Metric Distortion of Committee Election on Perturbation Stable Instances

Αβραμίδης, Δημήτριος Νικόλαος; Avramidis, Dimitrios Nikolaos

dc.contributor.author	Αβραμίδης, Δημήτριος Νικόλαος	el
dc.contributor.author	Avramidis, Dimitrios Nikolaos	en
dc.date.accessioned	2026-03-05T07:50:42Z
dc.date.available	2026-03-05T07:50:42Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/63806
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.31501
dc.rights	Default License
dc.subject	Εκλογή Επιτροπής	el
dc.subject	Μετρική Παραμόρφωση	el
dc.subject	Σταθερότητα Διαταραχής	el
dc.subject	Υπολογιστική Θεωρία Κοινωνικής Επιλογής	el
dc.subject	Κανόνες Ψηφοφορίας	el
dc.subject	Committee Election	en
dc.subject	Metric Distortion	en
dc.subject	Perturbation Stability	en
dc.subject	Computational Social Choice	en
dc.subject	Voting Rules	en
dc.title	Metric Distortion of Committee Election on Perturbation Stable Instances	en
dc.contributor.department	Τομέας Τεχνολογίας Πληροφορικής και Υπολογιστών	el
heal.type	bachelorThesis
heal.secondaryTitle	Μετρική Παραμόρφωση Κανόνων Εκλογής Επιτροπών σε Στιγμιότυπα με Σταθερότητα Διαταραχής	el
heal.classification	Computer Science	el
heal.language	el
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2025-09-09
heal.abstract	In this thesis, we study the design of voting rules for committee selection under metric preferences, and we analyze their metric distortion when the underlying clustering problem satisfies the property of perturbation stability. We consider a set of n voters and a set of m candidates, both embedded in some metric space. Our goal is to elect a committee of k members that minimizes the social cost, defined as the sum of the distances of all voters to their closest committee member. However, we assume that we only have access to the voters’ preference rankings and not to the exact distances. The metric distortion of a voting rule measures, in the worst case, the ratio between the cost of the committee selected by the rule and the minimum possible social cost. We present known results from the literature that provide upper and lower bounds on metric distortion, and we describe rules that achieve constant metric distortion using a limited number of distance queries. Subsequently, we study how structural properties arising from perturbation stability can be exploited in the design of more efficient algorithms. We focus on the case where k ≥ 3 and each voter’s cost is defined as their distance to the nearest committee member. Previous work has shown that metric distortion is generally unbounded in this setting without access to distance queries, and that O(poly(log n, k)) distance queries are required to guarantee constant distortion. The algorithms we present achieve constant metric distortion using only O(2^k) distance queries, i.e., a number independent of the number of voters.	en
heal.advisorName	Φωτάκης, Δημήτριος	el
heal.committeeMemberName	Φωτάκης, Δημήτριος	el
heal.committeeMemberName	Παγουρτζής, Αριστείδης	el
heal.committeeMemberName	Μαρκάκης, Ευάγγελος
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών. Τομέας Τεχνολογίας Πληροφορικής και Υπολογιστών	el
heal.academicPublisherID	ntua
heal.numberOfPages	106
heal.fullTextAvailability	false