arXiv subjects

Palash Dey

Publications and source records attributed to Palash Dey.

At least 37 records · Page 2Linked to original sources

arXiv2023

Evaluating District-based Election Surveys with Synthetic Dirichlet Likelihood

In district-based multi-party elections, electors cast votes in their respective districts. In each district, the party with maximum votes wins the corresponding seat in the governing body. Election Surveys try to predict the election outcome (vote shares and seat shares of parties) by querying a random sample of electors. However, the survey results are often inconsistent with the actual results, which could be due to multiple reasons. The aim of this work is to estimate a posterior distribution over the possible outcomes of the election, given one or more survey results. This is achieved using a prior distribution over vote shares, election models to simulate the complete election from the vote share, and survey models to simulate survey results from a complete election. The desired posterior distribution over the space of possible outcomes is constructed using Synthetic Dirichlet Likelihoods, whose parameters are estimated from Monte Carlo sampling of elections using the election models. We further show the same approach can also use be used to evaluate the surveys - whether they were biased or not, based on the true outcome once it is known. Our work offers the first-ever probabilistic model to analyze district-based election surveys. We illustrate our approach with extensive experiments on real and simulated data of district-based political elections in India.

stat.ME↗

arXiv2023

Parameterized Aspects of Distinct Kemeny Rank Aggregation

The Kemeny method is one of the popular tools for rank aggregation. However, computing an optimal Kemeny ranking is NP-hard. Consequently, the computational task of finding a Kemeny ranking has been studied under the lens of parameterized complexity with respect to many parameters. We first present a comprehensive relationship, both theoretical and empirical, among these parameters. Further, we study the problem of computing all distinct Kemeny rankings under the lens of parameterized complexity. We consider the target Kemeny score, number of candidates, average distance of input rankings, maximum range of any candidate, and unanimity width as our parameters. For all these parameters, we already have FPT algorithms. We find that any desirable number of Kemeny rankings can also be found without substantial increase in running time. We also present FPT approximation algorithms for Kemeny rank aggregation with respect to these parameters.

cs.DS↗

arXiv2023

How Hard is Safe Bribery?

Bribery in an election is one of the well-studied control problems in computational social choice. In this paper, we propose and study the safe bribery problem. Here the goal of the briber is to ask the bribed voters to vote in such a way that the briber never prefers the original winner (of the unbribed election) more than the new winner, even if the bribed voters do not fully follow the briber's advice. Indeed, in many applications of bribery, campaigning for example, the briber often has limited control on whether the bribed voters eventually follow her recommendation and thus it is conceivable that the bribed voters can either partially or fully ignore the briber's recommendation. We provide a comprehensive complexity theoretic landscape of the safe bribery problem for many common voting rules in this paper.

cs.GT↗

arXiv2023

Optimal Referral Auction Design

The auction of a single indivisible item is one of the most celebrated problems in mechanism design with transfers. Despite its simplicity, it provides arguably the cleanest and most insightful results in the literature. When the information that the auction is running is available to every participant, Myerson [20] provided a seminal result to characterize the incentive-compatible auctions along with revenue optimality. However, such a result does not hold in an auction on a network, where the information of the auction is spread via the agents, and they need incentives to forward the information. In recent times, a few auctions (e.g., [13, 18]) were designed that appropriately incentivized the intermediate nodes on the network to promulgate the information to potentially more valuable bidders. In this paper, we provide a Myerson-like characterization of incentive-compatible auctions on a network and show that the currently known auctions fall within this class of randomized auctions. We then consider a special class called the referral auctions that are inspired by the multi-level marketing mechanisms [1, 6, 7] and obtain the structure of a revenue optimal referral auction for i.i.d. bidders. Through experiments, we show that even for non-i.i.d. bidders there exist auctions following this characterization that can provide a higher revenue than the currently known auctions on networks.

cs.GT↗

arXiv2023

Feature-based Individual Fairness in k-Clustering

Ensuring fairness in machine learning algorithms is a challenging and essential task. We consider the problem of clustering a set of points while satisfying fairness constraints. While there have been several attempts to capture group fairness in the $k$-clustering problem, fairness at an individual level is relatively less explored. We introduce a new notion of individual fairness in $k$-clustering based on features not necessarily used for clustering. We show that this problem is NP-hard and does not admit a constant factor approximation. Therefore, we design a randomized algorithm that guarantees approximation both in terms of minimizing the clustering distance objective and individual fairness under natural restrictions on the distance metric and fairness constraints. Finally, our experimental results against six competing baselines validate that our algorithm produces individually fairer clusters than the fairest baseline by 12.5% on average while also being less costly in terms of the clustering objective than the best baseline by 34.5% on average.

cs.LG↗

arXiv2022

Sampling-Based Winner Prediction in District-Based Elections

In a district-based election, we apply a voting rule $r$ to decide the winners in each district, and a candidate who wins in a maximum number of districts is the winner of the election. We present efficient sampling-based algorithms to predict the winner of such district-based election systems in this paper. When $r$ is plurality and the margin of victory is known to be at least $\varepsilon$ fraction of the total population, we present an algorithm to predict the winner. The sample complexity of our algorithm is $\mathcal{O}\left(\frac{1}{\varepsilon^4}\log \frac{1}{\varepsilon}\log\frac{1}δ\right)$. We complement this result by proving that any algorithm, from a natural class of algorithms, for predicting the winner in a district-based election when $r$ is plurality, must sample at least $Ω\left(\frac{1}{\varepsilon^4}\log\frac{1}δ\right)$ votes. We then extend this result to any voting rule $r$. Loosely speaking, we show that we can predict the winner of a district-based election with an extra overhead of $\mathcal{O}\left(\frac{1}{\varepsilon^2}\log\frac{1}δ\right)$ over the sample complexity of predicting the single-district winner under $r$. We further extend our algorithm for the case when the margin of victory is unknown, but we have only two candidates. We then consider the median voting rule when the set of preferences in each district is single-peaked. We show that the winner of a district-based election can be predicted with $\mathcal{O}\left(\frac{1}{\varepsilon^4}\log\frac{1}{\varepsilon}\log\frac{1}δ\right)$ samples even when the harmonious order in different districts can be different and even unknown. Finally, we also show some results for estimating the margin of victory of a district-based election within both additive and multiplicative error bounds.

cs.AI↗

arXiv2021

On Parameterized Complexity of Binary Networked Public Goods Game

In the Binary Networked Public Goods game, every player needs to decide if she participates in a public project whose utility is shared equally by the community. We study the problem of deciding if there exists a pure strategy Nash equilibrium (PSNE) in such games. The problem is already known to be NP-complete. We provide fine-grained analysis of this problem under the lens of parameterized complexity theory. We consider various natural graph parameters and show either W[1]-hardness or exhibit an FPT algorithm. We finally exhibit some special graph classes, for example path, cycle, bi-clique, complete graph, etc., which always have a PSNE if the utility function of the players are fully homogeneous.

cs.GT↗

arXiv2020

Network Robustness via Global k-cores

Network robustness is a measure a network's ability to survive adversarial attacks. But not all parts of a network are equal. K-cores, which are dense subgraphs, are known to capture some of the key properties of many real-life networks. Therefore, previous work has attempted to model network robustness via the stability of its k-core. However, these approaches account for a single core value and thus fail to encode a global network resilience measure. In this paper, we address this limitation by proposing a novel notion of network resilience that is defined over all cores. In particular, we evaluate the stability of the network under node removals with respect to each node's initial core. Our goal is to compute robustness via a combinatorial problem: find b most critical nodes to delete such that the number of nodes that fall from their initial cores is maximized. One of our contributions is showing that it is NP-hard to achieve any polynomial factor approximation of the given objective. We also present a fine-grained complexity analysis of this problem under the lens of parameterized complexity theory for several natural parameters. Moreover, we show two applications of our notion of robustness: measuring the evolution of species and characterizing networks arising from different domains.

cs.SI↗

arXiv2020

Local Distance Constrained Bribery in Voting

Studying complexity of various bribery problems has been one of the main research focus in computational social choice. In all the models of bribery studied so far, the briber has to pay every voter some amount of money depending on what the briber wants the voter to report and the briber has some budget at her disposal. Although these models successfully capture many real world applications, in many other scenarios, the voters may be unwilling to deviate too much from their true preferences. In this paper, we study the computational complexity of the problem of finding a preference profile which is as close to the true preference profile as possible and still achieves the briber's goal subject to budget constraints. We call this problem Optimal Bribery. We consider three important measures of distances, namely, swap distance, footrule distance, and maximum displacement distance, and resolve the complexity of the optimal bribery problem for many common voting rules. We show that the problem is polynomial time solvable for the plurality and veto voting rules for all the three measures of distance. On the other hand, we prove that the problem is NP-complete for a class of scoring rules which includes the Borda voting rule, maximin, Copeland$^α$ for any $α\in[0,1]$, and Bucklin voting rules for all the three measures of distance even when the distance allowed per voter is $1$ for the swap and maximum displacement distances and $2$ for the footrule distance even without the budget constraints (which corresponds to having an infinite budget). For the $k$-approval voting rule for any constant $k>1$ and the simplified Bucklin voting rule, we show that the problem is NP-complete for the swap distance even when the distance allowed is $2$ and for the footrule distance even when the distance allowed is $4$ even without the budget constraints.

cs.GT↗

arXiv2020

On Parameterized Complexity of Liquid Democracy

In liquid democracy, each voter either votes herself or delegates her vote to some other voter. This gives rise to what is called a delegation graph. To decide the voters who eventually votes along with the subset of voters whose votes they give, we need to resolve the cycles in the delegation graph. This gives rise to the Resolve Delegation problem where we need to find an acyclic sub-graph of the delegation graph such that the number of voters whose votes they give is bounded above by some integer λ. Putting a cap on the number of voters whose votes a voter gives enable the system designer restrict the power of any individual voter. The Resolve Delegation problem is already known to be NP-hard. In this paper we study the parameterized complexity of this problem. We show that Resolve Delegation is para-NP-hard with respect to parameters λ, number of sink nodes and the maximum degree of the delegation graph. We also show that Resolve Delegation is W[1]-hard even with respect to the treewidth of the delegation graph. We complement our negative results by exhibiting FPT algorithms with respect to some other parameters. We finally show that a related problem, which we call Resolve Fractional Delegation, is polynomial time solvable.

cs.GT↗

arXiv2020

Distance Restricted Manipulation in Voting

We introduce the notion of {\em Distance Restricted Manipulation}, where colluding manipulator(s) need to compute if there exist votes which make their preferred alternative win the election when their knowledge about the others' votes is a little inaccurate. We use the Kendall-Tau distance to model the manipulators' confidence in the non-manipulators' votes. To this end, we study this problem in two settings - one where the manipulators need to compute a manipulating vote that succeeds irrespective of perturbations in others' votes ({\em Distance Restricted Strong Manipulation}), and the second where the manipulators need to compute a manipulating vote that succeeds for at least one possible vote profile of the others ({\em Distance Restricted Weak Manipulation}). We show that {\em Distance Restricted Strong Manipulation} admits polynomial-time algorithms for every scoring rule, maximin, Bucklin, and simplified Bucklin voting rules for a single manipulator, and for the $k$-approval rule for any number of manipulators, but becomes intractable for the Copeland$^α$ voting rule for every $α\in[0,1]$ even for a single manipulator. In contrast, {\em Distance Restricted Weak Manipulation} is intractable for almost all the common voting rules, with the exception of the plurality rule. For a constant number of alternatives, we show that both the problems are polynomial-time solvable for every anonymous and efficient voting rule.

cs.GT↗

arXiv2020

On the complexity of Winner Verification and Candidate Winner for Multiwinner Voting Rules

The Chamberlin-Courant and Monroe rules are fundamental and well-studied rules in the literature of multi-winner elections. The problem of determining if there exists a committee of size k that has a Chamberlin-Courant (respectively, Monroe) score of at most r is known to be NP-complete. We consider the following natural problems in this setting: a) given a committee S of size k as input, is it an optimal k-sized committee, and b) given a candidate c and a committee size k, does there exist an optimal k-sized committee that contains c? In this work, we resolve the complexity of both problems for the Chamberlin-Courant and Monroe voting rules in the settings of rankings as well as approval ballots. We show that verifying if a given committee is optimal is coNP-complete whilst the latter problem is complete for $Θ_{2}^{P}$. We also demonstrate efficient algorithms for the second problem when the input consists of single-peaked rankings. Our contribution fills an essential gap in the literature for these important multi-winner rules.

cs.DS↗

arXiv2020

Manipulating Node Similarity Measures in Networks

Node similarity measures quantify how similar a pair of nodes are in a network. These similarity measures turn out to be an important fundamental tool for many real world applications such as link prediction in networks, recommender systems etc. An important class of similarity measures are local similarity measures. Two nodes are considered similar under local similarity measures if they have large overlap between their neighboring set of nodes. Manipulating node similarity measures via removing edges is an important problem. This type of manipulation, for example, hinders effectiveness of link prediction in terrorists networks. Fortunately, all the popular computational problems formulated around manipulating similarity measures turn out to be NP-hard. We, in this paper, provide fine grained complexity results of these problems through the lens of parameterized complexity. In particular, we show that some of these problems are fixed parameter tractable (FPT) with respect to various natural parameters whereas other problems remain intractable W[1]-hard and W[2]-hard in particular). Finally we show the effectiveness of our proposed FPT algorithms on real world datasets as well as synthetic networks generated using Barabasi-Albert and Erdos-Renyi models.

cs.SI↗

arXiv2019

Minimizing Margin of Victory for Fair Political and Educational Districting

In many practical scenarios, a population is divided into disjoint groups for better administration, e.g., electorates into political districts, employees into departments, students into school districts, and so on. However, grouping people arbitrarily may lead to biased partitions, raising concerns of gerrymandering in political districting, racial segregation in schools, etc. To counter such issues, in this paper, we conceptualize such problems in a voting scenario, and propose FAIR DISTRICTING problem to divide a given set of people having preference over candidates into k groups such that the maximum margin of victory of any group is minimized. We also propose the FAIR CONNECTED DISTRICTING problem which additionally requires each group to be connected. We show that the FAIR DISTRICTING problem is NP-complete for plurality voting even if we have only 3 candidates but admits polynomial time algorithms if we assume k to be some constant or everyone can be moved to any group. In contrast, we show that the FAIR CONNECTED DISTRICTING problem is NP-complete for plurality voting even if we have only 2 candidates and k = 2. Finally, we propose heuristic algorithms for both the problems and show their effectiveness in UK political districting and in lowering racial segregation in public schools in the US.

cs.SI↗

arXiv2019

Gerrymandering: A Briber's Perspective

We initiate the study of bribery problem in the context of gerrymandering and reverse gerrymandering. In our most general problem, the input is a set of voters having votes over a set of alternatives, a graph on the voters, a partition of voters into connected districts, cost of every voter for changing her district, a budget for the briber, and a favorite alternative of the briber. The briber needs to compute if the given partition can be modified so that (i) the favorite alternative of the briber wins the resulting election, (ii) the modification is budget feasible, and (iii) every new district is connected. We study four natural variants of the above problem -- the graph on voter being arbitrary vs complete graph (corresponds to removing connectedness requirement for districts) and the cost of bribing every voter being uniform vs non-uniform. We show that all the four problems are NP-complete even under quite restrictive scenarios. Hence our results show that district based elections are quite resistant under this new kind of electoral attack. We complement our hardness results with polynomial time algorithms in some other cases.

cs.GT↗

arXiv2019

A Parameterized Perspective on Protecting Elections

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 outcome 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.

cs.MA↗

arXiv2019

Covert Networks: How Hard is It to Hide?

Covert networks are social networks that often consist of harmful users. Social Network Analysis (SNA) has played an important role in reducing criminal activities (e.g., counter terrorism) via detecting the influential users in such networks. There are various popular measures to quantify how influential or central any vertex is in a network. As expected, strategic and influential miscreants in covert networks would try to hide herself and her partners (called {\em leaders}) from being detected via these measures by introducing new edges. Waniek et al. show that the corresponding computational problem, called Hiding Leader, is NP-Complete for the degree and closeness centrality measures. We study the popular core centrality measure and show that the problem is NP-Complete even when the core centrality of every leader is only $3$. On the contrary, we prove that the problem becomes polynomial time solvable for the degree centrality measure if the degree of every leader is bounded above by any constant. We then focus on the optimization version of the problem and show that the Hiding Leader problem admits a $2$ factor approximation algorithm for the degree centrality measure. We complement it by proving that one cannot hope to have any $(2-\varepsilon)$ factor approximation algorithm for any constant $\varepsilon>0$ unless there is a $\varepsilon/2$ factor polynomial time algorithm for the Densest $k$-Subgraph problem which would be considered a significant breakthrough.

cs.SI↗

arXiv2019

Testing Preferential Domains Using Sampling

A preferential domain is a collection of sets of preferences which are linear orders over a set of alternatives. These domains have been studied extensively in social choice theory due to both its practical importance and theoretical elegance. Examples of some extensively studied preferential domains include single peaked, single crossing, Euclidean, etc. In this paper, we study the sample complexity of testing whether a given preference profile is close to some specific domain. We consider two notions of closeness: (a) closeness via preferences, and (b) closeness via alternatives. We further explore the effect of assuming that the {\em outlier} preferences/alternatives to be random (instead of arbitrary) on the sample complexity of the testing problem. In most cases, we show that the above testing problem can be solved with high probability for all commonly used domains by observing only a small number of samples (independent of the number of preferences, $n$, and often the number of alternatives, $m$). In the remaining few cases, we prove either impossibility results or $Ω(n)$ lower bound on the sample complexity. We complement our theoretical findings with extensive simulations to figure out the actual constant factors of our asymptotic sample complexity bounds.

cs.GT↗