18 research outputs found
Eliminating the Weakest Link: Making Manipulation Intractable?
Successive elimination of candidates is often a route to making manipulation
intractable to compute. We prove that eliminating candidates does not
necessarily increase the computational complexity of manipulation. However, for
many voting rules used in practice, the computational complexity increases. For
example, it is already known that it is NP-hard to compute how a single voter
can manipulate the result of single transferable voting (the elimination
version of plurality voting). We show here that it is NP-hard to compute how a
single voter can manipulate the result of the elimination version of veto
voting, of the closely related Coombs' rule, and of the elimination versions of
a general class of scoring rules.Comment: To appear in Proceedings of Twenty-Sixth Conference on Artificial
Intelligence (AAAI-12
Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges
Computational Social Choice is an interdisciplinary research area involving
Economics, Political Science, and Social Science on the one side, and
Mathematics and Computer Science (including Artificial Intelligence and
Multiagent Systems) on the other side. Typical computational problems studied
in this field include the vulnerability of voting procedures against attacks,
or preference aggregation in multi-agent systems. Parameterized Algorithmics is
a subfield of Theoretical Computer Science seeking to exploit meaningful
problem-specific parameters in order to identify tractable special cases of in
general computationally hard problems. In this paper, we propose nine of our
favorite research challenges concerning the parameterized complexity of
problems appearing in this context
A Smooth Transition from Powerlessness to Absolute Power
We study the phase transition of the coalitional manipulation problem for
generalized scoring rules. Previously it has been shown that, under some
conditions on the distribution of votes, if the number of manipulators is
, where is the number of voters, then the probability that a
random profile is manipulable by the coalition goes to zero as the number of
voters goes to infinity, whereas if the number of manipulators is
, then the probability that a random profile is manipulable
goes to one. Here we consider the critical window, where a coalition has size
, and we show that as goes from zero to infinity, the limiting
probability that a random profile is manipulable goes from zero to one in a
smooth fashion, i.e., there is a smooth phase transition between the two
regimes. This result analytically validates recent empirical results, and
suggests that deciding the coalitional manipulation problem may be of limited
computational hardness in practice.Comment: 22 pages; v2 contains minor changes and corrections; v3 contains
minor changes after comments of reviewer