Simple multi-criteria decisions are made by deriving priorities of importance for the criteria in terms of a goal and of the alternatives in terms of the criteria. Often one also considers benefits, opportunities, costs and risks and their synthesis in an overall outcome. The Analytic Hierarchy Process (AHP) with its independence assumptions, and its generalization to dependence among and within the clusters of a decision — the Analytic Network Process (ANP), are theories of prioritization and decision-making. Here we show how to derive priorities from pair-wise comparison judgments, give the fundamental scale for representing the judgments numerically and by way of validation illustrate its use with examples and then apply it to make a simple hierarchic decision in two ways: pair-wise comparisons of the alternatives and rating the alternatives with respect to an ideal. Network decisions are discussed and illustrated with market share examples. A mathematical appendix is also included.