Nowadays, we have seen a growing number of networks where nodes are connected to each other through different types of relationships. This makes identification of their topological structure and key elements both important and problematic. In this paper we propose a novel model for influence assessment in such networks using social choice rules. We evaluate node-to-node influence for each layer of the network and consider the problem of influence estimation as a problem of social choice or multi-criteria decision-making. We present various solutions that allow to aggregate information about node-to-node influence into a single vector representing the ranking of nodes or the ranking of the strongest connections in a network. Our approach takes into account individual attributes of nodes, the possibility of their group influence as well as their indirect connections. The presented model is mostly designed networks where there is no clear dependency among the layers. To present our approach we analyze the global trade food network with respect to three main products in order to identify the most important players in the field of food security.