  In this paper we will present the Multidimensional Byzantine Agreement (MBA)
Protocol, a leaderless Byzantine agreement protocol defined for complete and
synchronous networks that allows a network of nodes to reach consensus on a
vector of relevant information regarding a set of observed events.
  The consensus process is carried out in parallel on each component, and the
output is a vector whose components are either values with wide agreement in
the network (even if no individual node agrees on every value) or a special
value $\bot$ that signals irreconcilable disagreement. The MBA Protocol is
probabilistic and its execution halts with probability 1, and the number of
steps necessary to halt follows a Bernoulli-like distribution.
  The design combines a Multidimensional Graded Consensus and a
Multidimensional Binary Byzantine Agreement, the generalization to the
multidimensional case of two protocols by Micali and Feldman.
  We prove the correctness and security of the protocol assuming a synchronous
network where less than a third of the nodes are malicious.
