Decision Making, Feedback, and a Network View

[By Thomas Saaty]

In sports team A beats team B, team B beats team C but team C beats team A. Does team A beat team C or C beat A? An individual prefers apples to oranges and oranges to bananas, but at the store he buys more bananas than apples, does he really prefer apples absolutely to bananas or with some hesitation, and why does he buy so many bananas then? Our logic requires categorical answers of yes or no to these questions.

These examples show that things happen or are preferred with variable intensity and do not have categorical yes or no answers. What must we do to allow for such apparent contradictions to our logical cannons that would allow for circulatory reasoning as in the sports example rather than ban it from our logic? Because such events and preferences occur with varied intensities, we must use numbers to indicate how strong they are and those numbers must provide a faithful representation of what happens in the real world and not simply be examples of garbage in garbage out processing of information.

With numbers we can accumulate intensities and then it would make sense to determine how strongly one thing dominates another with respect to a certain occurrence or property. If it turns out that we can understand the world better with such a representation because it allows for circularity then we need to explore how it can be done and how much of an improvement we get from its outcome in the form of numbers as priorities than we currently get by using our linear yes-no logic to trace the outcome of influences. Meaning implies significance and significance implies priority and our outcomes would be on target to give us meaning for outcomes which may be circular. How can we do it and does it work?

To deal with the complexity of the real world and of the thinking mind, we must know the structure(s) of that complexity. We also need to know how to use judgments that express our understanding and even more, use them to measure the many intangibles side by side with the measurements of tangibles, to determine the importance of the influences that play a significant role in shaping complexity. Many people need to be involved in providing the judgments because often one person does not have the experience and adequate understanding to provide the judgments about all the factors that go into the process.

To develop a structure of the influences that shape complexity we identify the important sources and sinks of influences, whether they are from nature or from people with all the criteria that affect their intensity of occurrence. These structures take the form of a hierarchy with a goal at the top and alternative outcomes at the bottom, or a network with dependence and feedback. The object is to use experienced judgments to determine the priorities of the importance of the influences from which a best outcome or mix of outcomes is derived. It is done by synthesizing the priorities of the influences into a best final outcome, a process that would be extremely difficult to do by using words, language and deductive logic which is linear as relates one idea to one other idea sequentially and has no way to create priorities without operating on numerical judgments.

We have shown through many examples that for a complex problem, like the war in Iraq, logic does not lead to a single unique plausible outcome, nor do measurements of the number of months or years, people, soldiers, dollars, deaths and all other numbers that can be assembled, and finally nor do the opinions of a myriad people working individually or as a group tell us what the best way to solve this difficult problem is. But there is a tried and proven practical way to do it even if we have to involve the opinions of all the 6.8 billion inhabitants of this world and they may or may not use logic or all the known measurements. How?

The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP) provide comprehensive methods and structures for systematically improving our understanding of the gradual and finely organized influences that drive how we evaluate alternatives and make decisions. It overcomes the so called bounded rationality based on the assumption of transitivity by including in its structures and calculations, the sensitivity and depth of feelings associated with understanding and the imagination and awareness needed to address all the concerns. These processes acknowledge the inherent subjectivity in all decision making and make it explicit to the stakeholders through relative quantitative priorities.

The AHP/ANP requires that one not only follow an algorithm to put things together correctly, but even more importantly, a way to creatively construct a structure to base the algorithm on. In addition, unlike any other model in applied mathematics today, the AHP/ANP deals with intangible factors and derives measurements for them by using judgments with the participation of many people who provide the judgments individually. The AHP/ANP can combine these judgments into a single representative judgment for the group and also including the importance of the individuals themselves.