73 research outputs found
Complexity of Manipulative Actions When Voting with Ties
Most of the computational study of election problems has assumed that each
voter's preferences are, or should be extended to, a total order. However in
practice voters may have preferences with ties. We study the complexity of
manipulative actions on elections where voters can have ties, extending the
definitions of the election systems (when necessary) to handle voters with
ties. We show that for natural election systems allowing ties can both increase
and decrease the complexity of manipulation and bribery, and we state a general
result on the effect of voters with ties on the complexity of control.Comment: A version of this paper will appear in ADT-201
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
Computational Complexity Characterization of Protecting Elections from Bribery
The bribery problem in election has received considerable attention in the
literature, upon which various algorithmic and complexity results have been
obtained. It is thus natural to ask whether we can protect an election from
potential bribery. We assume that the protector can protect a voter with some
cost (e.g., by isolating the voter from potential bribers). A protected voter
cannot be bribed. Under this setting, we consider the following bi-level
decision problem: Is it possible for the protector to protect a proper subset
of voters such that no briber with a fixed budget on bribery can alter the
election result? The goal of this paper is to give a full picture on the
complexity of protection problems. We give an extensive study on the protection
problem and provide algorithmic and complexity results. Comparing our results
with that on the bribery problems, we observe that the protection problem is in
general significantly harder. Indeed, it becomes -complete even for
very restricted special cases, while most bribery problems lie in NP. However,
it is not necessarily the case that the protection problem is always harder.
Some of the protection problems can still be solved in polynomial time, while
some of them remain as hard as the bribery problem under the same setting.Comment: 28 Pages. The Article has been accepted in the 26th International
Computing and Combinatorics Conference (COCOON 2020
Using contracted solution graphs for solving reconfiguration problems.
We introduce a dynamic programming method for solving reconfiguration problems, based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions that decrease the graph size without losing any critical information needed to solve the reconfiguration problem under consideration. As an example, we consider a well-studied problem: given two k-colorings alpha and beta of a graph G, can alpha be modified into beta by recoloring one vertex of G at a time, while maintaining a k-coloring throughout? By applying our method in combination with a thorough exploitation of the graph structure we obtain a polynomial-time algorithm for (k-2)-connected chordal graphs
Using contracted solution graphs for solving reconfiguration problems
We introduce a dynamic programming method for solving reconfiguration problems, based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions that decrease the graph size without losing any critical information needed to solve the reconfiguration problem under consideration. As an example, we consider a well-studied problem: given two k-colorings alpha and beta of a graph G, can alpha be modified into beta by recoloring one vertex of G at a time, while maintaining a k-coloring throughout? By applying our method in combination with a thorough exploitation of the graph structure we obtain a polynomial-time algorithm for (k-2)-connected chordal graphs
Stably computing order statistics with arithmetic population protocols.
In this paper we initiate the study of populations of agents with very limited capabilities that are globally able to compute order statistics of their arithmetic input values via pair-wise meetings. To this extent, we introduce the Arithmetic Population Protocol (APP) model, embarking from the well known Population Protocol (PP) model and inspired by two recent papers in which states are treated as integer numbers. In the APP model, every agent has a state from a set Q of states, as well as a fixed number of registers (independent of the size of the population), each of which can store an element from a totally ordered set S of samples. Whenever two agents interact with each other, they update their states and the values stored in their registers according to a joint transition function. This transition function is also restricted; it only allows (a) comparisons and (b) copy / paste operations for the sample values that are stored in the registers of the two interacting agents. Agents can only meet in pairs via a fair scheduler and are required to eventually converge to the same output value of the function that the protocol globally and stably computes. We present two different APPs for stably computing the median of the input values, initially stored on the agents of the population. Our first APP, in which every agent has 3 registers and no states, stably computes (with probability 1) the median under any fair scheduler in any strongly connected directed (or connected undirected) interaction graph. Under the probabilistic scheduler, we show that our protocol stably computes the median in O(n^6) number of interactions in a connected undirected interaction graph of agents. Our second APP, in which every agent has 2 registers and O(n^2 log{n}) states, computes to the correct median of the input with high probability in O(n^3 log{n}) interactions, assuming the probabilistic scheduler and the complete interaction graph. Finally we present a third APP which, for any k, stably computes the k-th smallest element of the input of the population under any fair scheduler and in any strongly connected directed (or connected undirected) interaction graph. In this APP every agent has 2 registers and n states. Upon convergence every agent has a different state; all these states provide a total ordering of the agents with respect to their input values
Stably computing order statistics with arithmetic population protocols
In this paper we initiate the study of populations of agents with very limited capabilities that are globally able to compute order statistics of their arithmetic input values via pair-wise meetings. To this extent, we introduce the Arithmetic Population Protocol (APP) model, embarking from the well known Population Protocol (PP) model and inspired by two recent papers in which states are treated as integer numbers. In the APP model, every agent has a state from a set Q of states, as well as a fixed number of registers (independent of the size of the population), each of which can store an element from a totally ordered set S of samples. Whenever two agents interact with each other, they update their states and the values stored in their registers according to a joint transition function. This transition function is also restricted; it only allows (a) comparisons and (b) copy / paste operations for the sample values that are stored in the registers of the two interacting agents. Agents can only meet in pairs via a fair scheduler and are required to eventually converge to the same output value of the function that the protocol globally and stably computes. We present two different APPs for stably computing the median of the input values, initially stored on the agents of the population. Our first APP, in which every agent has 3 registers and no states, stably computes (with probability 1) the median under any fair scheduler in any strongly connected directed (or connected undirected) interaction graph. Under the probabilistic scheduler, we show that our protocol stably computes the median in O(n^6) number of interactions in a connected undirected interaction graph of agents. Our second APP, in which every agent has 2 registers and O(n^2 log{n}) states, computes to the correct median of the input with high probability in O(n^3 log{n}) interactions, assuming the probabilistic scheduler and the complete interaction graph. Finally we present a third APP which, for any k, stably computes the k-th smallest element of the input of the population under any fair scheduler and in any strongly connected directed (or connected undirected) interaction graph. In this APP every agent has 2 registers and n states. Upon convergence every agent has a different state; all these states provide a total ordering of the agents with respect to their input values
More Natural Models of Electoral Control by Partition
"Control" studies attempts to set the outcome of elections through the
addition, deletion, or partition of voters or candidates. The set of benchmark
control types was largely set in the seminal 1992 paper by Bartholdi, Tovey,
and Trick that introduced control, and there now is a large literature studying
how many of the benchmark types various election systems are vulnerable to,
i.e., have polynomial-time attack algorithms for.
However, although the longstanding benchmark models of addition and deletion
model relatively well the real-world settings that inspire them, the
longstanding benchmark models of partition model settings that are arguably
quite distant from those they seek to capture.
In this paper, we introduce--and for some important cases analyze the
complexity of--new partition models that seek to better capture many real-world
partition settings. In particular, in many partition settings one wants the two
parts of the partition to be of (almost) equal size, or is partitioning into
more than two parts, or has groups of actors who must be placed in the same
part of the partition. Our hope is that having these new partition types will
allow studies of control attacks to include such models that more realistically
capture many settings
False-Name Manipulation in Weighted Voting Games is Hard for Probabilistic Polynomial Time
False-name manipulation refers to the question of whether a player in a
weighted voting game can increase her power by splitting into several players
and distributing her weight among these false identities. Analogously to this
splitting problem, the beneficial merging problem asks whether a coalition of
players can increase their power in a weighted voting game by merging their
weights. Aziz et al. [ABEP11] analyze the problem of whether merging or
splitting players in weighted voting games is beneficial in terms of the
Shapley-Shubik and the normalized Banzhaf index, and so do Rey and Rothe [RR10]
for the probabilistic Banzhaf index. All these results provide merely
NP-hardness lower bounds for these problems, leaving the question about their
exact complexity open. For the Shapley--Shubik and the probabilistic Banzhaf
index, we raise these lower bounds to hardness for PP, "probabilistic
polynomial time", and provide matching upper bounds for beneficial merging and,
whenever the number of false identities is fixed, also for beneficial
splitting, thus resolving previous conjectures in the affirmative. It follows
from our results that beneficial merging and splitting for these two power
indices cannot be solved in NP, unless the polynomial hierarchy collapses,
which is considered highly unlikely
Combinatorial Voter Control in Elections
Voter control problems model situations such as an external agent trying to
affect the result of an election by adding voters, for example by convincing
some voters to vote who would otherwise not attend the election. Traditionally,
voters are added one at a time, with the goal of making a distinguished
alternative win by adding a minimum number of voters. In this paper, we
initiate the study of combinatorial variants of control by adding voters: In
our setting, when we choose to add a voter~, we also have to add a whole
bundle of voters associated with . We study the computational
complexity of this problem for two of the most basic voting rules, namely the
Plurality rule and the Condorcet rule.Comment: An extended abstract appears in MFCS 201
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