  While the terms "redundancy" and "consensus" are often used as synonyms in
the context of quantum objectivity, we show here that these should be
understood as two related but distinct notions, that quantify different
features of the quantum-to-classical transition. We show that the two main
frameworks used to measure quantum objectivity, namely spectrum broadcast
structure and quantum Darwinism, are best suited to quantify redundancy and
consensus, respectively. Furthermore, by analyzing explicit examples of states
with nonlocally encoded information, we highlight the potentially stark
difference between the degrees of redundancy and consensus. In particular, this
causes a break in the hierarchical relations between spectrum broadcast
structure and quantum Darwinism. Our framework provides a new perspective to
interpret known and future results in the context of quantum objectivity,
paving the way for a deeper understanding of the emergence of classicality from
the quantum realm.
