In this paper, it is discussed a framework combining traditional expected utility and weighted entropy (EU-WE)—also named mean contributive value index—which may be conceived as a decision aiding procedure, or a heuristic device generating compositional scenarios, based on information theory concepts, namely weighted entropy. New proofs concerning the maximum value of the index and the evaluation of optimal proportions are outlined, with emphasis on the optimal value of the Lagrange multiplier and its meaning. The rationale is a procedure of maximizing the combined value of a system expressed as a mosaic, denoted by characteristic values of the states and their proportions. Other perspectives of application of this EU-WE framework are suggested.