From Incomplete Preferences to Ranking via Optimization

We consider methods for aggregating preferences that are base d on the resolution of discrete optimization problems. For a review and references see Cook and Kress (1992), and Belkin and Levin (1990), and also David (1988) and Van B lokland-Vogelesang (1991). Some algorithmic aspects can be found in Barth elemy (1989) and Litvak (1982). The preferences are represented by arbitra ry binary relations (possibly weighted) or incomplete paired comparison matrices. The o utcome of an aggregation method is a set of "optimal" rankings (linear or weak ord ers) of the alternatives. Namely, a ranking is said to be optimal if it provides an ex tremum of some chosen objective function that expresses the connectio n (or proximity) between an arbitrary ranking and the original preferences.