Distance and Consensus for Preference Relations Corresponding to Ordered Partitions

Boris Mirkin () and Trevor I. Fenner ()
Additional contact information
Boris Mirkin: National Research University Higher School of Economics
Trevor I. Fenner: Birkbeck University of London

Journal of Classification, 2019, vol. 36, issue 2, No 10, 350-367

Abstract: Abstract Ranking is an important part of several areas of contemporary research, including social sciences, decision theory, data analysis, and information retrieval. The goal of this paper is to align developments in quantitative social sciences and decision theory with the current thought in Computer Science, including a few novel results. Specifically, we consider binary preference relations, the so-called weak orders that are in one-to-one correspondence with rankings. We show that the conventional symmetric difference distance between weak orders, considered as sets of ordered pairs, coincides with the celebrated Kemeny distance between the corresponding rankings, despite the seemingly much simpler structure of the former. Based on this, we review several properties of the geometric space of weak orders involving the ternary relation “between,” and contingency tables for cross-partitions. Next, we reformulate the consensus ranking problem as a variant of finding an optimal linear ordering, given a correspondingly defined consensus matrix. The difference is in a subtracted term, the partition concentration that depends only on the distribution of the objects in the individual parts. We apply our results to the conventional Likert scale to show that the Kemeny consensus rule is rather insensitive to the data under consideration and, therefore, should be supplemented with more sensitive consensus schemes.

Keywords: Ranking; Tied ranking; Ordered partition; Weak order; Distance; Consensus; Muchnik test (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00357-018-9290-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jclass:v:36:y:2019:i:2:d:10.1007_s00357-018-9290-x

Ordering information: This journal article can be ordered from
http://www.springer. ... hods/journal/357/PS2

DOI: 10.1007/s00357-018-9290-x

Access Statistics for this article

Journal of Classification is currently edited by Douglas Steinley

More articles in Journal of Classification from Springer, The Classification Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().