Main ideas behind OWA lead to a universal and optimal approximation scheme

In the arithmetic average, we combine all the estimates with equal weights. In some practical situations, it makes sense to give move weight to consistent estimates and less weight to estimates that axe far away from the consensus of the majority. Ordered weighted averaging (OWA) operators have been successfully applied in many practical problems. We explain this empirical success by showing that these operators are indeed guaranteed to work (i.e. universal), and that these operators are the best to use (in some reasonable sense).