### In the Discrete Case, Averaging Cannot Be Consistent

O. Kosheleva, V. Kreinovich
2018 №1(41) (2017)
When we have two estimates of the same quantity, it is desirable to combine them into a single more accurate estimate. In the usual case of continuous quantities, a natural idea is to take the arithmetic average of the two estimates. If we have four estimates, then we can divide them into two pairs, average each pair, and then average the resulting averages. Arithmetic average is {\em consistent} in the sense that the result does not depend on how we divide the original four estimates into two
more » ... estimates into two pairs. For discrete quantities - e.g., quantities described by integers - the arithmetic average of two integers is not always an integer. In this case, we need to select one of the two integers closest to the average. In this paper, we show that no matter how we select - even if we allow probabilistic selection - the resulting averaging cannot be always consistent.