[EM] Strategic voting in ratings

[Richard Moore]

Roy wrote:
> 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?

Well, if my ranking is A > C > D > B, with utilities 
distributed equally, then without knowing any deltaP values 
but knowing the poll values, I would vote full approval for 
A and C, and full disapproval for B. Now D is the only 
candidate I'd have to give more thought to. The deltaPs 
associated with D are probably not very high anyway, so the 
penalty for being wrong is statistically very small. In this 
case, A is twice as valuable to me than C utility-wise 
(relative to D), so I would take a guess at the chances that 
voting for D will hurt A and double them, then add my guess 
at the chances it will hurt C, and compare this to my guess 
of the chances it will hurt B. Since deltaB and deltaC are 
probably fairly close, and deltaA is smaller but has twice 
the utility cost associated with it, I'm pretty sure I'll 
fell safer in voting D down completely.

Note I'm working with guesses. This is an old discussion on 
this list (though we haven't really applied it to CR, just 
to Approval), but as I've said before I see nothing wrong 
with this "neural net" approach.

>>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.

I agree, if the probabilities are fuzzy enough then the best 
bet is to fall back on sincere CR. I think in public 
elections the polls will always give people enough 
knowledge, or at least make them think they have enough 
knowledge, to use the Approval-equivalent strategy. Of 
course, there are also those voters who don't have any 
notion of best strategy, and those who do but altruistically 
forgo strategy.

> 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 would think the best strategy in a poll would be to 
exagerrate ratings in the same direction as you would in the 
election, not to invert them. But it might depend on which 
group you want to win over. Maybe the Dukakis supporters in 
your example will say they like Bush, to frighten the 
Clinton supporters into adding Dukakis as an insurance vote.
But I can't say how effective that will be. Still, what 
counts is the voters' perception of who the front-runners are.

>>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

No, you missed the point. My choice of X is independent of 
what the other like-minded voters do. Let's say they've all 
made up their minds and vote full-scale (or some other 
value) for that candidate. I then start out thinking, I can 
vote X=50 (if the scale is 0 to 100). Then let's say I 
decide that X=55 will increase my utility expectation over 
X=50 by some amount, Y. If that is true, then voting X=100 
will increase my utility expectation by 10*Y. So if I gain 
by increasing my rating a little bit, I gain much more if I 
increase it to the max.

After all that, though, I have to admit that you are right 
in that a sufficient amount of doubt about the accuracy of 
the projections will cause those inclined to vote 
strategically to revert to sincere ratings. The strategic 
equivalence to Approval is true in an ideal statistical 
model but that might not always translate to reality.

Richard