Quantifying Bias and Variance of System Rankings

When used to assess the accuracy of system rankings, Kendall's tau and other rank correlation measures conflate bias and variance as sources of error. We derive from tau a distance between rankings in Euclidean space, from which we can determine the magnitude of bias, variance, and error. Using bootstrap estimation, we show that shallow pooling has substantially higher bias and insubstantially lower variance than probability-proportional-to-size sampling, coupled with the recently released dynAP estimator.