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In peer-to-peer (P2P) applications like computer supported cooperative work (CSCW), multiple peer processes are required to cooperate to make a global decision, e.g. fix a meeting schedule of multiple persons. We discuss how multiple peer processes make a decision to achieve some objectives in a peer-to-peer (P2P) overlay network. Here, every process is assumed to be peer and autonomous. That is, there is no centralized coordination. A domain of a process is a collection of possible values which the process can take. Each process first takes a value v in its domain and notifies the other processes of the value v. A process can change the value with another value on receipt of values from other processes. However, a process can take only some value depending on the value v. For example, a process may abort after notifying commit but cannot commit after notifying abort in the commitment control. An existentially (E)-precedent relation shows what values a process can take after taking a value. In addition, a process takes a more preferable value if the process can take one of multiple values. Thus, values are ordered in the preferentially (P)-precedent relation. Based on the E- and P- precedent relations, each process takes the most preferable one in the values which can be changed from the current value v. In this paper, we discuss how every process makes an agreement on a value while each process can change the value according to the relations. In this paper, we discuss a coordination protocol in a type of heterogeneous system where every pair of processes have different E-precedent relation and P-precedent relation on the same domain. Each process learns a part of the precedent relations of another process through exchanging values.