{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/concordance-and-the-smallest-covering-set-of","title":"Concordance and the Smallest Covering Set of Preference Orderings","arxiv_id":"1609.04722","date":"2016-09-15","proceeding":null,"authors":["Zhiwei Lin","Hui Wang","Cees H. Elzinga"],"abstract":"Preference orderings are orderings of a set of items according to the\npreferences (of judges). Such orderings arise in a variety of domains,\nincluding group decision making, consumer marketing, voting and machine\nlearning. Measuring the mutual information and extracting the common patterns\nin a set of preference orderings are key to these areas. In this paper we deal\nwith the representation of sets of preference orderings, the quantification of\nthe degree to which judges agree on their ordering of the items (i.e. the\nconcordance), and the efficient, meaningful description of such sets.\n  We propose to represent the orderings in a subsequence-based feature space\nand present a new algorithm to calculate the size of the set of all common\nsubsequences - the basis of a quantification of concordance, not only for pairs\nof orderings but also for sets of orderings. The new algorithm is fast and\nstorage efficient with a time complexity of only $O(Nn^2)$ for the orderings of\n$n$ items by $N$ judges and a space complexity of only $O(\\min\\{Nn,n^2\\})$.\n  Also, we propose to represent the set of all $N$ orderings through a smallest\nset of covering preferences and present an algorithm to construct this smallest\ncovering set.\n  The source code for the algorithms is available at\nhttps://github.com/zhiweiuu/secs","url_abs":"http://arxiv.org/abs/1609.04722v3","url_pdf":"http://arxiv.org/pdf/1609.04722v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"concordance-and-the-smallest-covering-set-of","repo_url":"https://github.com/zhiweiuu/secs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"decision-making","task_name":"Decision Making"},{"task_slug":"marketing","task_name":"Marketing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}