Ranking methods are fundamental tools in many areas. Popular methods aggregate the statements of 'experts' in different ways. As such, there are various reasonable ranking methods, each one of them more or less adapted to the environment under consideration. This paper introduces a new method,...

Ranking methods are fundamental tools in many areas. Popular methods aggregate the statements of 'experts' in different ways. As such, there are various reasonable ranking methods, each one of them more or less adapted to the environment under consideration. This paper introduces a new method,...

Ranking methods are fundamental tools in many areas. Popular methods aggregate the statements of `experts' in different ways. As such, there are various reasonable ranking methods, each one of them more or less adapted to the environment under consideration.This paper introduces a new method,...

We investigate the ways in which a linear order on a finite set A can be consistently extended to a linear order on a set Pk(A) of multisets on A of fixed cardinality k. We show that for card(A) = 3 all linear orders on Pk(A) are additive and classify them by means of Farey fractions. For...

Ranking by rating consists in evaluating the performances of items using exoge- nous rating functions and ranking these items according to their performance rat- ings. Any such method is separable: the ordering of two items does not depend on the performances of the remaining items. When...

Some researchers have addressed the problem of aggregating individual preferences or rankings by seeking a ranking that is closest to the individual rankings. Their methods differ according to the notion of distance that they use. The best known method of this sort is due to Kemeny. The first...

We consider the problem of ranking sets of objects, the members of which are mutually compatible. Assuming that each object is either good or bad, we axiomatically characterize three cardinality-based rules which arise naturally in this dichotomous setting. They are what we call the symmetric...

In this chapter, we seek to review some of the central concepts and results in the literature on positionalist voting rules, which goes back to Borda (1781) . After the introduction of the basic notation and definitions in earlier parts of the chapter, we explore in Section 3 the distinction...

We propose to establish wine rankings using scores that depend on the differences between favorable and unfavorable opinions about each wine, according to the Borda rule. Unlike alternative approaches and specifications, this method is well-defined even if the panelists' quality relations are...

One of the most famous ranking methods for digraphs is the ranking by Copeland score. The Copeland score of a node in a digraph is the difference between its outdegree (i.e. its number of outgoing arcs) and its indegree (i.e. its number of ingoing arcs). In the ranking by Copeland score, a node...