Multi-criteria decision analysis with pairwise criteria preference inference.
The boat paint comparison presented here is a decision problem in 7 dimensions (the criteria Price,
Performance, Human Hazard, Biocide Exposure, Environment, Boatyard CoCs, and VOC Exposure). The model we use
is a simple linear utility aggregation model.
To understand the model, look at its 3 main parts:
- For each dimension, each product's data is converted to a utility score between 0 and 100 (100 being the
- The user makes pairwise comparisons of the dimensions. The pairwise information is used to compute
weights for each of the dimensions (the higher the weight, the more relevant the dimension).
- For each product, the product utilities are summed up across the 7 dimensions, weighted by the
dimensional weights computed in the previous step.
This leads to the products' final utility scores (out of 100) that are used for the product ranking on the
Except for the performance dimension, the smaller the raw data, the better. For example, smaller biocide
exposure is better than larger biocide exposure. In each of these categories, the worst input data (i.e. the
largest) is assigned a utility of 1. The value 0 receives a utility of 100. Between 0 and the worst value, we
use a linear map from raw data to utilities. The only exception is the performance dimension. Here, a score of
0 has utility 0, a score of 5 has utility 100, and everything in between is mapped linearly.
Each of the pairwise comparison sliders allows the user to specify that one dimension is more important than
the other by a factor of up to 8. These inputs are then combined with the existing setting (starting from a
uniform prior) by computing the closest consistent set of dimension weights (computing the eigenvalues of the
linear problem). Using pairwise comparisons to come up with weights is part of a method known as the Analytic
Hierarchy Process. You can find some more information on that process here.
In the last step, the products' dimensional utilities are combined into a total product utility by using the
weights obtained in the last step. This is just a simple weighted sum. The higher the total utility, the
better. So we use the total product utility to rank the products according based on your specified preferences
among the criteria.