User:Louis F. Sander/Sandbox

Sections

• Lead/Introduction
• Where it is used
• How it works
• Criticisms (keep it short and objective)

Notes

Aspects of AHP

• Math
• Psychological
• Computerized now, with gadgets
• Disciplined look at a decision (focus on objectives, alternatives, more than voting)
• Handles rational, intuitive, irrational, all at the same time
• Lets you compare the alternatives and fiddle with them, vs. just giving the best one

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and has been successfully applied to many complex planning, resource allocation, and priority setting problems

Good Stuff

Problems with high stakes, involving human perceptions and judgements, and whose resolutions have long-term repercussions, call for a rational approach to their solution. (Bhushan promo)

You might also want to read the paper "The Analytic Hierarchy Process - An Exposition," E.J. Forman and S. I. Gass, Operations Research, 49, 4, July-August, 2001, pp. 469-486. (Saul Gass, U of MD)

Pairwise Comparisons

In AHP, we rank a group of items by comparing them to each other in pairs. AHP's mathematics converts our comparisons into numerical weights for each member of the group, and gives us feedback on the consistency of our comparisons.

For each pair, we express the importance of (or our preference for, etc.) one item versus the other by assigning it a weight from -9 to +9. To facilitate the assignment of numbers, we can use a verbal scale going from "Much Less Important" to "Moderately Less Important" to "Of Equal Importance," etc, up to "Much More Important."

When we have finished all the comparisons, AHP's mathematical processing evaluates them and assigns each item a numerical weight. The higher the number, the more important (or preferred, etc.) to us is the item to which it is assigned. For convenience, the numbers are normalized so their total is 100 (or, sometimes, 1). The processing also gives a numeric indicator of the consistency of our rankings.

To illustrate the power of this technique, imagine that we would like to know how important each of these is to us in a prospective mate: Brains, Looks, Personality, and Wealth. If we compare the factors two by two, AHP can use our comparisons to assign a numerical weight to each of them.

You can try it on THIS WEB SITE from the Canadian Conservation Institute. Here's what to do after opening the site:

1. On the first screen, enter the number 4, to specify how many criteria you will be comparing.
2. Click Continue, then enter the names of the criteria: Brains, Looks, Personality, and Wealth. (To facilitate our discussion, enter them in this order. Other than for that purpose, the order doesn't matter.)
3. Scroll down and select the Line-by-Line Method to facilitate entering the data.
4. Click Continue and begin your pairwise comparisons. (Note the bar chart showing that right now, all the criteria have equal importance.)
5. For each of the six pairs of items, compare the first to the second by entering a number between -9 and 9. Use the verbal scale to help you choose each number. (Example: If Brains are a little less important than Looks, enter a -3 for this pair. If Brains are very much more important, enter a 9.)
6. Click Calculate to see the results of your comparisons. The higher the number assigned to each criterion, the more important it is to you.
7. The Consistency Ratio is a measurement of the consistency of the data you entered. The higher it is, the less consistent were your entries. If it is greater than 0.100 or so, you might want to review your entries to see if they really reflect your thinking. (Don't worry too much about minor inconsistencies -- inconsistency is a part of human nature, and we are dealing fairly closely with human nature here.)

The example web site allows for easy modification of your judgments, and it can be instructive to change them and see how the changes affect the outcome. If you'd like to experiment a bit, enter a new problem with only three criteria: Brains, Looks, and Personality. Imagine that Brains are quite important to you, and that Looks and Personality are equally important, but moderately less important than Brains. You can indicate this by entering 5, 1, and 1 for the pairwise comparisons. The results will show your preference for brains, and will be perfectly consistent. If you modify your entries to show different preferences, you will be able to see how the modifications alter your results.