We investigate a renormalization group (RG) scheme for avalanche automata
introduced recently by Pietronero et al. to explain universality in self-organized
criticality models. Using a modified approach, we construct exact RG equations
Ibr a one-dimensional model whose detailed dynamics is exactly solvable. We
then investigate in detail the effect of approximations inherent in a practical
implementation of the RG translbrmation where exact dynamical inlbrmation is
unavaihtble.