Gehrlein Stable Committee with Multi-modal Preferences

Sushmita Gupta, Pallavi Jain, Daniel Lokshtanov, Sanjukta Roy, Saket Saurabh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Inspired by Gehrlein stability in multiwinner election, in this paper, we define several notions of stability that are applicable in multiwinner elections with multimodal preferences, a model recently proposed by Jain and Talmon [ECAI, 2020]. In this paper we take a two-pronged approach to this study: we introduce several natural notions of stability that are applicable to multiwinner multimodal elections (MME) and show an array of hardness and algorithmic results. In a multimodal election, we have a set of candidates, C, and a multi-set of ℓ different preference profiles, where each profile contains a multi-set of strictly ordered lists over C. The goal is to find a committee of a given size, say k, that satisfies certain notions of stability. In this context, we define the following notions of stability: global-strongly (weakly) stable, individual-strongly (weakly) stable, and pairwise-strongly (weakly) stable. In general, finding any of these committees is an intractable problem, and hence motivates us to study them for restricted domains, namely single-peaked and single-crossing, and when the number of voters is odd. Besides showing that several of these variants remain computationally intractable, we present several efficient algorithms for certain parameters and restricted domains.

Original languageEnglish
Title of host publicationAlgorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings
EditorsPanagiotis Kanellopoulos, Maria Kyropoulou, Alexandros Voudouris
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages18
ISBN (Print)9783031157134
StatePublished - 1 Jan 2022
Externally publishedYes
Event15th International Symposium on Algorithmic Game Theory, SAGT 2022 - Colchester, United Kingdom
Duration: 12 Sep 202215 Sep 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13584 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Symposium on Algorithmic Game Theory, SAGT 2022
Country/TerritoryUnited Kingdom


  • Multi-modal
  • Multiwinner Election
  • Parameterized Complexity
  • Stability

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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