Abstract The problem of finding a social choice function in a given space of preferences has been dominated by Arrow’s and Chichilnisky’s Impossibility Theorems. Based on previous work by Carrasquel, Lupton and Oprea, in this paper, we use tools from Algebraic Topology to introduce a notion of higher social choice complexity that determines the minimum number of local social choices that must be aggregated to cover all possible individual preferences. We prove that this invariant is bounded between two known topological invariants, the higher topological complexity and its symmetric version. This result shifts the focus onto the topological structure of the preference space when studying social choice processes.