Paxos is a consensus protocol. It requires a quorum (more than half) of the nodes to agree on something before it's "true". read more
Gossip protocol works beautifully in a decentralized network of nodes. It is a decentralized way of information exchange. Rules can be built on these nodes to determine the truthfulness of an information. read more
The blockchain protocol employs communication only once and only in one way, from the leader to the participants, and this corresponds to the phase 2a of Paxos: the Accept message Phase. Since the blockchain consensus protocol skips Phase 2b and Phase 3, it provides unavoidably a probabilistic consensus. read more