Egalitarians think that equality in the distribution of goods somehow matters. But what exactly is egalitarianism? This article argues for a characterization based on novel principles essentially involving risk. The characterization is used to resolve disputed questions about egalitarianism, such as its compatibility with strong separability and its relation to other distributive theories. But egalitarianism is subject to a particularly severe form of the levelling down objection, and is claimed to be false. (Paper can be obtained by emailing the author.)