On Calibration Error of Randomized Forecasting Algorithms

Recently, it was shown that calibration with an error less than δ > 0 is almost surely guaranteed with a randomized forecasting algorithm, where forecasts are chosen using randomized rounding up to δ of deterministic forecasts. We show that this error can not be improved for a large majority of sequences generated by a probabilistic algorithm: we prove that combining outcomes of coin-tossing and a transducer algorithm, it is possible to effectively generate with probability close to one a sequence “resistant” to any randomized rounding forecasting with an error much smaller than δ.