 Another prominent class of aggregation rules violating independence is given by the distance-based rules (Pigozzi 2006, building on Konieczny and Pino Pérez 2002; Miller and Osherson 2009). A distance-based rule is defined in terms of some distance metric between judgment sets, for example the Hamming distance, where, for any two judgment sets \(J\), \(J' \subseteq X\), \(d(J, J') = |\{p \in X : \text{ not } [p \in J \Leftrightarrow p \in J']\}|.\) Each profile \(\langle J_1, J_2 , \ldots ,J_n\rangle\) is mapped to a consistent and complete judgment set \(J\) that minimizes the sum-total distance from each of the \(J_i\)s. (As an aside: applied to the preference agenda, the Hamming-distanced-based rule becomes equivalent to the ‘Kemeny rule’, already briefly mentioned earlier.) Distance-based rules can be interpreted as capturing the idea of identifying compromise judgments. Unlike premise-based or sequential priority rules, they do not require a distinction between premises and conclusions or any other order of priority among the propositions.