (if not mathematical) argument to vote 
honestly.