Ranking Based on Triple Comparison

Abstract

In this paper, we are interested in deducing the order of a set of items, under certain practical constraints (e.g., difficult to rank all of them at the same time, or having noise in the ranking process), only noisy partial orders on smaller subsets with a specific cardinal of the items can be obtained. For example, 10 cyclists are going to race with speed, but the track only allows 3 of them to compete simultaneously. How to get a full rank of them if the observing outcome will always be a partial ranking?

Generally speaking, how do we congregate these noisy partial ranking results into a complete ranking, and under what condition can we guarantee the resulting ranking to be accurate? These are the questions we seek to develop understanding in this work.