AHP (along with other multiple objective methods --discussed below) differs in a significant way from most/all other Management Science/Operations Research methods which focus on an "objective" function – singular. Taking the "best" course of action, with very few exceptions, entails multiple objectives. The choice of the 'best' course of action involves trade-offs among the multiple objectives. However, the relative importance of the objectives is subjective. Therefore, all important decisions are subjective.
As a simple word proof of why all important decisions are subjective, consider the following. Time and money (or more elaborate manifestations of time and money) are objectives in every important decision. To a young, poor person, money is likely to be more important than time. To an old, wealthy person, time is likely to be more important than money. Therefore, the relative importance of time and money is dependent on the person (subject) making the decision. There can be no data, "formula" or objective way of ascertaining the relative importance of these two objectives. It depends on the subject. AHP is unique in its ability to elicit and accurately measure (see below) the relative importance of objectives to individual decision makers, or groups of decision makers.