Deriving rankings from incomplete preference information: A comparison of different approaches

Volume-based methods for decision making under incomplete information like the SMAA family of methods provide rich probabilistic information to support decision making. However, they usually do not directly generate a unique ranking of alternatives. Methods to create such a unique ranking from incomplete preference information typically select one parameter vector, either by mathematical programming approaches or by averaging, and then apply a preference model using this parameter vector. In the present paper, we develop several models to infer a complete ranking or a complete preorder of alternatives directly from the probabilistic information provided by volume-based methods without singling out a specific parameter vector. We compare the results obtained by these models to those obtained with a single parameter approach in a computational study. Results indicate small, but significant differences in the performance of methods, as well as in the probability that additional preference information might worsen, rather than improve, the results.