65 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
The Complexity of Manipulative Attacks in Nearly Single-Peaked Electorates
Many electoral bribery, control, and manipulation problems (which we will
refer to in general as "manipulative actions" problems) are NP-hard in the
general case. It has recently been noted that many of these problems fall into
polynomial time if the electorate is single-peaked (i.e., is polarized along
some axis/issue). However, real-world electorates are not truly single-peaked.
There are usually some mavericks, and so real-world electorates tend to merely
be nearly single-peaked. This paper studies the complexity of
manipulative-action algorithms for elections over nearly single-peaked
electorates, for various notions of nearness and various election systems. We
provide instances where even one maverick jumps the manipulative-action
complexity up to \np-hardness, but we also provide many instances where a
reasonable number of mavericks can be tolerated without increasing the
manipulative-action complexity.Comment: 35 pages, also appears as URCS-TR-2011-96
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
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
Complexity of control of Borda count elections
In this thesis, we discuss some existing and new results relating to computational aspects of voting. In particular, we consider, apparently for the first time, the computational complexity of the application of certain types of control to the Borda count voting system. We use control in the formal sense of attempts by an election\u27s administrator to make a specific candidate win or lose by various means. We consider control problems for weighted elections, as well as for unweighted elections with voter preferences input both individually and in succinct representation
Towards a Dichotomy for the Possible Winner Problem in Elections Based on Scoring Rules
To make a joint decision, agents (or voters) are often required to provide
their preferences as linear orders. To determine a winner, the given linear
orders can be aggregated according to a voting protocol. However, in realistic
settings, the voters may often only provide partial orders. This directly leads
to the Possible Winner problem that asks, given a set of partial votes, whether
a distinguished candidate can still become a winner. In this work, we consider
the computational complexity of Possible Winner for the broad class of voting
protocols defined by scoring rules. A scoring rule provides a score value for
every position which a candidate can have in a linear order. Prominent examples
include plurality, k-approval, and Borda. Generalizing previous NP-hardness
results for some special cases, we settle the computational complexity for all
but one scoring rule. More precisely, for an unbounded number of candidates and
unweighted voters, we show that Possible Winner is NP-complete for all pure
scoring rules except plurality, veto, and the scoring rule defined by the
scoring vector (2,1,...,1,0), while it is solvable in polynomial time for
plurality and veto.Comment: minor changes and updates; accepted for publication in JCSS, online
version available
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
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