Group Recommendation Systems (GRS) aim at recommending items that are relevant for the joint interest of a group of users. Voting mechanisms assume that users rate all items in order to identify an item that suits the preferences of all group members. This assumption is not feasible in sparse rating scenarios which are common in the recommender systems domain. In this paper we examine an application of voting theory to GRS. We propose a method to accurately determine the winning item while using a minimal set of the group members ratings, assuming that the recommender system has probabilistic knowledge about the distribution of users' ratings of items in the system. Since computing the optimal minimal set of ratings is computationally intractable, we propose two heuristic algorithms that proceed iteratively that aiming atto minimizing the number of required ratings, until identifying a "winning item". Experiments with the Netflix data show that the proposed algorithms reduce the required number of ratings for identifying the "winning item" by more than 50%.