Discrimination of average orientation by ideal observer

In a recent article, Allik et al (2022) reported that discrimination of the mean orientation of an ensemble of Gabor patterns can be based on generalized (or power) mean rather than simple arithmetic average. However, they did not propose any explanation of this observation. I argue that the manipulation of the proportion of informative elements (PIE) in their study can explain the observed using of power mean. When all the elements are informative, arithmetic average is an optimal decision variable. When few out of many elements are informative, averaging is not the best rule anymore. My simulations of an ideal observer for different values of PIE qualitatively predict the results from Allik et al (2022). I also show that the relatively complex ideal rules can be well approximated by more simple power mean. This analysis explains the main findings reported by Allik et al (2022) as well as usually observed arithmetic averaging when all the elements of an ensemble are equally informative.