Strategic Voting in the Context of Stable-Matching of Teams
Leora Schmerler, Noam Hazon, Sarit Kraus
TL;DR
The paper addresses strategic voting in stable-matching of teams where each side aggregates individual preferences via the Borda rule before running the Gale–Shapley algorithm with the proposing side $M$. It shows that single-manipulator manipulation on both the men's and women's sides is solvable in polynomial time, whereas coalitional manipulation is NP-hard; however, efficient approximation algorithms provide 1-additive and 2-additive guarantees, respectively. The authors introduce algorithms that construct manipulative votes and analyze their correctness using GS-specific lemmas and score-density arguments, including reductions from Permutation Sum to establish hardness. The results illuminate computational barriers to manipulating team-based stable matchings and offer practical approximation strategies, with potential impact on real-world team-advisor assignments and similar settings.
Abstract
In the celebrated stable-matching problem, there are two sets of agents M and W, and the members of M only have preferences over the members of W and vice versa. It is usually assumed that each member of M and W is a single entity. However, there are many cases in which each member of M or W represents a team that consists of several individuals with common interests. For example, students may need to be matched to professors for their final projects, but each project is carried out by a team of students. Thus, the students first form teams, and the matching is between teams of students and professors. When a team is considered as an agent from M or W, it needs to have a preference order that represents it. A voting rule is a natural mechanism for aggregating the preferences of the team members into a single preference order. In this paper, we investigate the problem of strategic voting in the context of stable-matching of teams. Specifically, we assume that members of each team use the Borda rule for generating the preference order of the team. Then, the Gale-Shapley algorithm is used for finding a stable-matching, where the set M is the proposing side. We show that the single-voter manipulation problem can be solved in polynomial time, both when the team is from M and when it is from W. We show that the coalitional manipulation problem is computationally hard, but it can be solved approximately both when the team is from M and when it is from W.