Related papers: Complexity of and Algorithms for Borda Manipulatio…
We provide an overview of some recent progress on the complexity of election systems. The issues studied include the complexity of the winner, manipulation, bribery, and control problems.
We view voting rules as classifiers that assign a winner (a class) to a profile of voters' preferences (an instance). We propose to apply techniques from formal explainability, most notably abductive and contrastive explanations, to…
In a voting problem with a finite set of alternatives to choose from, we study the manipulation of tops-only rules. Since all non-dictatorial (onto) voting rules are manipulable when there are more than two alternatives and all preferences…
We study the complexity of determining a winning committee under the Chamberlin--Courant voting rule when voters' preferences are single-crossing on a line, or, more generally, on a median graph (this class of graphs includes, e.g., trees…
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…
We consider a two-round election model involving $m$ voters and $n$ candidates. Each voter is endowed with a strict preference list ranking the candidates. In the first round, the candidates are partitioned into two subsets, $A$ and $B$,…
We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…
We consider the approval-based model of elections, and undertake a computational study of voting rules which select committees whose size is not predetermined. While voting rules that output committees with a predetermined number of winning…
In this paper, we study the multi-robot task allocation problem where a group of robots needs to be allocated to a set of tasks so that the tasks can be finished optimally. One task may need more than one robot to finish it. Therefore the…
We study here several variants of the covariates fine balance problem where we generalize some of these problems and introduce a number of others. We present here a comprehensive complexity study of the covariates problems providing…
We consider election scenarios with incomplete information, a situation that arises often in practice. There are several models of incomplete information and accordingly, different notions of outcomes of such elections. In one well-studied…
Partisan gerrymandering poses a threat to democracy. Moreover, the complexity of the districting task may exceed human capacities. One potential solution is using computational models to automate the districting process by optimizing…
Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…
We present an approximation notion for NP-hard optimization problems represented by binary functions. We prove that (assuming P != NP) the new notion is strictly stronger than FPTAS, but strictly weaker than having a polynomial-time…
We consider a committee voting setting in which each voter approves of a subset of candidates and based on the approvals, a target number of candidates are selected. Aziz et al. (2015) proposed two representation axioms called justified…
Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…