351 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
Are there any nicely structured preference~profiles~nearby?
We investigate the problem of deciding whether a given preference profile is
close to having a certain nice structure, as for instance single-peaked,
single-caved, single-crossing, value-restricted, best-restricted,
worst-restricted, medium-restricted, or group-separable profiles. We measure
this distance by the number of voters or alternatives that have to be deleted
to make the profile a nicely structured one. Our results classify the problem
variants with respect to their computational complexity, and draw a clear line
between computationally tractable (polynomial-time solvable) and
computationally intractable (NP-hard) questions
Signs of universality in the structure of culture
Understanding the dynamics of opinions, preferences and of culture as whole
requires more use of empirical data than has been done so far. It is clear that
an important role in driving this dynamics is played by social influence, which
is the essential ingredient of many quantitative models. Such models require
that all traits are fixed when specifying the "initial cultural state".
Typically, this initial state is randomly generated, from a uniform
distribution over the set of possible combinations of traits. However, recent
work has shown that the outcome of social influence dynamics strongly depends
on the nature of the initial state. If the latter is sampled from empirical
data instead of being generated in a uniformly random way, a higher level of
cultural diversity is found after long-term dynamics, for the same level of
propensity towards collective behavior in the short-term. Moreover, if the
initial state is randomized by shuffling the empirical traits among people, the
level of long-term cultural diversity is in-between those obtained for the
empirical and uniformly random counterparts. The current study repeats the
analysis for multiple empirical data sets, showing that the results are
remarkably similar, although the matrix of correlations between cultural
variables clearly differs across data sets. This points towards robust
structural properties inherent in empirical cultural states, possibly due to
universal laws governing the dynamics of culture in the real world. The results
also suggest that this dynamics might be characterized by criticality and
involve mechanisms beyond social influence.Comment: 16 pages, 7 figures; the same results as in version 3, but a shorter
Introduction, Discussion and Conclusio
Election-Attack Complexity for More Natural Models
Elections are arguably the best way that a group of agents with preferences over a set of choices can reach a decision. This can include political domains, as well as multiagent systems in artificial-intelligence settings. It is well-known that every reasonable election system is manipulable, but determining whether such a manipulation exists may be computationally infeasible. We build on an exciting line of research that considers the complexity of election-attack problems, which include voters misrepresenting their preferences (manipulation) and attacks on the structure of the election itself (control). We must properly model such attacks and the preferences of the electorate to give us insight into the difficulty of election attacks in natural settings. This includes models for how the voters can state their preferences, their structure, and new models for the election attack itself.
We study several different natural models on the structure of the voters. In the computational study of election attacks it is generally assumed that voters strictly rank all of the candidates from most to least preferred. We consider the very natural model where voters are able to cast votes with ties, and the model where they additionally have a single-peaked structure. Specifically, we explore how voters with varying amounts of ties and structure in their preferences affect the computational complexity of different election attacks and the complexity of determining whether a given electorate is single-peaked.
For the representation of the voters, we consider how representing the voters succinctly affects the complexity of election attacks and discuss how approaches for the nonsuccinct case can be adapted.
Control and manipulation are two of the most commonly studied election-attack problems. We introduce a model of electoral control in the setting where some of the voters act strategically (i.e., are manipulators), and consider both the case where the agent controlling the election and the manipulators share a goal, and the case where they have competing goals.
The computational study of election-attack problems allows us to better understand how different election systems compare to one another, and it is important to study these problems for natural settings, as this thesis does
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