Before revision:   Theoretical properties are examined and shown that this subclass improves the expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts, under mild conditions  .
After revision:  We show that a subclass of the recently developed framework of Bayesian predictive synthesis fits within this class. Theoretical properties are examined and shown that this subclass improves the expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts, under mild conditions .