The order of the input information plays a very important role in a distributed information processing system (DIPS). This paper proposes a novel data sorting mechanism named the ε-differential agreement (EDA) that can support parallel data sorting. EDA adopts the collaborative consensus mechanism which is different from the traditional consensus mechanisms using the competition mechanism, such as PoS, PoW, etc. In the system that employs the EDA mechanism, all participants work together to compute the order of the input information by using statistical and probability principles on a proportion of participants. Preliminary results show variable fault-tolerant rates and consensus delay for systems that have different configurations when reaching consensus, thus it suggests that it is possible to use EDA in a system and customize these parameters based on different requirements. With the unique mechanism, EDA can be used in DIPS of multi-center decision cluster, not just the rotating center decision cluster.