Approximate Sorting of Preference Data

We consider sorting data in noisy conditions. Whereas sorting itself is a well studied topic, ordering items when the comparisons between objects can suffer from noise is a rarely addressed question. However, the capability of handling noisy sorting can be of a prominent importance, in particular in applications such as preference analysis. Here, orderings represent consumer preferences (“rankings”) that should be reliably computed despite the fact that individual, simple pairwise comparisons may fail. This paper derives an information theoretic method for approximate sorting. It is optimal in the sense that it extracts as much information as possible from the given observed comparison data conditioned on the noise present in the data. The method is founded on the maximum approximation capacity principle [2, 3]. All formulas are provided together with experimental evidence demonstrating the validity of the new method and its superior rank prediction capability.