Group decision makings from partial preferences

Abstract

Group decision making is the situation that a group of agents makes collective choices over a set of alternatives. The input of group decision making is the partial preferences of agents, and its output is one (or more) candidates. This thesis focuses on a two-step (\emph{Preference learning} and \emph{rank aggregations}) group decision making framework. A preference learning method learns a statistical ranking model from the users' preferences, which might be partial rankings. In rank aggregations, the group decision is made according to the learned ranking model. Both preference learning and rank aggregations are highly challenging when the number of alternatives becomes large. This dissertation focuses on solving the following questions. How can we design efficient preference learning algorithms when the preferences are partial rankings? How can we design rank aggregation rules with privacy guarantees? The first part of this dissertation focuses on preference learning. We propose two preference learning algorithms, both compatible with partial preferences. Our main theoretical contributions are the complexity analysis of the proposed preference learning algorithms, which guarantees that all our proposed preference learning algorithms can finish in polynomial (or sub-polynomial) time. The experiments confirm that our algorithms are robust, efficient, and practical. Furthermore, this dissertation proposes a group of rank aggregation methods with privacy guarantees. We found Differential privacy (DP), a widely accepted notion of privacy, is unsuitable in many rank aggregation scenarios because it requires external noises. Thus, we proposed a novel privacy notion, smoothed DP, for rank aggregations. The smoothed DP notion can achieve a similar privacy guarantee with DP without requiring external noises. We theoretically proved and experimentally confirmed that most real-world elections are private under the smoothed DP notion. Finally, we apply the private group decision making framework to a downstream application, improving the robustness of interpretation maps. Interpretation maps explain the reason of why deep neural networks output a certain classification and can be used in the application scenarios like objective detection, medical recommendation, and transfer learning. Inspired by rank aggregation, we proposed the first interpretation method with theoretically guaranteed robustness against l_∞-norm attacks. The proposed method is not only ~30% more robust but also surprisingly more accurate than state of the art according to an experiment on real-world datasets.