Aggregation of Partial Rankings, p-Ratings and Top-m Lists

Abstract

We study the problem of aggregating partial rankings. This problem is motivated by applications such as meta-searching and information retrieval, search engine spam fighting, e-commerce, learning from experts, analysis of population preference sampling, committee decision making and more. We improve recent constant factor approximation algorithms for aggregation of full rankings and generalize them to partial rankings. Our algorithms improved constant factor approximation with respect to all metrics discussed in Fagin et al's recent important work on comparing partial rankings. We pay special attention to two important types of partial rankings: the well-known top-m lists and the more general p-ratings which we define. We provide first evidence for hardness of aggregating them for constant m, p.

Preference-based learning to rank

“…This result is in fact known from previous work (Ailon et al 2005;Ailon 2007) where it is proven directly without resorting to the intermediate inequality (23). In fact, a better factor of 2.5 is known to be achievable from that work using a more complicated algorithm, which gives hope for a 1.5 bound improving Theorem 1.…”

“…Thus, this work also adds a significant contribution to Ailon et al (2005), Ailon (2007) and Kenyon-Mathieu and Schudy (2007).…”

“…The technique developed in Lemma 1 is very general and can be used for a wide variety of loss functions and variants of QuickSort involving non-deterministic ordering rules (Ailon et al 2005;Ailon 2007 Ailon et al (2005) and Ailon (2007) to approximate certain NP-Hard weighted instances of the problem of minimum feedback arcset in tournaments (Alon 2006). There is much similarity between the techniques used in that work and those of the analyses of this work, but there is also a significant difference that should be noted.…”

“…They strengthened these bounds by considering non-deterministic pivoting rules arising from solutions to certain ranking LP's. This work was later extended by Ailon (2007) to deal with rankings with ties, in particular, top-k rankings. Hedge et al (2007) and Williamson and van Zuylen (2007) derandomized the random pivot selection step in QuickSort for many of the combinatorial optimization problems studied by Ailon et al (2005).…”

“…Here, we use a different algorithm, QuickSort, which has also been recently used for minimizing the feedback arcset in tournaments (Ailon et al 2005;Ailon 2007). The techniques presented build upon earlier work by Ailon et al (2005) and Ailon (2007) on combinatorial optimization problems over rankings and clustering.…”