Iterative Voting under Uncertainty for Group Recommender Systems Lihi Naamani-Dery, Meir Kalech, Lior Rokach, Bracha Shapira Department of Information Systems Engineering and Deutsche Telekom Laboratories, Ben-Gurion University, Israel {ln,kalech,liorrk,bshapira}@bgu.ac.il ABSTRACT 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 assump- tion 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 ac- curately 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". Ex- periments with the Netflix data show that the proposed algorithms reduce the required number of ratings for identifying the "winning item" by more than 50%. Categories and Subject Descriptors H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval General Terms Algorithms, Human Factors, Experimentation 1. INTRODUCTION Group Recommender Systems (GRS) provide recommendations for groups of users and are applicable for domains where a group of people participate in a single activity. This paper addresses the recommendation of one item, a definite "wining item" (e.g., a TV show) while assuming that the preferences for the items are not known in advance. The necessary preferences are acquired during the recommendation process. It is impractical to ask all members of the group for their pref- erences for all items. Some studies [3] deal with this challenge by computing the probabilities of the user preferences on candidate items and thus predict a probable winning item. We, on the other hand, assume that the distribution of the preferences of the users Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. RecSys2010, September 26–30, 2010, Barcelona, Spain. Copyright 2010 ACM 978-1-60558-906-0/10/09 ...$10.00. over the items is known and thus we compute the minimal set of re- quired references and query the users in order to identify a definite winning item. Unlike critique based GRS system [8], we ask the users to provide ratings of items rather than interactively critiquing critique on preferred features of the items. We propose to use a vot- ing mechanism as it allows users to rank possible items and choose a winning item that reflects their joint preferences. Specifically, we focus on Range voting in which users are asked to assign a rating within a specified range for the items. The ratings for each item are summed, and the item with the highest score is the winner. Range voting is relevant to many existing recommender systems applica- tions where users are asked to rate items within a specified range (e.g., Netflix). The voting mechanism discussed in this paper re- duces the number of user ratings required for reaching an accurate and definite recommendation. In voting theory, it is possible to determine a winner by specif- ically requesting users for certain preferences rather than for their whole set of preferences. A key question is what partial informa- tion is essential for determining a winner. To cope with this chal- lenge we assume in this paper that the recommender system has probabilistic knowledge about the distribution of the group mem- bers preferences for the candidate items. For instance, in the case of friends wishing to watch a TV show together, the distribution can be inferred by rankings of these TV shows by similar users using collaborative filtering methods as illustrated in Section 6. Computing the optimal minimal set of queries that are required to determine the winner is computationally intractable due to the combinatorial space of queries orders. Thus we propose two heuris- tic approaches to address this challenge. Both approaches proceed greedily and iteratively by querying a selected user about its rating for of a specific selected items. 2. RELATED WORK Hazon et al. [4] assume predefined probability distribution of the ratings. They show theoretical bounds for the ability to cal- culate the probability of an outcome. However, while they focus on calculating the winning probability for each item, we focus on finding the winner using a minimal amount of queries. Konczak et al. [6] address the case of partial information, where users do not set the preferences for all the items. They show how to compute the sets of possible winners and necessary winners. These sets determine which items no longer have a chance of win- ning and which are certain to win. We adopt their approach to propose a systematic preference aggregation protocol in which the users do not need to send their entire set of preferences. Walsh [9] surveys the computational complexity of possible and neces- sary winners in various voting rules. Walsh studies this problem by examining weighted or unweighted ratings and bounded or un- bounded items.