People like to talk about avoiding bias. Witness the large literature on cognitive bias, the blog Overcoming Bias, Less Wrong’s front page, etc.

Reducing bias is useful. But why don’t people care as much about variance?

Variance is another way you can be wrong. If you’re making predictions, bias is the *predictable* way in which you’re wrong—perhaps you always think things will take less time than they actually do. On the other hand, variance is the *unpredictable* component of how you’re wrong: perhaps your time estimates are typically off by 50%, but equally split between too high and too low. In statistics, the *total error* of an estimator (its squared distance from the true value) is equal to its variance plus the square of its bias.

In statistics we have the idea of a *bias-variance tradeoff*: when you’re comparing estimators of the same quantity, you often can choose between one with lower bias, and one with lower variance. One intuition for this is that you can take a biased estimator and make it unbiased by subtracting an estimate of the bias—but if your estimate of the bias is incorrect, then that incorrectness gets added to the original estimator’s variance, so you end up with a higher-variance estimator. Often, in fact, the high-variance estimator will have worse overall error.

If you have a way of getting a lot of independent estimates, then you don’t care about high variance—you can just get more estimates and take the average of all of them to reduce the variance. But if all you have is a single estimate, then variance can be just as much of a problem as bias, if not more.

Similarly, in real life, simply noting that you have some cognitive bias isn’t enough. First of all, to even think about compensating for your bias, you need to know not just *that* you are biased, but *how much* so. Then, you need to know that you’re not just trading bias for variance. That means that the naive strategies for “overcoming cognitive bias” can be ineffective or even harmful.

For instance, to avoid anchoring bias when guessing a number, you might try to “shade up” your estimate when you think you’ve been anchored downwards. But your susceptibility to anchoring probably varies by time and by what you’re estimating, and the magnitude of anchoring bias is not well-understood (as far as I know), so this will probably introduce a lot of extra variance into your guess. Without doing the experiments, it’s not clear to me whether it’s worth it to do this kind of compensatory de-biasing. Of course, the situation is even worse for less-easily-measured biases like confirmation bias or self-serving bias.

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