In your model of why to assume centrists are less biased: aren’t you assuming that the truth tends to be in the center of the spectrum? If we knew where the truth lay, there would be no point in studying which side is more biased or better rationalists. Right?
I think it depends on what we mean by assuming the truth is in the center of the spectrum. In the model at the end, we assume is at the extreme left of the initial distribution—i.e. µ=40, while everyone’s estimates are higher than 40. Even then, we end up with a spread where those who end up in the middle (ish—not exactly the middle) are both more accurate and less biased.
What we do need is that wherever the truth is, people will end up being on either side of it. Obviously in some cases that won’t hold. But in many cases it will—it’s basically inevitable if people’s estimates are subject to noise and people’s priors aren’t in the completely wrong region of logical space.
In your model of why to assume centrists are less biased: aren’t you assuming that the truth tends to be in the center of the spectrum? If we knew where the truth lay, there would be no point in studying which side is more biased or better rationalists. Right?
I think it depends on what we mean by assuming the truth is in the center of the spectrum. In the model at the end, we assume is at the extreme left of the initial distribution—i.e. µ=40, while everyone’s estimates are higher than 40. Even then, we end up with a spread where those who end up in the middle (ish—not exactly the middle) are both more accurate and less biased.
What we do need is that wherever the truth is, people will end up being on either side of it. Obviously in some cases that won’t hold. But in many cases it will—it’s basically inevitable if people’s estimates are subject to noise and people’s priors aren’t in the completely wrong region of logical space.