Monotonic relationships, in which more of one quantity would imply more of another, are found pervasively in economic analysis. Milgrom pioneered in the development of new mathematical methods for understanding monotonic relationships in economics. His work on auctions with Robert Weber introduced the concept of affiliation of random variables, to indicate systems of unknown quantities where learning that any one of them is higher than some given level would cause beliefs about others to be higher. His work with John Roberts and Chris Shannon advanced the use of supermodularity as a property of individuals' preferences that can yield general monotonicity results in economic analysis.