Heuristics for estimating the efficiency of Reduced Ordered Binary Decision Diagrams?
There is a relation between the width of an OBDD for a function $f$ and the communication complexity of a one-way communication protocol for the best-case partition of variables for $f$ (see E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge University Press, 1997).

This is a powerful tool for proving exponential size OBDDs for various functions (together with coauthors, we used this method for proving that $\epsilon$-bipartiteness is hard for OBDDs, see here). 
Basically, if there exists an OBDD of width at most $w$ that solves $f$, then $\kappa_{best}(f) \leq \log w$.
I think this is more intuitive to think in terms of communication complexity rather than OBDD.