  Multi-agent consensus problems can often be seen as a sequence of autonomous
and independent local choices between a finite set of decision options, with
each local choice undertaken simultaneously, and with a shared goal of
achieving a global consensus state. Being able to estimate probabilities for
the different outcomes and to predict how long it takes for a consensus to be
formed, if ever, are core issues for such protocols.
  Little attention has been given to protocols in which agents can remember
past or outdated states. In this paper, we propose a framework to study what we
call \emph{memory consensus protocol}. We show that the employment of memory
allows such processes to always converge, as well as, in some scenarios, such
as cycles, converge faster. We provide a theoretical analysis of the
probability of each option eventually winning such processes based on the
initial opinions expressed by agents. Further, we perform experiments to
investigate network topologies in which agents benefit from memory on the
expected time needed for consensus.
