95 research outputs found
How Hard Is It to Control an Election by Breaking Ties?
We study the computational complexity of controlling the result of an
election by breaking ties strategically. This problem is equivalent to the
problem of deciding the winner of an election under parallel universes
tie-breaking. When the chair of the election is only asked to break ties to
choose between one of the co-winners, the problem is trivially easy. However,
in multi-round elections, we prove that it can be NP-hard for the chair to
compute how to break ties to ensure a given result. Additionally, we show that
the form of the tie-breaking function can increase the opportunities for
control. Indeed, we prove that it can be NP-hard to control an election by
breaking ties even with a two-stage voting rule.Comment: Revised and expanded version including longer proofs and additional
result
Global SPACING Constraint (Technical Report)
We propose a new global SPACING constraint that is useful in modeling events
that are distributed over time, like learning units scheduled over a study
program or repeated patterns in music compositions. First, we investigate
theoretical properties of the constraint and identify tractable special cases.
We propose efficient DC filtering algorithms for these cases. Then, we
experimentally evaluate performance of the proposed algorithms on a music
composition problem and demonstrate that our filtering algorithms outperform
the state-of-the-art approach for solving this problem
Combining Voting Rules Together
We propose a simple method for combining together voting rules that performs
a run-off between the different winners of each voting rule. We prove that this
combinator has several good properties. For instance, even if just one of the
base voting rules has a desirable property like Condorcet consistency, the
combination inherits this property. In addition, we prove that combining voting
rules together in this way can make finding a manipulation more computationally
difficult. Finally, we study the impact of this combinator on approximation
methods that find close to optimal manipulations
Abduction-Based Explanations for Machine Learning Models
The growing range of applications of Machine Learning (ML) in a multitude of
settings motivates the ability of computing small explanations for predictions
made. Small explanations are generally accepted as easier for human decision
makers to understand. Most earlier work on computing explanations is based on
heuristic approaches, providing no guarantees of quality, in terms of how close
such solutions are from cardinality- or subset-minimal explanations. This paper
develops a constraint-agnostic solution for computing explanations for any ML
model. The proposed solution exploits abductive reasoning, and imposes the
requirement that the ML model can be represented as sets of constraints using
some target constraint reasoning system for which the decision problem can be
answered with some oracle. The experimental results, obtained on well-known
datasets, validate the scalability of the proposed approach as well as the
quality of the computed solutions
Complexity of and Algorithms for Borda Manipulation
We prove that it is NP-hard for a coalition of two manipulators to compute
how to manipulate the Borda voting rule. This resolves one of the last open
problems in the computational complexity of manipulating common voting rules.
Because of this NP-hardness, we treat computing a manipulation as an
approximation problem where we try to minimize the number of manipulators.
Based on ideas from bin packing and multiprocessor scheduling, we propose two
new approximation methods to compute manipulations of the Borda rule.
Experiments show that these methods significantly outperform the previous best
known %existing approximation method. We are able to find optimal manipulations
in almost all the randomly generated elections tested. Our results suggest
that, whilst computing a manipulation of the Borda rule by a coalition is
NP-hard, computational complexity may provide only a weak barrier against
manipulation in practice
- …