Personal information processing not only causes negative externalities such as data security risks,but also brings positive externalities such as the realization of sharing economy in the background of big data. The causes of double externalities can be revealed by the phenomenon of "Three Paradoxes of Big Data". Based on the theory of "internalization of externalities",both the negative externalities and the positive externalities from personal information processing will be regulated if the information subject is empowered with the rights to personal information,and the data controller is empowered with the rights to big data property. However,in the background of network big data,dual externalities of personal information processing are interacted with each other and faced with some dilemmas. The theory of "mutuality of damage" in law and economics provides an economic logical explanation for regulating personal information processing behavior based on the "risk-based approach". The development of big data industry depends on the "externalization of externalities" of personal information processing to realize its sharing economy. The theory of "comedy of the commons" in law and economics provides the economic logic proof for regulating personal information processing behavior based on the "externalization of externalities" in order to meet the needs of big data industry development. For the regulation of personal information processing in the background of big data,we should enforce the transformation from the "repressive law" to the "responsive law" on ideas,the coexistence of both the "internalization of externalities" and the "externalization of externalities" on mechanisms,the coordination of both the data resources rights allocation and the digital technology power intervention on measures,so that the organic balance between big data industry innovation and personal information security can be achieved.