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We consider spatial voting where candidates are located in the Euclidean $d$-dimensional space, and each voter ranks candidates based on their distance from the voter's ideal point. We explore the case where information about the location…
Separation logic and its variants can describe various properties on pointer programs. However, when it comes to properties on sequences, one may find it hard to formalize. To deal with properties on variable-length sequences and multilevel…
We introduce and study the property of orthogonal independence, a restricted additivity axiom applying when alternatives are orthogonal. The axiom requires that the preference for one marginal change over another should be maintained after…
The singular cubical homology theory for the category of quivers or digraphs can be constructed similarly to the classical singular homology theory for topological spaces. The case of digraphs and quivers differs from the topological case…
We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
The bribery problem in election has received considerable attention in the literature, upon which various algorithmic and complexity results have been obtained. It is thus natural to ask whether we can protect an election from potential…
We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…
We survey two key problems-Multi-Winner Determination and Hedonic Games in Computational Social Choice, with a special focus on their parameterized complexity, and propose some research challenges in the field.
We study the parameterized control complexity of fallback voting, a voting system that combines preference-based with approval voting. Electoral control is one of many different ways for an external agent to tamper with the outcome of an…
The integrity of elections is central to democratic systems. However, a myriad of malicious actors aspire to influence election outcomes for financial or political benefit. A common means to such ends is by manipulating perceptions of the…
Each voter $i \in I$ has $\alpha_i$ cards that (s)he distributes among the candidates $a \in A$ as a measure of approval. One (or several) candidate(s) who received the maximum number of cards is (are) elected. We provide polynomial…
The property of preserving the convexity and concavity of the Bernstein polynomial and of the B\'{e}zier curves is used to generate a method of approximating the reliability polynomial of a hammock network. The mutual behaviour of the…
How to design fair and (computationally) efficient voting rules is a central challenge in Computational Social Choice. In this paper, we aim at designing efficient algorithms for computing most equitable rules for large classes of…
Complexity theory is a useful tool to study computational issues surrounding the elicitation of preferences, as well as the strategic manipulation of elections aggregating together preferences of multiple agents. We study here the…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
We use the United States Supreme Court as an illuminative context in which to discuss three different spatial voting preference models: an instance of the widely used single-peaked preferences, and two models that are more novel in which…
Consider an undirected graph G, representing a social network, where each node is blue or red, corresponding to positive or negative opinion on a topic. In the voter model, in discrete time rounds, each node picks a neighbour uniformly at…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
Collective decision-making is vital for recent information and communications technologies. In our previous research, we mathematically derived conflict-free joint decision-making that optimally satisfies players' probabilistic preference…