The Blackwell relation defines no lattice
  Blackwell's theorem shows the equivalence of two preorders on the set of information channels. Here, we restate, and slightly generalize, his result in terms of random variables. Furthermore, we prove that the corresponding partial order is not a lattice; that is, least upper bounds and greatest lower bounds do not exist. 
Nils Bertschinger, Johannes Rauh
cs.IT math.IT math.ST stat.TH