The authors study a class of problems in which the characteristics of the objects in the frame of discernment U=(u/sub 1/,. . ., u/sub n/) are represented probabilistically. A hypothesis is defined by attributes A/sub 1/,. . .,A/sub s/ which takes values from the sets V/sub 1/,. . .,V/sub s/, respectively. Domain information describing a hypothesis specifies the probability of each attribute A/sub i/ assuming the values from V/sub i/. The domain information concerning attribute A/sub i/ is given by a matrix. The generation of support is driven by the acquisition of evidence concerning attribute values. To compare evidential support generation a simple urn model is constructed to provide the probabilistic domain information. An attribute-value domain is constructed to provide a baseline by which to compare the support generated by an iterative updating architecture, a belief network, and the Dempster-Shafer theory of evidential reasoning.