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While most vendors who utilize recommender systems rely exclusively on training data consisting of past transactions that took place through them, it would be beneficial to base recommendations on the rating data of more than one vendor. However, enlarging the training data by means of sharing information between different vendors may jeopardize the privacy of users. We devise here secure multi-party protocols that enable the practice of Collaborative Filtering (CF) in a manner that preserves the privacy of the vendors and users. Shmueli and Tassa [\n            <jats:xref ref-type=\"bibr\">38<\/jats:xref>\n            ] introduced privacy-preserving protocols of CF that involved a mediator; namely, an external entity that assists in performing the computations. They demonstrated the significant advantages of mediation in that context. We take here the mediation approach into the next level by using several independent mediators. Such distributed mediation maintains all of the advantages that were identified by Shmueli and Tassa, and offers additional ones, in comparison with the single-mediator protocols: stronger security and dramatically shorter runtimes. In addition, while all prior art assumed limited and unrealistic settings, in which each user can purchase any given item through only one vendor, we consider here a general and more realistic setting, which encompasses all previously considered settings, where users can choose between different competing vendors. We demonstrate the appealing performance of our protocols through extensive experimentation.\n          <\/jats:p>","DOI":"10.1145\/3542950","type":"journal-article","created":{"date-parts":[[2022,6,6]],"date-time":"2022-06-06T09:57:53Z","timestamp":1654509473000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Privacy-preserving Collaborative Filtering by Distributed Mediation"],"prefix":"10.1145","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9681-8824","authenticated-orcid":false,"given":"Tamir","family":"Tassa","sequence":"first","affiliation":[{"name":"The Open University, Raanana"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3836-5286","authenticated-orcid":false,"given":"Alon Ben","family":"Horin","sequence":"additional","affiliation":[{"name":"The Open University, Raanana"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2022,9,22]]},"reference":[{"key":"e_1_3_3_2_2","first-page":"273","volume-title":"Proceedings of the IAS","author":"Ahmad Waseem","year":"2007","unstructured":"Waseem Ahmad and Ashfaq A. 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