The global psychophysical theory of summation and magnitude production of R. D. Luce (2002) had joint presentations of pairs of intensities (measured above threshold) being matched asymmetrically, with 1 component being 0 intensity and the other the matching intensity. For loudness, an intensity pair to the 2 ears is matched by an intensity in just 1 ear. Realizing this experimentally has been difficult, and so, this article extends the theory to the use of symmetric matches with the same intensity being used in both components. In addition, the representational aspect is much improved; a new formulation of the results of the earlier theory is presented; the theory for symmetric matches is outlined; and it is shown that if 1 form of segregation, right or left, holds for asymmetric matches and 1 for symmetric ones, then all forms of segregation hold.