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 - Funding Information:
SG received funding from MATRICS Grant (MTR/2021/000869) and SERB-SUPRA Grant(SPR/2021/000860). PJ received funding from Seed Grant (IITJ/R&D/2022-23/07) and SERB-SUPRA Grant(SPR/2021/000860). SR is supported by the CTU Global postdoc fellowship program. SS received funding from European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant no. 819416), and
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 -