A Backward Strategy in a Peer-to-Peer Agreement Protocol

There are many discussions on agreement protocols of multiple peer processes (peers) where every peer just aims at agreeing on one value out of values shown by the peers. In meetings of human societies, agreement procedures are so flexible that persons can change their opinions and can use not only all-condition but also various types of agreement conditions like majority-condition. In this paper, we discuss a flexible agreement protocol of multiple peers by taking into account human behaviors. In order to model the social human behavior, we already discuss existentially and preferentially precedent relations which shows that a peer can take a value after taking the other one and prefer one value to others, respectively. If a peer autonomously takes values based on its precedent relations, the peers might not make an agreement even if there exists a satisfiable set of values. We discuss what previous values the peers can take again. In this paper, we try to find a satisfiable set named cut of previous values in a history of values which the peers have so far taken, in addition for each peer to taking a new value at each round.