The price system is generally thought to be the epitome of efficiency. In some cases, however, lotteries are preferred to the market as a social decision-making system for reasons of fairness. As recent research has shown, neither procedure is always well accepted among the general population. We analyze the social acceptability of both mechanisms and apply our framework to the allocation of social burdens, namely the siting of nuclear waste facilities. Lotteries are only acceptable if they are applied to a set of efficient options. The market is accepted if the production of fairness precedes the use of prices.