This has to be an unambiguous decision to prevent any disagreement about consensus or state evolution.
Bitcoin, for example, is just the accumulated proof of work -- an unbiased estimator of the amount of SHA256 hashes that were computed to produce the chain. Ethereum has a similar design currently, but wants to switch to proof of stake; the algorithm here is more complicated, but basically the longest chain that has no attestations against it on a competing chain.
I can't quite tell what Libra is offering here -- I think they create a group of validators (section 9.2), and the state is the one that the most validators have cumulatively agreed upon is the current state. How validators are unambiguously identified is unclear at this point; presumably the public keys will be shipped with the client so that they are effectively public knowledge, and eventually will be proof-of-stake based, so that key pairs that hold large amounts of LibraCoin will use their key to sign the state. There seems to be very little specificity here, though.