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Papers by palash dey

Proceedings of the Web Conference 2021

Theoretical Computer Science

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

We study the parameterized complexity of the optimal defense and optimal attack problems in votin... more We study the parameterized complexity of the optimal defense and optimal attack problems in voting. In both the problems, the input is a set of voter groups (every voter group is a set of votes) and two integers k_a and k_d corresponding to respectively the number of voter groups the attacker can attack and the number of voter groups the defender can defend. A voter group gets removed from the election if it is attacked but not defended. In the optimal defense problem, we want to know if it is possible for the defender to commit to a strategy of defending at most k_d voter groups such that, no matter which k_a voter groups the attacker attacks, the out-come of the election does not change. In the optimal attack problem, we want to know if it is possible for the attacker to commit to a strategy of attacking k_a voter groups such that, no matter which k_d voter groups the defender defends, the outcome of the election is always different from the original (without any attack) one. We s...

Theoretical Computer Science

Theoretical Computer Science

Theoretical Computer Science

Lu and Boutilier [LB11] proposed a novel approach based on "minimax regret" to use classical scor... more Lu and Boutilier [LB11] proposed a novel approach based on "minimax regret" to use classical score based voting rules in the setting where preferences can be any partial (instead of complete) orders over the set of alternatives. We show here that such an approach is vulnerable to a new kind of manipulation which was not present in the classical (where preferences are complete orders) world of voting. We call this attack "manipulative elicitation." More specifically, it may be possible to (partially) elicit the preferences of the agents in a way that makes some distinguished alternative win the election who may not be a winner if we elicit every preference completely. More alarmingly, we show that the related computational task is polynomial time solvable for a large class of voting rules which includes all scoring rules, maximin, Copeland α for every α ∈ [0, 1], simplified Bucklin voting rules, etc. We then show that introducing a parameter per pair of alternatives which specifies the minimum number of partial preferences where this pair of alternatives must be comparable makes the related computational task of manipulative elicitation NP-complete for all common voting rules including a class of scoring rules which includes the plurality, k-approval, k-veto, veto, and Borda voting rules, maximin, Copeland α for every α ∈ [0, 1], and simplified Bucklin voting rules. Hence, in this work, we discover a fundamental vulnerability in using minimax regret based approach in partial preferential setting and propose a novel way to tackle it.

Theoretical Computer Science

The Coalitional Manipulation problem has been studied extensively in the literature for many voti... more The Coalitional Manipulation problem has been studied extensively in the literature for many voting rules. However, most studies have focused on the complete information setting, wherein the manipulators know the votes of the non-manipulators. While this assumption is reasonable for purposes of showing intractability, it is unrealistic for algorithmic considerations. In most real-world scenarios, it is impractical to assume that the manipulators to have accurate knowledge of all the other votes. In this work, we investigate manipulation with incomplete information. In our framework, the manipulators know a partial order for each voter that is consistent with the true preference of that voter. In this setting, we formulate three natural computational notions of manipulation, namely weak, opportunistic, and strong manipulation. We say that an extension of a partial order is viable if there exists a manipulative vote for that extension. We propose the following notions of manipulation when manipulators have incomplete information about the votes of other voters.

ACM Transactions on Algorithms

Studies in Microeconomics

Classical results in voting theory show that strategic manipulation by voters is inevitable if a ... more Classical results in voting theory show that strategic manipulation by voters is inevitable if a voting rule simultaneously satisfy certain desirable properties. Motivated by this, we study the relevant question of how often a voting rule is manipulable. It is well known that elections with a large number of voters are rarely manipulable under impartial culture (IC) assumption. However, the manipulability of voting rules when the number of candidates is large has hardly been addressed in the literature and our paper focuses on this problem. First, we propose two properties (1) asymptotic strategy-proofness and (2) asymptotic collusion-proofness, with respect to new voters, which makes the two notions more relevant from the perspective of computational problem of manipulation. In addition to IC, we explore a new culture of society where all score vectors of the candidates are equally likely. This new notion has its motivation in computational social choice and we call it impartial scores culture (ISC) assumption. We study asymptotic strategy-proofness and asymptotic collusion-proofness for plurality, veto, k-approval, and Borda voting rules under IC as well as ISC assumptions. Specifically, we prove bounds for the fraction of manipulable profiles when the number of candidates is large. Our results show that the size of the coalition and the tie-breaking rule play a crucial role in determining whether or not a voting rule satisfies the above two properties.

Theoretical Computer Science, 2017

ABSTRACT Bribery in elections is an important problem in computational social choice theory. Howe... more ABSTRACT Bribery in elections is an important problem in computational social choice theory. However, bribery with money is often illegal in elections. Motivated by this, we introduce the notion of frugal bribery and formulate two new pertinent computational problems which we call Frugal-bribery and Frugal- $bribery to capture bribery without money in elections. In the proposed model, the briber is frugal in nature and this is captured by her inability to bribe votes of a certain kind, namely, non-vulnerable votes. In the Frugal-bribery problem, the goal is to make a certain candidate win the election by changing only vulnerable votes. In the Frugal-{dollar}bribery problem, the vulnerable votes have prices and the goal is to make a certain candidate win the election by changing only vulnerable votes, subject to a budget constraint of the briber. We further formulate two natural variants of the Frugal-{dollar}bribery problem namely Uniform-frugal-{dollar}bribery and Nonuniform-frugal-{dollar}bribery where the prices of the vulnerable votes are, respectively, all the same or different. We study the computational complexity of the above problems for unweighted and weighted elections for several commonly used voting rules. We observe that, even if we have only a small number of candidates, the problems are intractable for all voting rules studied here for weighted elections, with the sole exception of the Frugal-bribery problem for the plurality voting rule. In contrast, we have polynomial time algorithms for the Frugal-bribery problem for plurality, veto, k-approval, k-veto, and plurality with runoff voting rules for unweighted elections. However, the Frugal-{dollar}bribery problem is intractable for all the voting rules studied here barring the plurality and the veto voting rules for unweighted elections.

Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems - PODS '16, 2016

Theoretical Computer Science, 2016

In the Possible Winner problem in computational social choice theory, we are given a set of parti... more In the Possible Winner problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the Possible Winner problem, with number of candidates as the parameter. However, the corresponding kernelization question is still open and in fact, has been mentioned as a key research challenge [Bredereck et al., 2014a]. In this paper, we settle this open question for many common voting rules. We show that the Possible Winner problem for maximin, Copeland, Bucklin, ranked pairs, and a class of scoring rules that include the Borda voting rule do not admit a polynomial kernel with the number of candidates as the parameter. We show however that the Coalitional Manipulation problem which is an important special case of the Possible Winner problem does admit a polynomial kernel for maximin, Copeland, ranked pairs, and a class of scoring rules that includes the Borda voting rule, when the number of manipulators is polynomial in the number of candidates. A significant conclusion of our work is that the Possible Winner problem is harder than the Coalitional Manipulation problem since the Coalitional Manipulation problem admits a polynomial kernel whereas the Possible Winner problem does not admit a polynomial kernel.

The Coalitional Manipulation (CM) problem has been studied extensively in the literature for many... more The Coalitional Manipulation (CM) problem has been studied extensively in the literature for many voting rules. The CM problem, however, has been studied only in the complete information setting, that is, when the manipulators know the votes of the non-manipulators. A more realistic scenario is an incomplete information setting where the manipulators do not know the exact votes of the non- manipulators but may have some partial knowledge of the votes. In this paper, we study a setting where the manipulators know a partial order for each voter that is consistent with the vote of that voter. In this setting, we introduce and study two natural computational problems - (1) Weak Manipulation (WM) problem where the manipulators wish to vote in a way that makes their preferred candidate win in at least one extension of the partial votes of the non-manipulators; (2) Strong Manipulation (SM) problem where the manipulators wish to vote in a way that makes their preferred candidate win in all ...

ABSTRACT Manipulation is a problem of fundamental importance in the context of voting rules in wh... more ABSTRACT Manipulation is a problem of fundamental importance in the context of voting rules in which the voters vote strategically instead of voting honestly to avoid selection of an alternative that is less preferred. The Gibbard-Satterthwaite theorem shows that there is no strategy-proof voting rule that simultaneously satisfies certain combinations of desirable properties. Researchers have attempted to get around the impossibility results in several ways such as domain restriction and computational hardness of manipulation, etc. However these approaches have been shown to have limitations. Since prevention of manipulation seems to be elusive, a natural research direction therefore is detection of manipulation. Motivated by this, we study detection of possible manipulators in an election. We formulate two pertinent computational problems - Coalitional Possible Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW). For several popular voting rules, we provide polynomial time algorithms for both the CPM and CPMW problems. For certain other voting rules, we show that these two problems are in NPC. A striking observation of our study is that detecting manipulation is surprisingly easy for a few well known voting rules. We then move on to weighted elections and show similar results.

ABSTRACT In the \textsc{Possible Winner} problem in computational voting theory, we are given a s... more ABSTRACT In the \textsc{Possible Winner} problem in computational voting theory, we are given a set of partial preferences and the problem is to determine whether or not a specified candidate could be made winner by extending the partial preferences to linear ones. Previous work has provided algorithms for this problem in the context of many common voting rules that are fixed parameter tractable with the number of candidates as the parameter. However, the corresponding kernelization questions are still open. In this paper, we show that the \textsc{possible winner} problem for maximin, Copeland, Bucklin, and ranked pairs voting rules does not admit a polynomial kernel with number of candidates as the parameter. We also show that the \textsc{coalitional manipulation} problem, an important special case of the \textsc{possible winner} problem, admits polynomial kernels for maximin, Copeland, and ranked pairs voting rules when the number of manipulators is constant.

Predicting the winner of an election is a favorite problem both for news media pundits and comput... more Predicting the winner of an election is a favorite problem both for news media pundits and computational social choice theorists. Since it is often infeasible to elicit the preferences of all the voters in a typical prediction scenario, a common algorithm used for winner prediction is to run the election on a small sample of randomly chosen votes and output the winner as the prediction. We analyze the performance of this algorithm for many common voting rules. More formally, we introduce the (ε, δ)-winner determination problem, where given an election on n voters and m candidates in which the margin of victory is at least εn votes, the goal is to determine the winner with probability at least 1−δ. The margin of victory of an election is the smallest number of votes that need to be modified in order to change the election winner. We show interesting lower and upper bounds on the number of samples needed to solve the (ε, δ)-winner determination problem for many common voting rules, including scoring rules, approval, maximin, Copeland, Bucklin, plurality with runoff, and single transferable vote. Moreover, the lower and upper bounds match for many common voting rules in a wide range of practically appealing scenarios.

Lecture Notes in Computer Science, 2014

Lecture Notes in Computer Science, 2010

Multipath bandwidth provisioning is one of the prime interest of next generation optical networks... more Multipath bandwidth provisioning is one of the prime interest of next generation optical networks. It is a policy to distribute the requested bandwidth in multiple link disjoint paths on the basis of some optimization function. It also helps to increase network throughput. By using backup path provisioning, we can meet availability requirement of service level agreement (SLA). But multipath bandwidth provisioning leads to problem like jitter which is the difference of delay between two paths. In this paper, we propose a dynamic multipath bandwidth provisioning scheme in telecom mesh network which takes both throughput and jitter into account. It also meets SLA requirement of incoming requests. Our provisioning scheme is dynamic in the sense that it allocates bandwidth for service requests that arrive periodically with no knowledge of future requests and hence requiring an online algorithm. Our algorithm uses 1:N protection scheme against restoration since only protection can guarant...

Proceedings of the Web Conference 2021

Theoretical Computer Science

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

We study the parameterized complexity of the optimal defense and optimal attack problems in votin... more We study the parameterized complexity of the optimal defense and optimal attack problems in voting. In both the problems, the input is a set of voter groups (every voter group is a set of votes) and two integers k_a and k_d corresponding to respectively the number of voter groups the attacker can attack and the number of voter groups the defender can defend. A voter group gets removed from the election if it is attacked but not defended. In the optimal defense problem, we want to know if it is possible for the defender to commit to a strategy of defending at most k_d voter groups such that, no matter which k_a voter groups the attacker attacks, the out-come of the election does not change. In the optimal attack problem, we want to know if it is possible for the attacker to commit to a strategy of attacking k_a voter groups such that, no matter which k_d voter groups the defender defends, the outcome of the election is always different from the original (without any attack) one. We s...

Theoretical Computer Science

Theoretical Computer Science

Theoretical Computer Science

Lu and Boutilier [LB11] proposed a novel approach based on "minimax regret" to use classical scor... more Lu and Boutilier [LB11] proposed a novel approach based on "minimax regret" to use classical score based voting rules in the setting where preferences can be any partial (instead of complete) orders over the set of alternatives. We show here that such an approach is vulnerable to a new kind of manipulation which was not present in the classical (where preferences are complete orders) world of voting. We call this attack "manipulative elicitation." More specifically, it may be possible to (partially) elicit the preferences of the agents in a way that makes some distinguished alternative win the election who may not be a winner if we elicit every preference completely. More alarmingly, we show that the related computational task is polynomial time solvable for a large class of voting rules which includes all scoring rules, maximin, Copeland α for every α ∈ [0, 1], simplified Bucklin voting rules, etc. We then show that introducing a parameter per pair of alternatives which specifies the minimum number of partial preferences where this pair of alternatives must be comparable makes the related computational task of manipulative elicitation NP-complete for all common voting rules including a class of scoring rules which includes the plurality, k-approval, k-veto, veto, and Borda voting rules, maximin, Copeland α for every α ∈ [0, 1], and simplified Bucklin voting rules. Hence, in this work, we discover a fundamental vulnerability in using minimax regret based approach in partial preferential setting and propose a novel way to tackle it.

Theoretical Computer Science

The Coalitional Manipulation problem has been studied extensively in the literature for many voti... more The Coalitional Manipulation problem has been studied extensively in the literature for many voting rules. However, most studies have focused on the complete information setting, wherein the manipulators know the votes of the non-manipulators. While this assumption is reasonable for purposes of showing intractability, it is unrealistic for algorithmic considerations. In most real-world scenarios, it is impractical to assume that the manipulators to have accurate knowledge of all the other votes. In this work, we investigate manipulation with incomplete information. In our framework, the manipulators know a partial order for each voter that is consistent with the true preference of that voter. In this setting, we formulate three natural computational notions of manipulation, namely weak, opportunistic, and strong manipulation. We say that an extension of a partial order is viable if there exists a manipulative vote for that extension. We propose the following notions of manipulation when manipulators have incomplete information about the votes of other voters.

ACM Transactions on Algorithms

Studies in Microeconomics

Classical results in voting theory show that strategic manipulation by voters is inevitable if a ... more Classical results in voting theory show that strategic manipulation by voters is inevitable if a voting rule simultaneously satisfy certain desirable properties. Motivated by this, we study the relevant question of how often a voting rule is manipulable. It is well known that elections with a large number of voters are rarely manipulable under impartial culture (IC) assumption. However, the manipulability of voting rules when the number of candidates is large has hardly been addressed in the literature and our paper focuses on this problem. First, we propose two properties (1) asymptotic strategy-proofness and (2) asymptotic collusion-proofness, with respect to new voters, which makes the two notions more relevant from the perspective of computational problem of manipulation. In addition to IC, we explore a new culture of society where all score vectors of the candidates are equally likely. This new notion has its motivation in computational social choice and we call it impartial scores culture (ISC) assumption. We study asymptotic strategy-proofness and asymptotic collusion-proofness for plurality, veto, k-approval, and Borda voting rules under IC as well as ISC assumptions. Specifically, we prove bounds for the fraction of manipulable profiles when the number of candidates is large. Our results show that the size of the coalition and the tie-breaking rule play a crucial role in determining whether or not a voting rule satisfies the above two properties.

Theoretical Computer Science, 2017

ABSTRACT Bribery in elections is an important problem in computational social choice theory. Howe... more ABSTRACT Bribery in elections is an important problem in computational social choice theory. However, bribery with money is often illegal in elections. Motivated by this, we introduce the notion of frugal bribery and formulate two new pertinent computational problems which we call Frugal-bribery and Frugal- $bribery to capture bribery without money in elections. In the proposed model, the briber is frugal in nature and this is captured by her inability to bribe votes of a certain kind, namely, non-vulnerable votes. In the Frugal-bribery problem, the goal is to make a certain candidate win the election by changing only vulnerable votes. In the Frugal-{dollar}bribery problem, the vulnerable votes have prices and the goal is to make a certain candidate win the election by changing only vulnerable votes, subject to a budget constraint of the briber. We further formulate two natural variants of the Frugal-{dollar}bribery problem namely Uniform-frugal-{dollar}bribery and Nonuniform-frugal-{dollar}bribery where the prices of the vulnerable votes are, respectively, all the same or different. We study the computational complexity of the above problems for unweighted and weighted elections for several commonly used voting rules. We observe that, even if we have only a small number of candidates, the problems are intractable for all voting rules studied here for weighted elections, with the sole exception of the Frugal-bribery problem for the plurality voting rule. In contrast, we have polynomial time algorithms for the Frugal-bribery problem for plurality, veto, k-approval, k-veto, and plurality with runoff voting rules for unweighted elections. However, the Frugal-{dollar}bribery problem is intractable for all the voting rules studied here barring the plurality and the veto voting rules for unweighted elections.

Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems - PODS '16, 2016

Theoretical Computer Science, 2016

In the Possible Winner problem in computational social choice theory, we are given a set of parti... more In the Possible Winner problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the Possible Winner problem, with number of candidates as the parameter. However, the corresponding kernelization question is still open and in fact, has been mentioned as a key research challenge [Bredereck et al., 2014a]. In this paper, we settle this open question for many common voting rules. We show that the Possible Winner problem for maximin, Copeland, Bucklin, ranked pairs, and a class of scoring rules that include the Borda voting rule do not admit a polynomial kernel with the number of candidates as the parameter. We show however that the Coalitional Manipulation problem which is an important special case of the Possible Winner problem does admit a polynomial kernel for maximin, Copeland, ranked pairs, and a class of scoring rules that includes the Borda voting rule, when the number of manipulators is polynomial in the number of candidates. A significant conclusion of our work is that the Possible Winner problem is harder than the Coalitional Manipulation problem since the Coalitional Manipulation problem admits a polynomial kernel whereas the Possible Winner problem does not admit a polynomial kernel.

The Coalitional Manipulation (CM) problem has been studied extensively in the literature for many... more The Coalitional Manipulation (CM) problem has been studied extensively in the literature for many voting rules. The CM problem, however, has been studied only in the complete information setting, that is, when the manipulators know the votes of the non-manipulators. A more realistic scenario is an incomplete information setting where the manipulators do not know the exact votes of the non- manipulators but may have some partial knowledge of the votes. In this paper, we study a setting where the manipulators know a partial order for each voter that is consistent with the vote of that voter. In this setting, we introduce and study two natural computational problems - (1) Weak Manipulation (WM) problem where the manipulators wish to vote in a way that makes their preferred candidate win in at least one extension of the partial votes of the non-manipulators; (2) Strong Manipulation (SM) problem where the manipulators wish to vote in a way that makes their preferred candidate win in all ...

ABSTRACT Manipulation is a problem of fundamental importance in the context of voting rules in wh... more ABSTRACT Manipulation is a problem of fundamental importance in the context of voting rules in which the voters vote strategically instead of voting honestly to avoid selection of an alternative that is less preferred. The Gibbard-Satterthwaite theorem shows that there is no strategy-proof voting rule that simultaneously satisfies certain combinations of desirable properties. Researchers have attempted to get around the impossibility results in several ways such as domain restriction and computational hardness of manipulation, etc. However these approaches have been shown to have limitations. Since prevention of manipulation seems to be elusive, a natural research direction therefore is detection of manipulation. Motivated by this, we study detection of possible manipulators in an election. We formulate two pertinent computational problems - Coalitional Possible Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW). For several popular voting rules, we provide polynomial time algorithms for both the CPM and CPMW problems. For certain other voting rules, we show that these two problems are in NPC. A striking observation of our study is that detecting manipulation is surprisingly easy for a few well known voting rules. We then move on to weighted elections and show similar results.

ABSTRACT In the \textsc{Possible Winner} problem in computational voting theory, we are given a s... more ABSTRACT In the \textsc{Possible Winner} problem in computational voting theory, we are given a set of partial preferences and the problem is to determine whether or not a specified candidate could be made winner by extending the partial preferences to linear ones. Previous work has provided algorithms for this problem in the context of many common voting rules that are fixed parameter tractable with the number of candidates as the parameter. However, the corresponding kernelization questions are still open. In this paper, we show that the \textsc{possible winner} problem for maximin, Copeland, Bucklin, and ranked pairs voting rules does not admit a polynomial kernel with number of candidates as the parameter. We also show that the \textsc{coalitional manipulation} problem, an important special case of the \textsc{possible winner} problem, admits polynomial kernels for maximin, Copeland, and ranked pairs voting rules when the number of manipulators is constant.

Predicting the winner of an election is a favorite problem both for news media pundits and comput... more Predicting the winner of an election is a favorite problem both for news media pundits and computational social choice theorists. Since it is often infeasible to elicit the preferences of all the voters in a typical prediction scenario, a common algorithm used for winner prediction is to run the election on a small sample of randomly chosen votes and output the winner as the prediction. We analyze the performance of this algorithm for many common voting rules. More formally, we introduce the (ε, δ)-winner determination problem, where given an election on n voters and m candidates in which the margin of victory is at least εn votes, the goal is to determine the winner with probability at least 1−δ. The margin of victory of an election is the smallest number of votes that need to be modified in order to change the election winner. We show interesting lower and upper bounds on the number of samples needed to solve the (ε, δ)-winner determination problem for many common voting rules, including scoring rules, approval, maximin, Copeland, Bucklin, plurality with runoff, and single transferable vote. Moreover, the lower and upper bounds match for many common voting rules in a wide range of practically appealing scenarios.

Lecture Notes in Computer Science, 2014

Lecture Notes in Computer Science, 2010

Multipath bandwidth provisioning is one of the prime interest of next generation optical networks... more Multipath bandwidth provisioning is one of the prime interest of next generation optical networks. It is a policy to distribute the requested bandwidth in multiple link disjoint paths on the basis of some optimization function. It also helps to increase network throughput. By using backup path provisioning, we can meet availability requirement of service level agreement (SLA). But multipath bandwidth provisioning leads to problem like jitter which is the difference of delay between two paths. In this paper, we propose a dynamic multipath bandwidth provisioning scheme in telecom mesh network which takes both throughput and jitter into account. It also meets SLA requirement of incoming requests. Our provisioning scheme is dynamic in the sense that it allocates bandwidth for service requests that arrive periodically with no knowledge of future requests and hence requiring an online algorithm. Our algorithm uses 1:N protection scheme against restoration since only protection can guarant...