Byteball data is stored and ordered using directed acyclic graph (https://en.wikipedia.org/wiki/Directed_acyclic_graph) (DAG) rather than blockchain. This allows all users to secure each other's data by referencing earlier data units created by other users, and also removes scalability limits common for blockchains, such as blocksize issue.
The consensus algorithm used to protect from double-spends is based on establishing a total order within the DAG. This is achieved by selecting a chain, called main chain, which gravitates towards units issued by commonly recognized reputable users — witnesses. See the white paper for details: https://byteball.org/Byteball.pdf