Using Pairwise Comparison

by G. Peterson, PetersonGIS
4/29/2008, updated 5/6/2009

Creating a GIS decision model often involves weighting criteria in order to reflect their relative contribution to the model or their effect on the variable being measured. To do this, we usually start by ranking the inputs to the model in order of importance and then trying to set some weights according to our ranking. The process of choosing the ranking and weights can be decided by one person or a group of people. Essentially the process winds up being a "whoever shouts out the loudest wins" kind of thing as opposed to a disciplined scientific ranking based on facts.

Let's take a gander at a more qualitative approach, shall we? The pairwise comparison method is thoroughly explained in GIS and Multicriteria Decision Analysis but I will go over the basics here. Essentially, you take all of the model's criteria that you want to weight, put them in a matrix where they are repeated on both the horizontal and vertical axes, then fill in the cells where they meet with numbers representing their relative importance. The brilliance of this is that you are only comparing two criteria at a time instead of trying to rank the whole list at once.

For each comparison you ask yourself or your team: Is X criterion way more important relative to Y criterion, somewhat more important, or of equal importance? Now, when you run an actual pairwise comparison you will use 9 gradations of importance running the gamut from way more important to equal importance, with 1 being that the two are of equal importance and 9 being that the horizontal criterion is of extreme importance relative to the vertical criterion.

Once all of the numbers are filled in to the matrix you run a bunch of calculations on them and at the end of it all you get an ordered list of criteria with weights for each. But wait, there's more! You also get to do a test with the numbers to make sure they are significantly different from one another. If, for example, you have filled in the matrix with all the pairs being essentially equal to each other, then the test will fail. In other words, you need to have criteria that are different enough in importance to make a ranking worthwhile. Otherwise all the criteria should just go into the model without being weighted at all.

If this sounds like the path you want to follow for your next modeling endeavor, check out the Malczewski book linked above and follow his calculations. I recommend creating a spreadsheet with all the calculations in it so that you can go back and change your comparisons if you find that you need to.