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Opinion dynamics, aiming to understand the evolution of collective behavior through various interaction mechanisms of opinions, represents one of the most challenges in natural and social science. To elucidate this issue clearly, binary opinion model becomes a useful framework, where agents can take an independent opinion. Inspired by the realistic observations, here we propose two basic interaction mechanisms of binary opinion model: one is the so-called BSO model in which players benefit from holding the same opinion; the other is called BDO model in which players benefit from taking different opinions. In terms of these two basic models, the synthetical effect of opinion preference and equivocators on the evolution of binary opinion is studied under the framework of evolutionary game theory (EGT), where the replicator equation (RE) is employed to mimick the evolution of opinions. By means of numerous simulations, we show the theoretical equilibrium states of binary opinion dynamics, and mathematically analyze the stability of each equilibrium state as well., Comment: 15 pages, 6 figures