 Gaussian absolute-difference expectation

For independent errors $E_1,E_2\sim N(0,{\sigma }^2)$, their difference is normal with variance $2{\sigma }^2$. Hence $\mathbb{E}|E_1-E_2|=2\sigma /\sqrt{\pi }$. To verify the constant, a standard normal variable $Z$ satisfies $\mathbb{E}|Z|=2{\int }_0^{\infty }z{e}^{-z^2/2}dz/\sqrt{2\pi }=\sqrt{2/\pi }$; multiply by $\sqrt{2}\sigma$. Thus an absolute difference of unbiased noisy ratings has a positive expectation even without a true difference.