 Alternatives, votes, and aggregation. Let \(\mathcal{A}\) be a non-empty set of “alternatives” in the most general sense—e.g., choice alternatives, belief or judgment sets, or value assignments to options. A decision-making group selects one alternative based on the members’ votes, applying some aggregation rule \(F\) that maps each profile \((a_{1},\ldots,a_{n})\in\mathcal{A}^{n}\) of any number \(n\geq 1\) of votes to a decision \(F(a_{1},\ldots,a_{n})\in\mathcal{A}\) (or perhaps a subset \(F(a_{1} ,\ldots,a_{n})\subseteq\mathcal{A}\), to allow for indeterminate  outcomes).[21]  For example, for majority rule (assuming \(\mathcal{A}\) contains just two alternatives), \(F(a_{1},\ldots,a_{n})\) is the alternative in \(\mathcal{A}\) occurring more than \(n/2\) times among  \(a_{1},\ldots,a_{n}\).[22]