The paper introduces the Squared Kemeny rule as an alternative to the well-known Kemeny rule for aggregating multiple rankings into a single collective ranking.
The key insights are:
The Squared Kemeny rule behaves like an "average" of the input rankings, ensuring that each ranking has proportional influence on the output. In contrast, the Kemeny rule behaves more like a "median", where rankings with a majority weight can dominate the output.
The authors provide an axiomatic characterization of the Squared Kemeny rule, showing that it is the unique rule satisfying neutrality, reinforcement, continuity, and a "2-Rankings-Proportionality" axiom. This axiom formalizes the idea of proportional influence.
The paper also establishes theoretical bounds on how far the Squared Kemeny output can be from any input ranking, as a function of the ranking's weight. This provides guarantees of proportional representation.
Empirical analysis demonstrates the Squared Kemeny rule's behavior, showing how it smoothly interpolates between input rankings based on their weights, unlike the more majoritarian Kemeny rule.
The Squared Kemeny rule is proposed as a desirable alternative for rank aggregation settings where proportional influence of the input rankings is important, such as hotel/product sorting, university rankings, and group decision-making.
Egy másik nyelvre
a forrásanyagból
arxiv.org
Mélyebb kérdések