792 research outputs found
Resolving the Complexity of Some Fundamental Problems in Computational Social Choice
This thesis is in the area called computational social choice which is an
intersection area of algorithms and social choice theory.Comment: Ph.D. Thesi
Computational aspects of voting: a literature survey
Preference aggregation is a topic of study in different fields such as philosophy, mathematics, economics and political science. Recently, computational aspects of preference aggregation have gained especial attention and “computational politics” has emerged as a marked line of research in computer science with a clear concentration on voting protocols. The field of voting systems, rooted in social choice theory, has expanded notably in both depth and breadth in the last few decades. A significant amount of this growth comes from studies concerning the computational aspects of voting systems. This thesis comprehensively reviews the work on voting systems (from a computing perspective) by listing, classifying and comparing the results obtained by different researchers in the field. This survey covers a wide range of new and historical results yet provides a profound commentary on related work as individual studies and in relation to other related work and to the field in general. The deliverables serve as an overview where students and novice researchers in the field can start and also as a depository that can be referred to when searching for specific results. A comprehensive literature survey of the computational aspects of voting is a task that has not been undertaken yet and is initially realized here. Part of this research was dedicated to creating a web-depository that contains material and references related to the topic based on the survey. The purpose was to create a dynamic version of the survey that can be updated with latest findings and as an online practical reference
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
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
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
Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem
This paper provides a general framework to explore the possibility of agenda
manipulation-proof and proper consensus-based preference aggregation rules, so
powerfully called in doubt by a disputable if widely shared understanding of
Arrow's `general possibility theorem'. We consider two alternative versions of
agenda manipulation-proofness for social welfare functions, that are
distinguished by `parallel' vs. `sequential' execution of agenda formation and
preference elicitation, respectively. Under the `parallel' version, it is shown
that a large class of anonymous and idempotent social welfare functions that
satisfy both agenda manipulation-proofness and strategy-proofness on a natural
domain of single-peaked `meta-preferences' induced by arbitrary total
preference preorders are indeed available. It is only under the second,
`sequential' version that agenda manipulation-proofness on the same natural
domain of single-peaked `meta-preferences' is in fact shown to be tightly
related to the classic Arrowian `independence of irrelevant alternatives' (IIA)
for social welfare functions. In particular, it is shown that using IIA to
secure such `sequential' version of agenda manipulation-proofness and combining
it with a very minimal requirement of distributed responsiveness results in a
characterization of the `global stalemate' social welfare function, the
constant function which invariably selects universal social indifference. It is
also argued that, altogether, the foregoing results provide new significant
insights concerning the actual content and the constructive implications of
Arrow's `general possibility theorem' from a mechanism-design perspective
Preference Learning
This report documents the program and the outcomes of Dagstuhl Seminar 14101 “Preference Learning”. Preferences have recently received considerable attention in disciplines such as machine learning, knowledge discovery, information retrieval, statistics, social choice theory, multiple criteria decision making, decision under risk and uncertainty, operations research, and others. The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies
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