arXiv subjects

Y. Narahari

Publications and source records attributed to Y. Narahari.

At least 37 records · Page 2Linked to original sources

arXiv2017

Frugal Bribery in Voting

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.

cs.AI↗

arXiv2017

Cooperative Game Theoretic Solution Concepts for top-$k$ Problems

The problem of finding the $k$ most critical nodes, referred to as the $top\text{-}k$ problem, is a very important one in several contexts such as information diffusion and preference aggregation in social networks, clustering of data points, etc. It has been observed in the literature that the value allotted to a node by most of the popular cooperative game theoretic solution concepts, acts as a good measure of appropriateness of that node (or a data point) to be included in the $top\text{-}k$ set, by itself. However, in general, nodes having the highest $k$ values are not the desirable $top\text{-}k$ nodes, because the appropriateness of a node to be a part of the $top\text{-}k$ set depends on other nodes in the set. As this is not explicitly captured by cooperative game theoretic solution concepts, it is necessary to post-process the obtained values in order to output the suitable $top\text{-}k$ nodes. In this paper, we propose several such post-processing methods and give reasoning behind each of them, and also propose a standalone algorithm that combines cooperative game theoretic solution concepts with the popular greedy hill-climbing algorithm.

cs.SI↗

arXiv2016

An Iterative Transfer Learning Based Ensemble Technique for Automatic Short Answer Grading

Automatic short answer grading (ASAG) techniques are designed to automatically assess short answers to questions in natural language, having a length of a few words to a few sentences. Supervised ASAG techniques have been demonstrated to be effective but suffer from a couple of key practical limitations. They are greatly reliant on instructor provided model answers and need labeled training data in the form of graded student answers for every assessment task. To overcome these, in this paper, we introduce an ASAG technique with two novel features. We propose an iterative technique on an ensemble of (a) a text classifier of student answers and (b) a classifier using numeric features derived from various similarity measures with respect to model answers. Second, we employ canonical correlation analysis based transfer learning on a common feature representation to build the classifier ensemble for questions having no labelled data. The proposed technique handsomely beats all winning supervised entries on the SCIENTSBANK dataset from the Student Response Analysis task of SemEval 2013. Additionally, we demonstrate generalizability and benefits of the proposed technique through evaluation on multiple ASAG datasets from different subject topics and standards.

cs.CL↗

arXiv2016

Referral-Embedded Provision Point Mechanisms for Crowdfunding of Public Projects

Civic Crowdfunding is emerging as a popular means to mobilize funding from citizens for public projects. A popular mechanism deployed on civic crowdfunding platforms is a provision point mechanism, wherein, the total contributions must reach a predetermined threshold in order for the project to be provisioned (undertaken). Such a mechanism may have multiple equilibria; unfortunately, in many of these equilibria, the project is not funded even if it is highly valued among the agents. Recent work has proposed mechanisms with refund bonuses where the project gets funded in equilibrium if its net value is higher than a threshold among the agents who are aware of the crowdfunding effort. In this paper, we formalize the notion of social desirability of a public project and propose mechanisms which use the idea of referrals to expand the pool of participants and achieve an equilibrium in which the project gets funded if its net value exceeds a threshold among the entire agent population. We call this new class of mechanisms Referral-Embedded Provision Point Mechanisms (REPPM). We specifically propose two variants of REPPM and both these mechanisms have the remarkable property that, at equilibrium, referral bonuses are offered but there is no need for actual payment of these bonuses. We establish that any given agent's equilibrium strategy is to refer other agents and to contribute in proportion to the agent's true value for the project. By referring others to contribute, an agent can, in fact, reduce his equilibrium contribution. In our view, the proposed mechanisms will lead to an increase in the number of projects that are funded on civic crowdfunding platforms.

cs.GT↗

arXiv2016

Topic Model Based Multi-Label Classification from the Crowd

Multi-label classification is a common supervised machine learning problem where each instance is associated with multiple classes. The key challenge in this problem is learning the correlations between the classes. An additional challenge arises when the labels of the training instances are provided by noisy, heterogeneous crowdworkers with unknown qualities. We first assume labels from a perfect source and propose a novel topic model where the present as well as the absent classes generate the latent topics and hence the words. We non-trivially extend our topic model to the scenario where the labels are provided by noisy crowdworkers. Extensive experimentation on real world datasets reveals the superior performance of the proposed model. The proposed model learns the qualities of the annotators as well, even with minimal training data.

cs.LG↗

arXiv2016

A Robust UCB Scheme for Active Learning in Regression from Strategic Crowds

We study the problem of training an accurate linear regression model by procuring labels from multiple noisy crowd annotators, under a budget constraint. We propose a Bayesian model for linear regression in crowdsourcing and use variational inference for parameter estimation. To minimize the number of labels crowdsourced from the annotators, we adopt an active learning approach. In this specific context, we prove the equivalence of well-studied criteria of active learning like entropy minimization and expected error reduction. Interestingly, we observe that we can decouple the problems of identifying an optimal unlabeled instance and identifying an annotator to label it. We observe a useful connection between the multi-armed bandit framework and the annotator selection in active learning. Due to the nature of the distribution of the rewards on the arms, we use the Robust Upper Confidence Bound (UCB) scheme with truncated empirical mean estimator to solve the annotator selection problem. This yields provable guarantees on the regret. We further apply our model to the scenario where annotators are strategic and design suitable incentives to induce them to put in their best efforts.

cs.LG↗

arXiv2015

On Choosing Committees Based on Approval Votes in the Presence of Outliers

We study the computational complexity of committee selection problem for several approval-based voting rules in the presence of outliers. Our first result shows that outlier consideration makes committee selection problem intractable for approval, net approval, and minisum approval voting rules. We then study parameterized complexity of this problem with five natural parameters, namely the target score, the size of the committee (and its dual parameter, the number of candidates outside the committee), the number of outliers (and its dual parameter, the number of non-outliers). For net approval and minisum approval voting rules, we provide a dichotomous result, resolving the parameterized complexity of this problem for all subsets of five natural parameters considered (by showing either FPT or W[1]-hardness for all subsets of parameters). For the approval voting rule, we resolve the parameterized complexity of this problem for all subsets of parameters except one. We also study approximation algorithms for this problem. We show that there does not exist any alpha(.) factor approximation algorithm for approval and net approval voting rules, for any computable function alpha(.), unless P=NP. For the minisum voting rule, we provide a pseudopolynomial (1+eps) factor approximation algorithm.

cs.MA↗

arXiv2015

Dynamic Mechanism Design with Interdependent Valuations

We consider an infinite horizon dynamic mechanism design problem with interdependent valuations. In this setting the type of each agent is assumed to be evolving according to a first order Markov process and is independent of the types of other agents. However, the valuation of an agent can depend on the types of other agents, which makes the problem fall into an interdependent valuation setting. Designing truthful mechanisms in this setting is non-trivial in view of an impossibility result which says that for interdependent valuations, any efficient and ex-post incentive compatible mechanism must be a constant mechanism, even in a static setting. Mezzetti (2004) circumvents this problem by splitting the decisions of allocation and payment into two stages. However, Mezzetti's result is limited to a static setting and moreover in the second stage of that mechanism, agents are weakly indifferent about reporting their valuations truthfully. This paper provides a first attempt at designing a dynamic mechanism which is efficient, `strict' ex-post incentive compatible and ex-post individually rational in a setting with interdependent values and Markovian type evolution.

cs.GT↗

arXiv2015

An Incentive Compatible Multi-Armed-Bandit Crowdsourcing Mechanism with Quality Assurance

Consider a requester who wishes to crowdsource a series of identical binary labeling tasks to a pool of workers so as to achieve an assured accuracy for each task, in a cost optimal way. The workers are heterogeneous with unknown but fixed qualities and their costs are private. The problem is to select for each task an optimal subset of workers so that the outcome obtained from the selected workers guarantees a target accuracy level. The problem is a challenging one even in a non strategic setting since the accuracy of aggregated label depends on unknown qualities. We develop a novel multi-armed bandit (MAB) mechanism for solving this problem. First, we propose a framework, Assured Accuracy Bandit (AAB), which leads to an MAB algorithm, Constrained Confidence Bound for a Non Strategic setting (CCB-NS). We derive an upper bound on the number of time steps the algorithm chooses a sub-optimal set that depends on the target accuracy level and true qualities. A more challenging situation arises when the requester not only has to learn the qualities of the workers but also elicit their true costs. We modify the CCB-NS algorithm to obtain an adaptive exploration separated algorithm which we call { \em Constrained Confidence Bound for a Strategic setting (CCB-S)}. CCB-S algorithm produces an ex-post monotone allocation rule and thus can be transformed into an ex-post incentive compatible and ex-post individually rational mechanism that learns the qualities of the workers and guarantees a given target accuracy level in a cost optimal way. We provide a lower bound on the number of times any algorithm should select a sub-optimal set and we see that the lower bound matches our upper bound upto a constant factor. We provide insights on the practical implementation of this framework through an illustrative example and we show the efficacy of our algorithms through simulations.

cs.GT↗

arXiv2015

Estimating the Margin of Victory of an Election using Sampling

The margin of victory of an election is a useful measure to capture the robustness of an election outcome. It also plays a crucial role in determining the sample size of various algorithms in post election audit, polling etc. In this work, we present efficient sampling based algorithms for estimating the margin of victory of elections. More formally, we introduce the \textsc{$(c, ε, δ)$--Margin of Victory} problem, where given an election $\mathcal{E}$ on $n$ voters, the goal is to estimate the margin of victory $M(\mathcal{E})$ of $\mathcal{E}$ within an additive factor of $c MoV(\mathcal{E})+εn$. We study the \textsc{$(c, ε, δ)$--Margin of Victory} problem for many commonly used voting rules including scoring rules, approval, Bucklin, maximin, and Copeland$^α.$ We observe that even for the voting rules for which computing the margin of victory is NP-Hard, there may exist efficient sampling based algorithms, as observed in the cases of maximin and Copeland$^α$ voting rules.

cs.AI↗

arXiv2015

Manipulation is Harder with Incomplete Votes

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 possible extensions of the partial votes of the non-manipulators. We study the computational complexity of the WM and the SM problems for commonly used voting rules such as plurality, veto, k-approval, k-veto, maximin, Copeland, and Bucklin. Our key finding is that, barring a few exceptions, manipulation becomes a significantly harder problem in the setting of incomplete votes.

cs.AI↗

arXiv2015

An Optimal Bidimensional Multi-Armed Bandit Auction for Multi-unit Procurement

We study the problem of a buyer (aka auctioneer) who gains stochastic rewards by procuring multiple units of a service or item from a pool of heterogeneous strategic agents. The reward obtained for a single unit from an allocated agent depends on the inherent quality of the agent; the agent's quality is fixed but unknown. Each agent can only supply a limited number of units (capacity of the agent). The costs incurred per unit and capacities are private information of the agents. The auctioneer is required to elicit costs as well as capacities (making the mechanism design bidimensional) and further, learn the qualities of the agents as well, with a view to maximize her utility. Motivated by this, we design a bidimensional multi-armed bandit procurement auction that seeks to maximize the expected utility of the auctioneer subject to incentive compatibility and individual rationality while simultaneously learning the unknown qualities of the agents. We first assume that the qualities are known and propose an optimal, truthful mechanism 2D-OPT for the auctioneer to elicit costs and capacities. Next, in order to learn the qualities of the agents in addition, we provide sufficient conditions for a learning algorithm to be Bayesian incentive compatible and individually rational. We finally design a novel learning mechanism, 2D-UCB that is stochastic Bayesian incentive compatible and individually rational.

cs.GT↗

arXiv2015

Profit Maximizing Prior-free Multi-unit Procurement Auctions with Capacitated Sellers

In this paper, we derive bounds for profit maximizing prior-free procurement auctions where a buyer wishes to procure multiple units of a homogeneous item from n sellers who are strategic about their per unit valuation. The buyer earns the profit by reselling these units in an external consumer market. The paper looks at three scenarios of increasing complexity. First, we look at unit capacity sellers where per unit valuation is private information of each seller and the revenue curve is concave. For this setting, we define two benchmarks. We show that no randomized prior free auction can be constant competitive against any of these two benchmarks. However, for a lightly constrained benchmark we design a prior-free auction PEPA (Profit Extracting Procurement Auction) which is 4-competitive and we show this bound is tight. Second, we study a setting where the sellers have non-unit capacities that are common knowledge and derive similar results. In particular, we propose a prior free auction PEPAC (Profit Extracting Procurement Auction with Capacity) which is truthful for any concave revenue curve. Third, we obtain results in the inherently harder bi-dimensional case where per unit valuation as well as capacities are private information of the sellers. We show that PEPAC is truthful and constant competitive for the specific case of linear revenue curves. We believe that this paper represents the first set of results on single dimensional and bi-dimensional profit maximizing prior-free multi-unit procurement auctions.

cs.GT↗

arXiv2015

A Multi-phase Approach for Improving Information Diffusion in Social Networks

For maximizing influence spread in a social network, given a certain budget on the number of seed nodes, we investigate the effects of selecting and activating the seed nodes in multiple phases. In particular, we formulate an appropriate objective function for two-phase influence maximization under the independent cascade model, investigate its properties, and propose algorithms for determining the seed nodes in the two phases. We also study the problem of determining an optimal budget-split and delay between the two phases.

cs.SI↗

arXiv2015

Asymptotic Collusion-Proofness of Voting Rules: The Case of Large Number of Candidates

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.

cs.GT↗

arXiv2015

Detecting Possible Manipulators in Elections

Manipulation is a problem of fundamental importance in the context of voting in which the voters exercise their votes strategically instead of voting honestly to prevent 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. However these approaches have been shown to have limitations. Since prevention of manipulation seems to be elusive, an interesting research direction therefore is detection of manipulation. Motivated by this, we initiate the study of detection of possible manipulators in an election. We formulate two pertinent computational problems - Coalitional Possible Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW), where a suspect group of voters is provided as input to compute whether they can be a potential coalition of possible manipulators. In the absence of any suspect group, we formulate two more computational problems namely Coalitional Possible Manipulators Search (CPMS), and Coalitional Possible Manipulators Search given Winner (CPMSW). We provide polynomial time algorithms for these problems, for several popular voting rules. For a few other voting rules, we show that these problems are in NP-complete. We observe that detecting manipulation maybe easy even when manipulation is hard, as seen for example, in the case of the Borda voting rule.

cs.MA↗

arXiv2015

Kernelization Complexity of Possible Winner and Coalitional Manipulation Problems in Voting

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. 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.

cs.GT↗

arXiv2014

Sufficient Conditions for Formation of a Network Topology by Self-interested Agents

Networks such as organizational network of a global company play an important role in a variety of knowledge management and information diffusion tasks. The nodes in these networks correspond to individuals who are self-interested. The topology of these networks often plays a crucial role in deciding the ease and speed with which certain tasks can be accomplished using these networks. Consequently, growing a stable network having a certain topology is of interest. Motivated by this, we study the following important problem: given a certain desired network topology, under what conditions would best response (link addition/deletion) strategies played by self-interested agents lead to formation of a pairwise stable network with only that topology. We study this interesting reverse engineering problem by proposing a natural model of recursive network formation. In this model, nodes enter the network sequentially and the utility of a node captures principal determinants of network formation, namely (1) benefits from immediate neighbors, (2) costs of maintaining links with immediate neighbors, (3) benefits from indirect neighbors, (4) bridging benefits, and (5) network entry fee. Based on this model, we analyze relevant network topologies such as star graph, complete graph, bipartite Turan graph, and multiple stars with interconnected centers, and derive a set of sufficient conditions under which these topologies emerge as pairwise stable networks. We also study the social welfare properties of the above topologies.

cs.GT↗