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We prove that, for any given set of networks satisfying suitable conditions,the net-oudegree network solution, the net-indegree network solution, and thetotal network solution are the unique network solutions on that set satisfyingneutrality, consistency and cancellation. The generality of the result obtainedallows to get an analogous result for social choice correspondences: for anygiven set of preference profiles satisfying suitable conditions, thenet-oudegree social choice correspondence, the net-indegree social choicecorrespondence and the total social choice correspondence are the unique socialchoice correspondences on that set satisfying neutrality, consistency andcancellation. Using the notable fact that several well-known voting rulescoincide with the restriction of net-oudegree social choice correspondence toappropriate sets of preference profiles, we are able to deduce a variety of newand known characterization theorems for the Borda rule, the Partial Borda rule,the Averaged Borda rule, the Approval Voting, the Plurality rule and theanti-Plurality rule, among which Young's characterization of the Borda rule andFishburn's characterization of the Approval Voting.

A generalization to networks of Young's characterization of the Borda rule