749 research outputs found
The Complexity of Online Manipulation of Sequential Elections
Most work on manipulation assumes that all preferences are known to the
manipulators. However, in many settings elections are open and sequential, and
manipulators may know the already cast votes but may not know the future votes.
We introduce a framework, in which manipulators can see the past votes but not
the future ones, to model online coalitional manipulation of sequential
elections, and we show that in this setting manipulation can be extremely
complex even for election systems with simple winner problems. Yet we also show
that for some of the most important election systems such manipulation is
simple in certain settings. This suggests that when using sequential voting,
one should pay great attention to the details of the setting in choosing one's
voting rule. Among the highlights of our classifications are: We show that,
depending on the size of the manipulative coalition, the online manipulation
problem can be complete for each level of the polynomial hierarchy or even for
PSPACE. We obtain the most dramatic contrast to date between the
nonunique-winner and unique-winner models: Online weighted manipulation for
plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive
case) and NP-hard (destructive case) in the unique-winner model. And we obtain
what to the best of our knowledge are the first P^NP[1]-completeness and
P^NP-completeness results in the field of computational social choice, in
particular proving such completeness for, respectively, the complexity of
3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition
manipulation of veto elections.Comment: 24 page
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
On the Exact Amount of Missing Information that Makes Finding Possible Winners Hard
We consider election scenarios with incomplete information, a situation that arises often in practice. There are several models of incomplete information and accordingly, different notions of outcomes of such elections. In one well-studied model of incompleteness, the votes are given by partial orders over the candidates. In this context we can frame the problem of finding a possible winner, which involves determining whether a given candidate wins in at least one completion of a given set of partial votes for a specific voting rule.
The Possible Winner problem is well-known to be NP-Complete in general, and it is in fact known to be NP-Complete for several voting rules where the number of undetermined pairs in every vote is bounded only by some constant. In this paper, we address the question of determining precisely the smallest number of undetermined pairs for which the Possible Winner problem remains NP-Complete. In particular, we find the exact values of t for which the Possible Winner problem transitions to being NP-Complete from being in P, where t is the maximum number of undetermined pairs in every vote. We demonstrate tight results for a broad subclass of scoring rules which includes all the commonly used scoring rules (such as plurality, veto, Borda, and k-approval), Copeland^alpha for every alpha in [0,1], maximin, and Bucklin voting rules. A somewhat surprising aspect of our results is that for many of these rules, the Possible Winner problem turns out to be hard even if every vote has at most one undetermined pair of candidates
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
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
Resistance to bribery when aggregating soft constraints
Abstract We consider a multi-agent scenario, where the preferences of several agents are modelled via soft constraint problems and need to be aggregated to compute a single "socially optimal" solution. We study the resistance of various ways to compute such a solution to influence the result, such as those based on the notion of bribery. In doing this, we link the cost of bribing an agent to the effort needed by the agent to make a certain solution optimal, by only changing preferences associated to parts of the solution. This leads to the definition of four notions of distance from optimality of a solution in a soft constraint problem. The notions differ on the amount of information considered when evaluating the effort
Robust Draws in Balanced Knockout Tournaments
Balanced knockout tournaments are ubiquitous in sports competitions and are
also used in decision-making and elections. The traditional computational
question, that asks to compute a draw (optimal draw) that maximizes the winning
probability for a distinguished player, has received a lot of attention.
Previous works consider the problem where the pairwise winning probabilities
are known precisely, while we study how robust is the winning probability with
respect to small errors in the pairwise winning probabilities. First, we
present several illuminating examples to establish: (a)~there exist
deterministic tournaments (where the pairwise winning probabilities are~0 or~1)
where one optimal draw is much more robust than the other; and (b)~in general,
there exist tournaments with slightly suboptimal draws that are more robust
than all the optimal draws. The above examples motivate the study of the
computational problem of robust draws that guarantee a specified winning
probability. Second, we present a polynomial-time algorithm for approximating
the robustness of a draw for sufficiently small errors in pairwise winning
probabilities, and obtain that the stated computational problem is NP-complete.
We also show that two natural cases of deterministic tournaments where the
optimal draw could be computed in polynomial time also admit polynomial-time
algorithms to compute robust optimal draws
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