[EM] Strategic voting in ratings

[Richard Moore]

Roy wrote:
> Richard Moore <rmoore4 at h...> wrote:
> 
>>	deltaEU = X*( 100*deltaPa + 50*deltaPb )
>>...
>>Consider that if
>>100*deltaPa + 50*deltaPb is positive, you will get a
>>positive strategic benefit ...
>>maximized if X is set to the full-scale positive 
>>rating. On the other hand, if the value in parentheses is 
>>negative, ...you would want to minimize the negative impact by 
>>voting B at the lowest end of the scale.
>>
> 
> So we'd have to know deltaPa and deltaPb to know how to vote 
> strategically, or at least know whether the magnitude of dPb is > 
> twice dPa. I presume that if dPb = -2dPa, we vote sincerely.

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.

> Strategic voting (at least, among non-statisticians) is based on a 
> perceived runoff: a sense that the race is really between (or among) 
> a subset of the candidates. When voters have that perception, they 
> will normalize their votes for those who are. Granted. I don't think 
> that necessitates degenerating completely to Approval. Those who 
> aren't considered in the race would still be voted sincerely (to 
> scale).

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. True, if the probabilities 
aren't that clear I will probably vote intermediate ratings
for some of the middle candidates.

> Your example seems to ignore deltaPc, which has positive utility to 
> the voter. Is that because the support for C is zero?

No, it isn't ignored, it's just hidden within a system of 
simultaneous relationships. Remember that

	deltaPa + deltaPb + deltaPc = 0

so if we can write

	deltaPb > -2*deltaPa

we can also write

	- deltaPc - deltaPa > -2*deltaPa

which is the same as

	deltaPc < deltaPa.

So another way of stating the strategy is that if deltaPc is 
less (more negative) than deltaPa, we should vote B up. This 
is pretty intuitive, actually: If B is rated halfway between 
A and C and voting for B hurts C more than it hurts A, vote 
for B.

>  I'm not sure
> that multiplication can properly be applied to utility. Is a utility 
> of 1 really infinitely more -- um, utilitous than a utility of zero? 

Not sure what you're asking. The multiplications I was doing 
  were to get a statistically expected value of the utility 
of the outcome. It's simply a matter of summing the products 
of the probabilities of each outcome and the utilities of 
each outcome. To get a differential of the expected value, 
use the probability differentials instead of absolute 
probabilities (the utilities are constants).

> The other thing your example ignores is group dynamics: when a lot of 
> people are in the same situation, they will have similar decisions to 
> make, and a lot of them will choose similarly. Hence, the linearity 
> in X is questionable, because the population might effectively be 
> made small by a lot of people acting as one. (cf Goedel, Escher, Bach)

But each person's decision on X is still independent from 
everyone else's. 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 but it doesn't affect the proportional nature of 
your expected utility's response to your personal choice of 
X. If you change X by some amount (say, based on a roll of 
dice) the group dynamics won't amplify your random perturbation.

Richard