TY - GEN
T1 - Gehrlein Stable Committee with Multi-modal Preferences
AU - Gupta, Sushmita
AU - Jain, Pallavi
AU - Lokshtanov, Daniel
AU - Roy, Sanjukta
AU - Saurabh, Saket
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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.
AB - 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.
KW - Multi-modal
KW - Multiwinner Election
KW - Parameterized Complexity
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=85138794167&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-15714-1_29
DO - 10.1007/978-3-031-15714-1_29
M3 - Conference contribution
AN - SCOPUS:85138794167
SN - 9783031157134
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 508
EP - 525
BT - Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings
A2 - Kanellopoulos, Panagiotis
A2 - Kyropoulou, Maria
A2 - Voudouris, Alexandros
PB - Springer Science and Business Media Deutschland GmbH
T2 - 15th International Symposium on Algorithmic Game Theory, SAGT 2022
Y2 - 12 September 2022 through 15 September 2022
ER -