What are the trade-offs between taking a gradual or "big-bang" approach to reducing the long-run rate of inflation?

In  terms of output foregone, there is not much to choose between them. In fact, an example in the transparencies suggests that the sacrifice ratio is essentially the same whether one takes a gradual or rapid approach. So, the choice between them is largely political: can a government survive better with a protracted but mild recession, or a short but severe downturn?