Collective decision-making is ubiquitous across the living world and artificial societies. Individuals often choose an option based on intrinsic values of options. However, individual decision-making is also swayed by neighbors' choices, generating local social influence. Hence, an important question arises naturally, yet remains unanswered: when such social influence is integrated into the individual evaluation process for option choices, how does it affect collective decision-making outcomes in structured populations modeled by graphs. To address this, we consider a baseline model of binary options with social influence and assume that individuals not only evaluate the intrinsic values of options, but are also influenced by their neighbors' choices. We propose a perceived utility function integrating these two aspects for individual decision-making. By means of theoretical analysis, we first derive the average frequency of an option on static weighted connected graphs and present the mathematical condition under which this option prevails in the population. We find that the introduction of social influence can amplify the advantage of a superior option or compensate for the deficiency of an inferior one. We also reveal that the average degree of network exerts a dual effect on collective decision outcomes. Furthermore, we consider our evolutionary model on dynamic networks switching among distinct graph configurations. Our theoretical analysis shows that the evolutionary outcomes depend not only on the average degree of each network configuration, but also on its expected duration. We perform computer simulations to verify our theoretical predictions on static and dynamic networks.

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