We develop a stochastic model to rank different policies (tax, fixed cap and relative cap) according to their expected total social costs. Three types of uncertainties are taken into account: uncertainty about abatement costs, business-as-usual (BAU) emissions and future economic output (the two latter being correlated). Two parameters: the ratio of slopes of marginal benefits and marginal costs, and the above-mentioned correlation, are crucial to determine which instrument is preferred. When marginal benefits are relatively flatter than marginal costs, prices are preferred over fixed caps (Weitzman's result). When the former correlation is higher than a parameter- dependent threshold, relative caps are preferred to fixed caps. An intermediate condition is found to compare the tax instrument and the relative cap. The model is then empirically tested for seven different regions (China, the United States, Europe, India, Russia, Brazil and Japan). We find that tax is preferred to caps (absolute or relative) in all cases, and that relative caps are preferred to fixed caps in the US and emerging countries (except Brazil where it is ambiguous), whereas fixed cap are preferred to relative cap in Europe and Japan.