Universal coding for distributions over co-trees

For an arbitrary ordered set, we consider the model of all distributions P for which an element which precedes another element is considered the more significant one in the sense that the implication a les b rArr P(a) ges P(b) holds. It will be shown that if the ordered set is a finite co-tree, then the universal predictor for the indicated model or, equivalently, the corresponding universal code, can be determined exactly via an algorithm of reasonably low complexity.