The idea that equity has to do with allocating, say, income, between different actors proportionately to their inputs, deserts, or needs goes back at least to Aristotle, and has been the object of a number of modern examinations, reformulations, and refinements. We base our analysis on a partial order and are concerned with the de.nition and properties of ‘a step in the direction of more equity’ when the total to be allocated is constant. While this approach to equity seems to be novel, we obtain results that are remarkably consistent with those of earlier work.