Nowadays, using the consensus of collectives for solving problems plays an
essential role in our lives. The rapid development of information technology
has facilitated the collection of distributed knowledge from autonomous
sources to find solutions to problems. Consequently, the size of collectives
has increased rapidly. Determining consensus for a large collective is very
time-consuming and expensive. Thus, this study proposes a vertical partition
method (VPM) to find consensus in large collectives. In the VPM, the primary
collective is first vertically partitioned into small parts. Then, a
consensus-based algorithm is used to determine the consensus for each smaller
part. Finally, the consensus of the collective is determined based on the
consensuses of the smaller parts. The study demonstrates, both theoretically
and experimentally, that the computational complexity of the VPM is lower
than 57.1% that of the basic consensus method. This ratio reduces quickly if
the number of smaller parts reduces.