43 research outputs found
The Shield that Never Was: Societies with Single-Peaked Preferences are More Open to Manipulation and Control
Much work has been devoted, during the past twenty years, to using complexity
to protect elections from manipulation and control. Many results have been
obtained showing NP-hardness shields, and recently there has been much focus on
whether such worst-case hardness protections can be bypassed by frequently
correct heuristics or by approximations. This paper takes a very different
approach: We argue that when electorates follow the canonical political science
model of societal preferences the complexity shield never existed in the first
place. In particular, we show that for electorates having single-peaked
preferences, many existing NP-hardness results on manipulation and control
evaporate.Comment: 38 pages, 2 figure
Empirical Evaluation of Real World Tournaments
Computational Social Choice (ComSoc) is a rapidly developing field at the
intersection of computer science, economics, social choice, and political
science. The study of tournaments is fundamental to ComSoc and many results
have been published about tournament solution sets and reasoning in
tournaments. Theoretical results in ComSoc tend to be worst case and tell us
little about performance in practice. To this end we detail some experiments on
tournaments using real wold data from soccer and tennis. We make three main
contributions to the understanding of tournaments using real world data from
English Premier League, the German Bundesliga, and the ATP World Tour: (1) we
find that the NP-hard question of finding a seeding for which a given team can
win a tournament is easily solvable in real world instances, (2) using detailed
and principled methodology from statistical physics we show that our real world
data obeys a log-normal distribution; and (3) leveraging our log-normal
distribution result and using robust statistical methods, we show that the
popular Condorcet Random (CR) tournament model does not generate realistic
tournament data.Comment: 2 Figure
Computational Aspects of Multi-Winner Approval Voting
We study computational aspects of three prominent voting rules that use
approval ballots to elect multiple winners. These rules are satisfaction
approval voting, proportional approval voting, and reweighted approval voting.
We first show that computing the winner for proportional approval voting is
NP-hard, closing a long standing open problem. As none of the rules are
strategyproof, even for dichotomous preferences, we study various strategic
aspects of the rules. In particular, we examine the computational complexity of
computing a best response for both a single agent and a group of agents. In
many settings, we show that it is NP-hard for an agent or agents to compute how
best to vote given a fixed set of approval ballots from the other agents
Dominating Manipulations in Voting with Partial Information
We consider manipulation problems when the manipulator only has partial
information about the votes of the nonmanipulators. Such partial information is
described by an information set, which is the set of profiles of the
nonmanipulators that are indistinguishable to the manipulator. Given such an
information set, a dominating manipulation is a non-truthful vote that the
manipulator can cast which makes the winner at least as preferable (and
sometimes more preferable) as the winner when the manipulator votes truthfully.
When the manipulator has full information, computing whether or not there
exists a dominating manipulation is in P for many common voting rules (by known
results). We show that when the manipulator has no information, there is no
dominating manipulation for many common voting rules. When the manipulator's
information is represented by partial orders and only a small portion of the
preferences are unknown, computing a dominating manipulation is NP-hard for
many common voting rules. Our results thus throw light on whether we can
prevent strategic behavior by limiting information about the votes of other
voters.Comment: 7 pages by arxiv pdflatex, 1 figure. The 6-page version has the same
content and will be published in Proceedings of the Twenty-Fifth AAAI
Conference on Artificial Intelligence (AAAI-11
Detecting Possible Manipulators in Elections
Manipulation is a problem of fundamental importance in the context of voting
in which the voters exercise their votes strategically instead of voting
honestly to prevent selection of an alternative that is less preferred. The
Gibbard-Satterthwaite theorem shows that there is no strategy-proof voting rule
that simultaneously satisfies certain combinations of desirable properties.
Researchers have attempted to get around the impossibility results in several
ways such as domain restriction and computational hardness of manipulation.
However these approaches have been shown to have limitations. Since prevention
of manipulation seems to be elusive, an interesting research direction
therefore is detection of manipulation. Motivated by this, we initiate the
study of detection of possible manipulators in an election.
We formulate two pertinent computational problems - Coalitional Possible
Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW),
where a suspect group of voters is provided as input to compute whether they
can be a potential coalition of possible manipulators. In the absence of any
suspect group, we formulate two more computational problems namely Coalitional
Possible Manipulators Search (CPMS), and Coalitional Possible Manipulators
Search given Winner (CPMSW). We provide polynomial time algorithms for these
problems, for several popular voting rules. For a few other voting rules, we
show that these problems are in NP-complete. We observe that detecting
manipulation maybe easy even when manipulation is hard, as seen for example, in
the case of the Borda voting rule.Comment: Accepted in AAMAS 201