116 research outputs found
Computational Aspects of Nearly Single-Peaked Electorates
Manipulation, bribery, and control are well-studied ways of changing the
outcome of an election. Many voting rules are, in the general case,
computationally resistant to some of these manipulative actions. However when
restricted to single-peaked electorates, these rules suddenly become easy to
manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra studied the
computational complexity of strategic behavior in nearly single-peaked
electorates. These are electorates that are not single-peaked but close to it
according to some distance measure.
In this paper we introduce several new distance measures regarding
single-peakedness. We prove that determining whether a given profile is nearly
single-peaked is NP-complete in many cases. For one case we present a
polynomial-time algorithm. In case the single-peaked axis is given, we show
that determining the distance is always possible in polynomial time.
Furthermore, we explore the relations between the new notions introduced in
this paper and existing notions from the literature.Comment: Published in the Journal of Artificial Intelligence Research (JAIR).
A short version of this paper appeared in the proceedings of the
Twenty-Seventh AAAI Conference on Artificial Intelligence (AAAI 2013). An
even earlier version appeared in the proceedings of the Fourth International
Workshop on Computational Social Choice 2012 (COMSOC 2012
Reinstating Combinatorial Protections for Manipulation and Bribery in Single-Peaked and Nearly Single-Peaked Electorates
Understanding when and how computational complexity can be used to protect
elections against different manipulative actions has been a highly active
research area over the past two decades. A recent body of work, however, has
shown that many of the NP-hardness shields, previously obtained, vanish when
the electorate has single-peaked or nearly single-peaked preferences. In light
of these results, we investigate whether it is possible to reimpose NP-hardness
shields for such electorates by allowing the voters to specify partial
preferences instead of insisting they cast complete ballots. In particular, we
show that in single-peaked and nearly single-peaked electorates, if voters are
allowed to submit top-truncated ballots, then the complexity of manipulation
and bribery for many voting rules increases from being in P to being
NP-complete.Comment: 28 pages; A shorter version of this paper will appear at the 30th
AAAI Conference on Artificial Intelligence (AAAI-16
Testing Top Monotonicity
Top monotonicity is a relaxation of various well-known domain restrictions
such as single-peaked and single-crossing for which negative impossibility
results are circumvented and for which the median-voter theorem still holds. We
examine the problem of testing top monotonicity and present a characterization
of top monotonicity with respect to non-betweenness constraints. We then extend
the definition of top monotonicity to partial orders and show that testing top
monotonicity of partial orders is NP-complete
Structure in Dichotomous Preferences
Many hard computational social choice problems are known to become tractable
when voters' preferences belong to a restricted domain, such as those of
single-peaked or single-crossing preferences. However, to date, all algorithmic
results of this type have been obtained for the setting where each voter's
preference list is a total order of candidates. The goal of this paper is to
extend this line of research to the setting where voters' preferences are
dichotomous, i.e., each voter approves a subset of candidates and disapproves
the remaining candidates. We propose several analogues of the notions of
single-peaked and single-crossing preferences for dichotomous profiles and
investigate the relationships among them. We then demonstrate that for some of
these notions the respective restricted domains admit efficient algorithms for
computationally hard approval-based multi-winner rules.Comment: A preliminary version appeared in the proceedings of IJCAI 2015, the
International Joint Conference on Artificial Intelligenc
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
Are there any nicely structured preference~profiles~nearby?
We investigate the problem of deciding whether a given preference profile is
close to having a certain nice structure, as for instance single-peaked,
single-caved, single-crossing, value-restricted, best-restricted,
worst-restricted, medium-restricted, or group-separable profiles. We measure
this distance by the number of voters or alternatives that have to be deleted
to make the profile a nicely structured one. Our results classify the problem
variants with respect to their computational complexity, and draw a clear line
between computationally tractable (polynomial-time solvable) and
computationally intractable (NP-hard) questions
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
The Complexity of Fully Proportional Representation for Single-Crossing Electorates
We study the complexity of winner determination in single-crossing elections
under two classic fully proportional representation
rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for
these rules is known to be NP-hard for unrestricted preferences. We show that
for single-crossing preferences this problem admits a polynomial-time algorithm
for Chamberlin--Courant's rule, but remains NP-hard for Monroe's rule. Our
algorithm for Chamberlin--Courant's rule can be modified to work for elections
with bounded single-crossing width. To circumvent the hardness result for
Monroe's rule, we consider single-crossing elections that satisfy an additional
constraint, namely, ones where each candidate is ranked first by at least one
voter (such elections are called narcissistic). For single-crossing
narcissistic elections, we provide an efficient algorithm for the egalitarian
version of Monroe's rule.Comment: 23 page
Election Manipulation in Social Networks with Single-Peaked Agents
Several elections run in the last years have been characterized by attempts
to manipulate the result of the election through the diffusion of fake or
malicious news over social networks. This problem has been recognized as a
critical issue for the robustness of our democracy. Analyzing and understanding
how such manipulations may occur is crucial to the design of effective
countermeasures to these practices.
Many studies have observed that, in general, to design an optimal
manipulation is usually a computationally hard task. Nevertheless, literature
on bribery in voting and election manipulation has frequently observed that
most hardness results melt down when one focuses on the setting of (nearly)
single-peaked agents, i.e., when each voter has a preferred candidate (usually,
the one closer to her own belief) and preferences of remaining candidates are
inversely proportional to the distance between the candidate position and the
voter's belief. Unfortunately, no such analysis has been done for election
manipulations run in social networks.
In this work, we try to close this gap: specifically, we consider a setting
for election manipulation that naturally raises (nearly) single-peaked
preferences, and we evaluate the complexity of election manipulation problem in
this setting: while most of the hardness and approximation results still hold,
we will show that single-peaked preferences allow to design simple, efficient
and effective heuristics for election manipulation
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