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.
翻译：在众所周知的稳定匹配问题中,有两组M和W代理,而M成员只对W成员有偏好,反之亦然。通常假定M和W的每个成员都是单一实体。然而,在许多情况下,M或W的每个成员代表一个由若干具有共同利益的个人组成的团队。例如,学生可能需要与教授匹配,但每个项目都由一组学生执行。因此,学生先组成团队,而学生和教授之间的匹配则是一组。当一个团队被视为来自M或W的代理时,它需要有一个代表该团队的偏好顺序。表决规则是将小组成员的偏好集中到一个单一偏好顺序的自然机制。在本文中,我们从团队稳定匹配的角度来调查战略投票问题。具体地说,我们假设每个团队的成员使用博尔达规则来创造团队的偏好秩序。然后,Gale-Shaply算法用于寻找一个稳定的匹配,而该团队则需要有一个代表该团队的偏好组合的偏好组合。当我们提出操纵的时候,我们展示一个单一的逻辑,在团队中可以从团队中找到一个解时,当M和M在团队之间的时候,当我们从团队中可以从中间进行操纵的时候,我们展示一个单一的计算的时候,我们可以展示一个单一的逻辑时, 当它从团队的时候, 当它从一个解时, 当我们可以从团队的时候可以展示一个单一的排列的时候可以从一个单一的排列。
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