Three-way Preference Completion via Preference Graph

With the personal partial rankings from agents over a subset of alternatives, the goal of preference completion is to infer the agent’s personalized preference over all alternatives including those the agent has not yet handled from uncertain preference of third parties. By combining the partial rankings of the target agent and the partial rankings from third parties to settle some disagreement with three-way preference completion, which includes a general strategy, an optimal strategy, and a pessimistic strategy, it forms the weighted preference graph. Technically, to settle the disagreement and obtain the completed preference of the target agent in the weighted preference graph, maximum likelihood estimation (MLE) under Mallows is proposed and validated theoretically by removing edges with the minimum weight in the weighted preference graph. However, it is not easy to locate the edges with the minimum weight efficiently in a big graph. Hence, an optimal MLE algorithm and three greedy MLE algorithms are proposed to process the MLE. Furthermore, these proposed algorithms are experimentally validated and compared with each other by both the synthetic dataset and the Flixter dataset.