Related papers: The Smoothed Complexity of Computing Kemeny and Sl…
The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus).…
The computational complexity of winner determination is a classical and important problem in computational social choice. Previous work based on worst-case analysis has established NP-hardness of winner determination for some classic voting…
The computational study of elections generally assumes that the preferences of the electorate come in as a list of votes. Depending on the context, it may be much more natural to represent the list succinctly, as the distinct votes of the…
The assumption that voters' preferences share some common structure is a standard way to circumvent NP-hardness results in social choice problems. While the Kemeny ranking problem is NP-hard in the general case, it is known to become easy…
The Possible-Winner problem asks, given an election where the voters' preferences over the set of candidates is partially specified, whether a distinguished candidate can become a winner. In this work, we consider the computational…
Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and AvgP, respectively. While…
An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the…
Smoothed analysis is a framework for analyzing the complexity of an algorithm, acting as a bridge between average and worst-case behaviour. For example, Quicksort and the Simplex algorithm are widely used in practical applications, despite…
We propose a unifying framework for smoothed analysis of combinatorial local optimization problems, and show how a diverse selection of problems within the complexity class PLS can be cast within this model. This abstraction allows us to…
A canonical problem in social choice is how to aggregate ranked votes: given $n$ voters' rankings over $m$ candidates, what voting rule $f$ should we use to aggregate these votes into a single winner? One standard method for comparing…
Rank aggregation is an essential approach for aggregating the preferences of multiple agents. One rule of particular interest is the Kemeny rule, which maximises the number of pairwise agreements between the final ranking and the existing…
We develop a framework that leverages the smoothed complexity analysis by Spielman and Teng to circumvent paradoxes and impossibility theorems in social choice, motivated by modern applications of social choice powered by AI and ML. For…
To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings,…
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…
The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are…
Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We…
The important Kemeny problem, which consists of computing median consensus rankings of an election with respect to the Kemeny voting rule, admits important applications in biology and computational social choice and was generalized recently…
Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a…
Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We…
When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s).…