level are all equal. They are called the hierarchy's default priorities. If a fifth Criterion were added to this hierarchy, the default priority for each Criterion would be .200. If there were only two Alternatives, each would have a default priority of .500. Two additional concepts apply when a hierarchy has more than one level of criteria: local priorities and global priorities. Consider the hierarchy shown below, which has several Subcriteria under each Criterion. The local priorities, shown in gray, represent the relative weights of the nodes within a group of siblings with respect to their parent. The local priorities of each group of Criteria and their sibling Subcriteria add up to 1.000. The global priorities, shown in black, are obtained by multiplying the local priorities of the siblings by their parent's global priority. The global priorities for all the subcriteria in the level add up to 1.000. The rule is this: Within a hierarchy, the global priorities of child nodes always add up to the global priority of their parent. Within a group of children, the local priorities add up to 1.000. So far, we have looked only at default priorities. As the Analytical Hierarchy Process moves forward, the priorities will change from their default values as the decision makers input information about the importance of the various nodes. They do this by making a series of pairwise comparisons. Practical examples Experienced practitioners know that the best way to understand the AHP is to work through cases and examples. Two detailed case studies, specifically designed as in-depth teaching examples, are provided as appendices to this article: Simple step-by-step example with four Criteria and three Alternatives: Choosing a leader for an organization. More complex step-by-step example with ten Criteria/Subcriteria and six Alternatives: Buying a family car and Machinery Selection Example. Some of the books on AHP contain practical examples of its use, though they are not typically intended to be step-by-step learning aids. One of them contains a handful of expanded examples, plus about 400 AHP hierarchies briefly described and illustrated with figures. Many examples are discussed, mostly for professional audiences, in papers published by the International Symposium on the Analytic Hierarchy Process. Criticisms The AHP is included in most operations research and management science textbooks, and is taught in numerous universities; it is used extensively in organizations that have carefully investigated its theoretical underpinnings. While the general consensus is