The discussion here clearly indicates that each of us is using the term slightly differently. When I think of bias, I think of it as something closer to the statistical, whereas my reading of Eliezer’s comments is that he thinks of cognitive bias as something that is relatively unconscious and that cannot be useful in the sense of leading to true beliefs.

Is there a better term than ‘”useful bias” for the idea of adding a large error in a known direction to reduce the possibility of small (or in the case of alcoholism large) errors in an unknown direction?

a. Sometimes, rationality and correct perception of reality isn’t the best way to accomplish a goal. Evolution has outfitted us with biases that probably are based on this fact. For whatever reasons, it paid off historically for, say, parents to perceive their kids as prettier and smarter and nicer than they really were. So we have this bias which was adaptive in some environment. I take Hal Finney’s alcoholism example this way–even if each social drinking event has only a low probability of leading the alcoholic back into disaster, it may be more adaptive for him to believe that a single drink is death.

b. Sometimes, we use mental modules in our own minds, or the minds of other people, as tools. Then, it’s often easier to introduce an intentional bias in the perceived or claimed facts input into the module than to redesign it. A nice example of this is leading the target when you’re shooting. Instead of reprogramming your mind to calculate the path of the bullet and the bird, you just lead the bird by a certain amount. I think this is the set into which the original example falls. There are all kinds of similar tricks, right? How many of us set a clock ahead 10 minutes to help ourselves get out the door on time? We’re lying to some module or part of our brain, in order to get it to function better.

http://en.wikipedia.org/wiki/Bias_of_an_estimator

Are there perhaps analogies with beliefs?

That is one way to think of the alcoholism situation. Alcoholics who had an unbiased view of the possibilities of safe social drinking might imbibe to an unhealthy degree, because they would overestimate the short-term pleasures of social drinking relative to the long-term harm of relapsing into alcoholism. By adopting the biased view that no amount of social drinking is safe, they avoid falling into the trap induced by the other bias which over-weights short term pleasures compared to long-term harm.

Please note: decisions and beliefs are not the same thing. The artillery officer who overshoots knows that he is overshooting – he does not have a mistaken, non-veridical, false belief. Instead he makes a decision, as a matter of calculated utility, to shoot higher than he believes will hit the target. Since this whole method relies on knowing – having veridical beliefs – about the direction in which your action overshoots the target, it would be calamitous indeed were the artillery officer to actually bias his beliefs.