  This paper introduces an evolutionary dynamics based on imitate the better
realization (IBR) rule. Under this rule, agents in a population game imitate
the strategy of a randomly chosen opponent whenever the opponent`s realized
payoff is higher than their own. Such behavior generates an ordinal mean
dynamics which is polynomial in strategy utilization frequencies. We
demonstrate that while the dynamics does not possess Nash stationarity or
payoff monotonicity, under it pure strategies iteratively strictly dominated by
pure strategies are eliminated and strict equilibria are locally stable. We
investigate the relationship between the dynamics based on the IBR rule and the
replicator dynamics. In trivial cases, the two dynamics are topologically
equivalent. In Rock-Paper-Scissors games we conjecture that both dynamics
exhibit the same types of behavior, but the partitions of the game set do not
coincide. In other cases, the IBR dynamics exhibits behaviors that are
impossible under the replicator dynamics.
