We propose a new pairwise Fermi updating rule by considering a social average payoff when an agent copies a neighbor's strategy. In the update rule, a focal agent compares her payoff with the social average payoff of the same strategy that her pairwise opponent has. This concept might be justified by the fact that people reference global and, somehow, statistical information, not local information when imitating social behaviors. We presume several possible ways for the social average. Simulation results prove that the social average of some limited agents realizes more significant cooperation than that of the entire population.