Algorithmic aspects of resource allocation and multiwinner voting : theory and experiments
This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notion...
Ausführliche Beschreibung
Autor*in: |
Kaczmarczyk, Andrzej [verfasserIn] |
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Format: |
E-Book |
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Sprache: |
Englisch |
Erschienen: |
Berlin: Universitätsverlag der Technischen Universität Berlin ; 2021 |
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Rechteinformationen: |
Open Access Creative Commons ; https://creativecommons.org/licenses/by/4.0 |
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Schlagwörter: |
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Umfang: |
1 Online-Ressource (241 p.) |
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Reihe: |
Foundations of computing ; 15 |
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Links: | |
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ISBN: |
978-3-7983-3215-7 978-3-7983-3216-4 |
Katalog-ID: |
1836521804 |
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520 | |a This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice | ||
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9783798332157 978-3-7983-3215-7 9783798332164 978-3-7983-3216-4 (DE-627)1836521804 (DE-599)KEP077649826 (OCoLC)1366200971 (OAPEN)54062 (EBP)077649826 DE-627 eng DE-627 rda eng PBW bicssc UMB bicssc Kaczmarczyk, Andrzej verfasserin aut Algorithmic aspects of resource allocation and multiwinner voting theory and experiments Berlin Universitätsverlag der Technischen Universität Berlin 2021 1 Online-Ressource (241 p.) Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Foundations of computing 15 Open Access Unrestricted online access star This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice Creative Commons https://creativecommons.org/licenses/by/4.0 cc English Algorithms & data structures Applied mathematics Algorithms and data structures https://library.oapen.org/bitstream/id/7014bcf0-78ec-4f85-967b-a93b537fa93b/kaczmarczyk_andrzej.pdf X:OAPEN Verlag kostenfrei https://library.oapen.org/handle/20.500.12657/54062 X:OAPEN Verlag kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280177600 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280729972 OLR-OAPEN f z 01-03-23 30 01 0104 4281091084 GBV-OAPEN z 01-03-23 31 01 0027 4280372381 z 01-03-23 34 01 3551 4278927886 OLR-OAPEN zi002 01-03-23 39 01 0547 4281282513 GBV-OAPEN ke 01-03-23 40 01 0007 4279996482 OLR-OAPEN xsn 01-03-23 63 01 3401 4281666311 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281916024 OLR-OAPEN z 01-03-23 70 01 0089 4280550891 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278750544 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343278204 OLR-OAL Vervielfältigungen (z.B. 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Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 01-03-23 161 01 0960 4278184662 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 187 01 3520 4278569041 JSTOR Open Access eBook z 28-02-23 213 01 0551 4279283052 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 230 01 0552 427946023X OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 283 01 3283 4279819149 OLR-OAL z 01-03-23 293 01 3293 4278363400 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 370 01 4370 4279105626 OLR-FREE Kostenloser Zugriff z 01-03-23 603 01 4603 4278006357 OLR-OAPEN Bitte beachten Sie die Nutzungsbedingungen und Copyright-Bestimmungen des Verlages/Herausgebers. z 28-02-23 808 01 4808 4280909121 OLR-OAPEN OAPEN Library zg 01-03-23 2403 01 DE-LFER 4308619858 00 --%%-- --%%-- n --%%-- l01 13-04-23 22 01 0018 Volltextzugang https://library.oapen.org/handle/20.500.12657/54062 23 01 0830 https://library.oapen.org/handle/20.500.12657/54062 30 01 0104 Open Access https://library.oapen.org/handle/20.500.12657/54062 31 01 0027 eBook GBV-OAPEN https://library.oapen.org/handle/20.500.12657/54062 34 01 3551 OpenAccess https://library.oapen.org/handle/20.500.12657/54062 40 01 0007 Volltext, Open Access https://library.oapen.org/handle/20.500.12657/54062 63 01 3401 E-Book https://library.oapen.org/handle/20.500.12657/54062 65 01 0003 Open Access https://library.oapen.org/handle/20.500.12657/54062 65 01 0003 Dieser Titel ist Teil einer Datenbank http://www.bibliothek.uni-regensburg.de/dbinfo/detail.php?titel_id=10728&bib_id=ulb_hal 70 01 0089 https://library.oapen.org/handle/20.500.12657/54062 LF 72 01 0035 https://library.oapen.org/handle/20.500.12657/54062 95 01 3095 https://library.oapen.org/handle/20.500.12657/54062 110 01 3110 Open Access https://library.oapen.org/handle/20.500.12657/54062 136 01 3526 Open Access https://library.oapen.org/handle/20.500.12657/54062 147 01 3528 https://library.oapen.org/handle/20.500.12657/54062 161 01 0960 https://library.oapen.org/handle/20.500.12657/54062 LF 187 01 3520 https://library.oapen.org/handle/20.500.12657/54062 213 01 0551 https://library.oapen.org/handle/20.500.12657/54062 230 01 0552 https://library.oapen.org/handle/20.500.12657/54062 283 01 3283 https://library.oapen.org/handle/20.500.12657/54062 293 01 3293 https://library.oapen.org/handle/20.500.12657/54062 LF 370 01 4370 https://library.oapen.org/handle/20.500.12657/54062 603 01 4603 https://library.oapen.org/handle/20.500.12657/54062 808 01 4808 Volltextzugang https://library.oapen.org/handle/20.500.12657/54062 2403 01 DE-LFER https://library.oapen.org/bitstream/id/7014bcf0-78ec-4f85-967b-a93b537fa93b/kaczmarczyk_andrzej.pdf 31 01 0027 00 eBook GBV-OAPEN 22 01 0018 OLR-ZDB-94-OAL 23 01 0830 OLR-OAPEN 30 01 0104 GBV-OAPEN 34 01 3551 OLR-OAPEN 39 01 0547 GBV-OAPEN 39 01 0547 LF 40 01 0007 OLR-OAPEN 63 01 3401 E-Books LF GBV-OAPEN 65 01 0003 OLR-OAPEN 70 01 0089 OLR-OAPEN-OA 72 01 0035 OLR-OAPEN-OA 95 01 3095 OLR-OAL 110 01 3110 OLR-GBV-OAPEN 136 01 3526 OLR-OAPEN 147 01 3528 OLR-OAPEN 161 01 0960 OLR-OAPEN 213 01 0551 OLR-OAPEN 230 01 0552 OLR-OAPEN 283 01 3283 OLR-OAL 293 01 3293 OLR-OAPEN 370 01 4370 OLR-FREE 370 01 4370 olr-ebook GBV-OAPEN 603 01 4603 OLR-OAPEN 808 01 4808 OLR-OAPEN |
spelling |
9783798332157 978-3-7983-3215-7 9783798332164 978-3-7983-3216-4 (DE-627)1836521804 (DE-599)KEP077649826 (OCoLC)1366200971 (OAPEN)54062 (EBP)077649826 DE-627 eng DE-627 rda eng PBW bicssc UMB bicssc Kaczmarczyk, Andrzej verfasserin aut Algorithmic aspects of resource allocation and multiwinner voting theory and experiments Berlin Universitätsverlag der Technischen Universität Berlin 2021 1 Online-Ressource (241 p.) Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Foundations of computing 15 Open Access Unrestricted online access star This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice Creative Commons https://creativecommons.org/licenses/by/4.0 cc English Algorithms & data structures Applied mathematics Algorithms and data structures https://library.oapen.org/bitstream/id/7014bcf0-78ec-4f85-967b-a93b537fa93b/kaczmarczyk_andrzej.pdf X:OAPEN Verlag kostenfrei https://library.oapen.org/handle/20.500.12657/54062 X:OAPEN Verlag kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280177600 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280729972 OLR-OAPEN f z 01-03-23 30 01 0104 4281091084 GBV-OAPEN z 01-03-23 31 01 0027 4280372381 z 01-03-23 34 01 3551 4278927886 OLR-OAPEN zi002 01-03-23 39 01 0547 4281282513 GBV-OAPEN ke 01-03-23 40 01 0007 4279996482 OLR-OAPEN xsn 01-03-23 63 01 3401 4281666311 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281916024 OLR-OAPEN z 01-03-23 70 01 0089 4280550891 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278750544 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343278204 OLR-OAL Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 24-06-23 110 01 3110 4281468455 OLR-GBV-OAPEN Open Access z 01-03-23 136 01 3526 4279641854 OLR-OAPEN z 01-03-23 147 01 3528 4282114185 OLR-OAPEN frei verfügbar für Europa-Universität Flensburg, Hochschule Flensburg und Zentrale Hochschulbibliothek Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 01-03-23 161 01 0960 4278184662 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 187 01 3520 4278569041 JSTOR Open Access eBook z 28-02-23 213 01 0551 4279283052 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 230 01 0552 427946023X OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 283 01 3283 4279819149 OLR-OAL z 01-03-23 293 01 3293 4278363400 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 370 01 4370 4279105626 OLR-FREE Kostenloser Zugriff z 01-03-23 603 01 4603 4278006357 OLR-OAPEN Bitte beachten Sie die Nutzungsbedingungen und Copyright-Bestimmungen des Verlages/Herausgebers. z 28-02-23 808 01 4808 4280909121 OLR-OAPEN OAPEN Library zg 01-03-23 2403 01 DE-LFER 4308619858 00 --%%-- --%%-- n --%%-- l01 13-04-23 22 01 0018 Volltextzugang https://library.oapen.org/handle/20.500.12657/54062 23 01 0830 https://library.oapen.org/handle/20.500.12657/54062 30 01 0104 Open Access https://library.oapen.org/handle/20.500.12657/54062 31 01 0027 eBook GBV-OAPEN https://library.oapen.org/handle/20.500.12657/54062 34 01 3551 OpenAccess https://library.oapen.org/handle/20.500.12657/54062 40 01 0007 Volltext, Open Access https://library.oapen.org/handle/20.500.12657/54062 63 01 3401 E-Book https://library.oapen.org/handle/20.500.12657/54062 65 01 0003 Open Access https://library.oapen.org/handle/20.500.12657/54062 65 01 0003 Dieser Titel ist Teil einer Datenbank http://www.bibliothek.uni-regensburg.de/dbinfo/detail.php?titel_id=10728&bib_id=ulb_hal 70 01 0089 https://library.oapen.org/handle/20.500.12657/54062 LF 72 01 0035 https://library.oapen.org/handle/20.500.12657/54062 95 01 3095 https://library.oapen.org/handle/20.500.12657/54062 110 01 3110 Open Access https://library.oapen.org/handle/20.500.12657/54062 136 01 3526 Open Access https://library.oapen.org/handle/20.500.12657/54062 147 01 3528 https://library.oapen.org/handle/20.500.12657/54062 161 01 0960 https://library.oapen.org/handle/20.500.12657/54062 LF 187 01 3520 https://library.oapen.org/handle/20.500.12657/54062 213 01 0551 https://library.oapen.org/handle/20.500.12657/54062 230 01 0552 https://library.oapen.org/handle/20.500.12657/54062 283 01 3283 https://library.oapen.org/handle/20.500.12657/54062 293 01 3293 https://library.oapen.org/handle/20.500.12657/54062 LF 370 01 4370 https://library.oapen.org/handle/20.500.12657/54062 603 01 4603 https://library.oapen.org/handle/20.500.12657/54062 808 01 4808 Volltextzugang https://library.oapen.org/handle/20.500.12657/54062 2403 01 DE-LFER https://library.oapen.org/bitstream/id/7014bcf0-78ec-4f85-967b-a93b537fa93b/kaczmarczyk_andrzej.pdf 31 01 0027 00 eBook GBV-OAPEN 22 01 0018 OLR-ZDB-94-OAL 23 01 0830 OLR-OAPEN 30 01 0104 GBV-OAPEN 34 01 3551 OLR-OAPEN 39 01 0547 GBV-OAPEN 39 01 0547 LF 40 01 0007 OLR-OAPEN 63 01 3401 E-Books LF GBV-OAPEN 65 01 0003 OLR-OAPEN 70 01 0089 OLR-OAPEN-OA 72 01 0035 OLR-OAPEN-OA 95 01 3095 OLR-OAL 110 01 3110 OLR-GBV-OAPEN 136 01 3526 OLR-OAPEN 147 01 3528 OLR-OAPEN 161 01 0960 OLR-OAPEN 213 01 0551 OLR-OAPEN 230 01 0552 OLR-OAPEN 283 01 3283 OLR-OAL 293 01 3293 OLR-OAPEN 370 01 4370 OLR-FREE 370 01 4370 olr-ebook GBV-OAPEN 603 01 4603 OLR-OAPEN 808 01 4808 OLR-OAPEN |
allfields_unstemmed |
9783798332157 978-3-7983-3215-7 9783798332164 978-3-7983-3216-4 (DE-627)1836521804 (DE-599)KEP077649826 (OCoLC)1366200971 (OAPEN)54062 (EBP)077649826 DE-627 eng DE-627 rda eng PBW bicssc UMB bicssc Kaczmarczyk, Andrzej verfasserin aut Algorithmic aspects of resource allocation and multiwinner voting theory and experiments Berlin Universitätsverlag der Technischen Universität Berlin 2021 1 Online-Ressource (241 p.) Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Foundations of computing 15 Open Access Unrestricted online access star This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice Creative Commons https://creativecommons.org/licenses/by/4.0 cc English Algorithms & data structures Applied mathematics Algorithms and data structures https://library.oapen.org/bitstream/id/7014bcf0-78ec-4f85-967b-a93b537fa93b/kaczmarczyk_andrzej.pdf X:OAPEN Verlag kostenfrei https://library.oapen.org/handle/20.500.12657/54062 X:OAPEN Verlag kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280177600 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280729972 OLR-OAPEN f z 01-03-23 30 01 0104 4281091084 GBV-OAPEN z 01-03-23 31 01 0027 4280372381 z 01-03-23 34 01 3551 4278927886 OLR-OAPEN zi002 01-03-23 39 01 0547 4281282513 GBV-OAPEN ke 01-03-23 40 01 0007 4279996482 OLR-OAPEN xsn 01-03-23 63 01 3401 4281666311 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281916024 OLR-OAPEN z 01-03-23 70 01 0089 4280550891 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278750544 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343278204 OLR-OAL Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 24-06-23 110 01 3110 4281468455 OLR-GBV-OAPEN Open Access z 01-03-23 136 01 3526 4279641854 OLR-OAPEN z 01-03-23 147 01 3528 4282114185 OLR-OAPEN frei verfügbar für Europa-Universität Flensburg, Hochschule Flensburg und Zentrale Hochschulbibliothek Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 01-03-23 161 01 0960 4278184662 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 187 01 3520 4278569041 JSTOR Open Access eBook z 28-02-23 213 01 0551 4279283052 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 230 01 0552 427946023X OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 283 01 3283 4279819149 OLR-OAL z 01-03-23 293 01 3293 4278363400 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 370 01 4370 4279105626 OLR-FREE Kostenloser Zugriff z 01-03-23 603 01 4603 4278006357 OLR-OAPEN Bitte beachten Sie die Nutzungsbedingungen und Copyright-Bestimmungen des Verlages/Herausgebers. z 28-02-23 808 01 4808 4280909121 OLR-OAPEN OAPEN Library zg 01-03-23 2403 01 DE-LFER 4308619858 00 --%%-- --%%-- n --%%-- l01 13-04-23 22 01 0018 Volltextzugang https://library.oapen.org/handle/20.500.12657/54062 23 01 0830 https://library.oapen.org/handle/20.500.12657/54062 30 01 0104 Open Access https://library.oapen.org/handle/20.500.12657/54062 31 01 0027 eBook GBV-OAPEN https://library.oapen.org/handle/20.500.12657/54062 34 01 3551 OpenAccess https://library.oapen.org/handle/20.500.12657/54062 40 01 0007 Volltext, Open Access https://library.oapen.org/handle/20.500.12657/54062 63 01 3401 E-Book https://library.oapen.org/handle/20.500.12657/54062 65 01 0003 Open Access https://library.oapen.org/handle/20.500.12657/54062 65 01 0003 Dieser Titel ist Teil einer Datenbank http://www.bibliothek.uni-regensburg.de/dbinfo/detail.php?titel_id=10728&bib_id=ulb_hal 70 01 0089 https://library.oapen.org/handle/20.500.12657/54062 LF 72 01 0035 https://library.oapen.org/handle/20.500.12657/54062 95 01 3095 https://library.oapen.org/handle/20.500.12657/54062 110 01 3110 Open Access https://library.oapen.org/handle/20.500.12657/54062 136 01 3526 Open Access https://library.oapen.org/handle/20.500.12657/54062 147 01 3528 https://library.oapen.org/handle/20.500.12657/54062 161 01 0960 https://library.oapen.org/handle/20.500.12657/54062 LF 187 01 3520 https://library.oapen.org/handle/20.500.12657/54062 213 01 0551 https://library.oapen.org/handle/20.500.12657/54062 230 01 0552 https://library.oapen.org/handle/20.500.12657/54062 283 01 3283 https://library.oapen.org/handle/20.500.12657/54062 293 01 3293 https://library.oapen.org/handle/20.500.12657/54062 LF 370 01 4370 https://library.oapen.org/handle/20.500.12657/54062 603 01 4603 https://library.oapen.org/handle/20.500.12657/54062 808 01 4808 Volltextzugang https://library.oapen.org/handle/20.500.12657/54062 2403 01 DE-LFER https://library.oapen.org/bitstream/id/7014bcf0-78ec-4f85-967b-a93b537fa93b/kaczmarczyk_andrzej.pdf 31 01 0027 00 eBook GBV-OAPEN 22 01 0018 OLR-ZDB-94-OAL 23 01 0830 OLR-OAPEN 30 01 0104 GBV-OAPEN 34 01 3551 OLR-OAPEN 39 01 0547 GBV-OAPEN 39 01 0547 LF 40 01 0007 OLR-OAPEN 63 01 3401 E-Books LF GBV-OAPEN 65 01 0003 OLR-OAPEN 70 01 0089 OLR-OAPEN-OA 72 01 0035 OLR-OAPEN-OA 95 01 3095 OLR-OAL 110 01 3110 OLR-GBV-OAPEN 136 01 3526 OLR-OAPEN 147 01 3528 OLR-OAPEN 161 01 0960 OLR-OAPEN 213 01 0551 OLR-OAPEN 230 01 0552 OLR-OAPEN 283 01 3283 OLR-OAL 293 01 3293 OLR-OAPEN 370 01 4370 OLR-FREE 370 01 4370 olr-ebook GBV-OAPEN 603 01 4603 OLR-OAPEN 808 01 4808 OLR-OAPEN |
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9783798332157 978-3-7983-3215-7 9783798332164 978-3-7983-3216-4 (DE-627)1836521804 (DE-599)KEP077649826 (OCoLC)1366200971 (OAPEN)54062 (EBP)077649826 DE-627 eng DE-627 rda eng PBW bicssc UMB bicssc Kaczmarczyk, Andrzej verfasserin aut Algorithmic aspects of resource allocation and multiwinner voting theory and experiments Berlin Universitätsverlag der Technischen Universität Berlin 2021 1 Online-Ressource (241 p.) Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Foundations of computing 15 Open Access Unrestricted online access star This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice Creative Commons https://creativecommons.org/licenses/by/4.0 cc English Algorithms & data structures Applied mathematics Algorithms and data structures https://library.oapen.org/bitstream/id/7014bcf0-78ec-4f85-967b-a93b537fa93b/kaczmarczyk_andrzej.pdf X:OAPEN Verlag kostenfrei https://library.oapen.org/handle/20.500.12657/54062 X:OAPEN Verlag kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280177600 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280729972 OLR-OAPEN f z 01-03-23 30 01 0104 4281091084 GBV-OAPEN z 01-03-23 31 01 0027 4280372381 z 01-03-23 34 01 3551 4278927886 OLR-OAPEN zi002 01-03-23 39 01 0547 4281282513 GBV-OAPEN ke 01-03-23 40 01 0007 4279996482 OLR-OAPEN xsn 01-03-23 63 01 3401 4281666311 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281916024 OLR-OAPEN z 01-03-23 70 01 0089 4280550891 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278750544 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343278204 OLR-OAL Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 24-06-23 110 01 3110 4281468455 OLR-GBV-OAPEN Open Access z 01-03-23 136 01 3526 4279641854 OLR-OAPEN z 01-03-23 147 01 3528 4282114185 OLR-OAPEN frei verfügbar für Europa-Universität Flensburg, Hochschule Flensburg und Zentrale Hochschulbibliothek Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 01-03-23 161 01 0960 4278184662 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 187 01 3520 4278569041 JSTOR Open Access eBook z 28-02-23 213 01 0551 4279283052 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 230 01 0552 427946023X OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 283 01 3283 4279819149 OLR-OAL z 01-03-23 293 01 3293 4278363400 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 370 01 4370 4279105626 OLR-FREE Kostenloser Zugriff z 01-03-23 603 01 4603 4278006357 OLR-OAPEN Bitte beachten Sie die Nutzungsbedingungen und Copyright-Bestimmungen des Verlages/Herausgebers. z 28-02-23 808 01 4808 4280909121 OLR-OAPEN OAPEN Library zg 01-03-23 2403 01 DE-LFER 4308619858 00 --%%-- --%%-- n --%%-- l01 13-04-23 22 01 0018 Volltextzugang https://library.oapen.org/handle/20.500.12657/54062 23 01 0830 https://library.oapen.org/handle/20.500.12657/54062 30 01 0104 Open Access https://library.oapen.org/handle/20.500.12657/54062 31 01 0027 eBook GBV-OAPEN https://library.oapen.org/handle/20.500.12657/54062 34 01 3551 OpenAccess https://library.oapen.org/handle/20.500.12657/54062 40 01 0007 Volltext, Open Access https://library.oapen.org/handle/20.500.12657/54062 63 01 3401 E-Book https://library.oapen.org/handle/20.500.12657/54062 65 01 0003 Open Access https://library.oapen.org/handle/20.500.12657/54062 65 01 0003 Dieser Titel ist Teil einer Datenbank http://www.bibliothek.uni-regensburg.de/dbinfo/detail.php?titel_id=10728&bib_id=ulb_hal 70 01 0089 https://library.oapen.org/handle/20.500.12657/54062 LF 72 01 0035 https://library.oapen.org/handle/20.500.12657/54062 95 01 3095 https://library.oapen.org/handle/20.500.12657/54062 110 01 3110 Open Access https://library.oapen.org/handle/20.500.12657/54062 136 01 3526 Open Access https://library.oapen.org/handle/20.500.12657/54062 147 01 3528 https://library.oapen.org/handle/20.500.12657/54062 161 01 0960 https://library.oapen.org/handle/20.500.12657/54062 LF 187 01 3520 https://library.oapen.org/handle/20.500.12657/54062 213 01 0551 https://library.oapen.org/handle/20.500.12657/54062 230 01 0552 https://library.oapen.org/handle/20.500.12657/54062 283 01 3283 https://library.oapen.org/handle/20.500.12657/54062 293 01 3293 https://library.oapen.org/handle/20.500.12657/54062 LF 370 01 4370 https://library.oapen.org/handle/20.500.12657/54062 603 01 4603 https://library.oapen.org/handle/20.500.12657/54062 808 01 4808 Volltextzugang https://library.oapen.org/handle/20.500.12657/54062 2403 01 DE-LFER https://library.oapen.org/bitstream/id/7014bcf0-78ec-4f85-967b-a93b537fa93b/kaczmarczyk_andrzej.pdf 31 01 0027 00 eBook GBV-OAPEN 22 01 0018 OLR-ZDB-94-OAL 23 01 0830 OLR-OAPEN 30 01 0104 GBV-OAPEN 34 01 3551 OLR-OAPEN 39 01 0547 GBV-OAPEN 39 01 0547 LF 40 01 0007 OLR-OAPEN 63 01 3401 E-Books LF GBV-OAPEN 65 01 0003 OLR-OAPEN 70 01 0089 OLR-OAPEN-OA 72 01 0035 OLR-OAPEN-OA 95 01 3095 OLR-OAL 110 01 3110 OLR-GBV-OAPEN 136 01 3526 OLR-OAPEN 147 01 3528 OLR-OAPEN 161 01 0960 OLR-OAPEN 213 01 0551 OLR-OAPEN 230 01 0552 OLR-OAPEN 283 01 3283 OLR-OAL 293 01 3293 OLR-OAPEN 370 01 4370 OLR-FREE 370 01 4370 olr-ebook GBV-OAPEN 603 01 4603 OLR-OAPEN 808 01 4808 OLR-OAPEN |
allfieldsSound |
9783798332157 978-3-7983-3215-7 9783798332164 978-3-7983-3216-4 (DE-627)1836521804 (DE-599)KEP077649826 (OCoLC)1366200971 (OAPEN)54062 (EBP)077649826 DE-627 eng DE-627 rda eng PBW bicssc UMB bicssc Kaczmarczyk, Andrzej verfasserin aut Algorithmic aspects of resource allocation and multiwinner voting theory and experiments Berlin Universitätsverlag der Technischen Universität Berlin 2021 1 Online-Ressource (241 p.) Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Foundations of computing 15 Open Access Unrestricted online access star This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice Creative Commons https://creativecommons.org/licenses/by/4.0 cc English Algorithms & data structures Applied mathematics Algorithms and data structures https://library.oapen.org/bitstream/id/7014bcf0-78ec-4f85-967b-a93b537fa93b/kaczmarczyk_andrzej.pdf X:OAPEN Verlag kostenfrei https://library.oapen.org/handle/20.500.12657/54062 X:OAPEN Verlag kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280177600 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280729972 OLR-OAPEN f z 01-03-23 30 01 0104 4281091084 GBV-OAPEN z 01-03-23 31 01 0027 4280372381 z 01-03-23 34 01 3551 4278927886 OLR-OAPEN zi002 01-03-23 39 01 0547 4281282513 GBV-OAPEN ke 01-03-23 40 01 0007 4279996482 OLR-OAPEN xsn 01-03-23 63 01 3401 4281666311 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281916024 OLR-OAPEN z 01-03-23 70 01 0089 4280550891 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278750544 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343278204 OLR-OAL Vervielfältigungen (z.B. 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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000cam a22002652 4500</leader><controlfield tag="001">1836521804</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20241008063257.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220426s2021 xx |||||o 00| ||eng c</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783798332157</subfield><subfield code="9">978-3-7983-3215-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783798332164</subfield><subfield code="9">978-3-7983-3216-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)1836521804</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)KEP077649826</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1366200971</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OAPEN)54062</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(EBP)077649826</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">eng</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">PBW</subfield><subfield code="2">bicssc</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">UMB</subfield><subfield code="2">bicssc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kaczmarczyk, Andrzej</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algorithmic aspects of resource allocation and multiwinner voting</subfield><subfield code="b">theory and experiments</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin</subfield><subfield code="b">Universitätsverlag der Technischen Universität Berlin</subfield><subfield code="c">2021</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (241 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Foundations of computing</subfield><subfield code="v">15</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">Open Access</subfield><subfield code="f">Unrestricted online access</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. 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Kaczmarczyk, Andrzej |
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31 01 0027 00 eBook GBV-OAPEN Algorithmic aspects of resource allocation and multiwinner voting theory and experiments Algorithms & data structures Applied mathematics Algorithms and data structures |
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Algorithmic aspects of resource allocation and multiwinner voting theory and experiments |
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Kaczmarczyk, Andrzej |
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algorithmic aspects of resource allocation and multiwinner votingtheory and experiments |
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Algorithmic aspects of resource allocation and multiwinner voting theory and experiments |
abstract |
This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice |
abstractGer |
This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice |
abstract_unstemmed |
This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice |
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title_short |
Algorithmic aspects of resource allocation and multiwinner voting |
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score |
7.167901 |