The mathematical programming and consensus questions to be considered have interested the two principal investigators, during their previous research efforts. Since hierarchical classification can be viewed as a problem in mathematical programming, the possibility of linearizing in such a way as to admit use of Karamarkar's algorithm will be investigated. The consensus questions to be considered arise when one is confronted with several classifications for the same collection of objects and needs to determine the agreement among them. Much of the research which will be undertaken involves Stinebrickner's s- consensus method which simultaneously produces a consensus classification and an index measuring the degree of agreement. A revised s-consensus method has been shown to satisfy three minimal and reasonable axioms which describe consensus behavior. Efforts will focus on the discovery of new methods which produce a consensus classification and index simultaneously and the discovery of new axioms which consensus methods may satisfy. Undergraduate students will be trained and collaborate in this project.//
