9,437 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
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
Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results
A preference profile is single-peaked on a tree if the candidate set can be
equipped with a tree structure so that the preferences of each voter are
decreasing from their top candidate along all paths in the tree. This notion
was introduced by Demange (1982), and subsequently Trick (1989) described an
efficient algorithm for deciding if a given profile is single-peaked on a tree.
We study the complexity of multiwinner elections under several variants of the
Chamberlin-Courant rule for preferences single-peaked on trees. We show that
the egalitarian version of this problem admits a polynomial-time algorithm. For
the utilitarian version, we prove that winner determination remains NP-hard,
even for the Borda scoring function; however, a winning committee can be found
in polynomial time if either the number of leaves or the number of internal
vertices of the underlying tree is bounded by a constant. To benefit from these
positive results, we need a procedure that can determine whether a given
profile is single-peaked on a tree that has additional desirable properties
(such as, e.g., a small number of leaves). To address this challenge, we
develop a structural approach that enables us to compactly represent all trees
with respect to which a given profile is single-peaked. We show how to use this
representation to efficiently find the best tree for a given profile for use
with our winner determination algorithms: Given a profile, we can efficiently
find a tree with the minimum number of leaves, or a tree with the minimum
number of internal vertices among trees on which the profile is single-peaked.
We also consider several other optimization criteria for trees: for some we
obtain polynomial-time algorithms, while for others we show NP-hardness
results.Comment: 44 pages, extends works published at AAAI 2016 and IJCAI 201
Why a World State is Unavoidable in Planetary Defense: On Loopholes in the Vision of a Cosmopolitan Governance
The main claim of this chapter is that planetary defense against asteroids cannot be implemented under a decentralized model of democratic global governance, as espoused elsewhere in this book. All relevant indices point to the necessity of establishing a centralized global political authority with legitimate coercive powers. It remains to be seen, however, whether such a political system can be in any recognizable sense democratic. It seems unconvincing that planetary-wide physical-threat, all-comprehensive macrosecuritization, coupled with deep transformations of international law, global centralization of core decision-making powers, de-stigmatization of nuclear weapons and the like can proceed, succeed, and be implemented in a non-hierarchical international system where planetary defense constitutes only one regime among many, and where states basically remain the decisive actors. Although rationally and scientifically robust, the project suffers from oversimplification, as well as naivety with respect to how both international and domestic politics works. Among other topics, this chapter discusses problems associated with the rule of law and constituent powers, political representation and sources of legitimacy, conditions of multilevel collective action, or limits of theoretical idealization. The general message is that the planetary defense community needs to be more aware of the social and political context of its own enterprise
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