Abstract. In this paper, we introduce the first protocols for multiparty, privacy-preserving, fair reconciliation of ordered sets. Our contributions are twofold. First, we show that it is possible to extend the round-based construction for fair, two-party privacy-preserving reconciliation of ordered sets to multiple parties using a multi-party privacy-preserving set intersection protocol. Second, we propose new constructions for fair, multi-party, privacy-preserving reconciliation of ordered sets based on multiset operations. We prove that all our protocols are privacy-preserving in the semi-honest model. We furthermore provide a detailed performance analysis of our new protocols and show that the constructions based on multisets generally outperform the round-based approach.