A "rule" is an assignment of a value to every tuple (of every size up to some bound) over a given domain. This talk is concerned with the issue of how to modify a rule to apply to the case where certain arguments are weighted to be more important than others. We give an explicit formula for incorporating weights that can be applied no matter what the underlying rule is. The formula is surprisingly simple, in that it involves far fewer terms than one might have guessed. Under certain natural assumptions, the formula gives the unique possible answer. We will focus in particular on rules that combine scores into an overall score. One application is to weighting the importance of search terms in information retrieval, such as in a search of the World-Wide Web. One other application that we will mention of particular relevance to economics is to multicriterion decision making, where the formula allows us to weight the importance of each criterion. This talk, which represents joint research with Ed Wimmers, will be completely self-contained.