22 research outputs found
Complexity Results for Manipulation, Bribery and Control of the Kemeny Judgment Aggregation Procedure
We study the computational complexity of several scenarios of strategic
behavior for the Kemeny procedure in the setting of judgment aggregation. In
particular, we investigate (1) manipulation, where an individual aims to
achieve a better group outcome by reporting an insincere individual opinion,
(2) bribery, where an external agent aims to achieve an outcome with certain
properties by bribing a number of individuals, and (3) control (by adding or
deleting issues), where an external agent aims to achieve an outcome with
certain properties by influencing the set of issues in the judgment aggregation
situation. We show that determining whether these types of strategic behavior
are possible (and if so, computing a policy for successful strategic behavior)
is complete for the second level of the Polynomial Hierarchy. That is, we show
that these problems are -complete
Complexity of Judgment Aggregation
We analyse the computational complexity of three problems in judgment aggregation:
(1) computing a collective judgment from a profile of individual judgments (the winner
determination problem); (2) deciding whether a given agent can influence the outcome
of a judgment aggregation procedure in her favour by reporting insincere judgments (the
strategic manipulation problem); and (3) deciding whether a given judgment aggregation
scenario is guaranteed to result in a logically consistent outcome, independently from what
the judgments supplied by the individuals are (the problem of the safety of the agenda).
We provide results both for specific aggregation procedures (the quota rules, the premisebased
procedure, and a distance-based procedure) and for classes of aggregation procedures
characterised in terms of fundamental axioms
Very Hard Electoral Control Problems
It is important to understand how the outcome of an election can be modified
by an agent with control over the structure of the election. Electoral control
has been studied for many election systems, but for all studied systems the
winner problem is in P, and so control is in NP. There are election systems,
such as Kemeny, that have many desirable properties, but whose winner problems
are not in NP. Thus for such systems control is not in NP, and in fact we show
that it is typically complete for (i.e., , the
second level of the polynomial hierarchy). This is a very high level of
complexity. Approaches that perform quite well for solving NP problems do not
necessarily work for -complete problems. However, answer set
programming is suited to express problems in , and we present an
encoding for Kemeny control.Comment: A version of this paper will appear in the Proceedings of AAAI-201
The Complexity Landscape of Outcome Determination in Judgment Aggregation
We provide a comprehensive analysis of the computational complexity of the outcome determination problem for the most important aggregation rules proposed in the literature on logic-based judgment aggregation. Judgment aggregation is a powerful and flexible framework for studying problems of collective decision making that has attracted interest in a range of disciplines, including Legal Theory, Philosophy, Economics, Political Science, and Artificial Intelligence. The problem of computing the outcome for a given list of individual judgments to be aggregated into a single collective judgment is the most fundamental algorithmic challenge arising in this context. Our analysis applies to several different variants of the basic framework of judgment aggregation that have been discussed in the literature, as well as to a new framework that encompasses all existing such frameworks in terms of expressive power and representational succinctness.publishedVersio
A deep exploration of the complexity border of strategic voting problems
Voting has found applications in a variety of areas. Unfortunately, in a voting activity there may exist strategic individuals who have incentives to attack the election by performing some strategic behavior. One possible way to address this issue is to use computational complexity as a barrier against the strategic behavior. The point is that if it is NP-hard to successfully perform a strategic behavior, the strategic individuals may give up their plan of attacking the election.
This thesis is concerned with strategic behavior in restricted elections, in the sense that the given elections are subject to some combinatorial restrictions. The goal is to find out how the complexity of the strategic behavior changes from the very restricted case to the general case.Abstimmungen werden auf verschiedene Gebiete angewendet. Leider kann es bei einer Abstimmung einzelne Teilnehmer geben, die Vorteile daraus ziehen, die Wahl durch strategisches Verhalten zu manipulieren. Eine Möglichkeit diesem Problem zu begegnen ist es, die Berechnungskomplexität als Hindernis gegen strategisches Verhalten zu nutzen. Die Annahme ist, dass falls es NP-schwer ist, um strategisches Verhalten erfolgreich anzuwenden, der strategisch Handelnde vielleicht den Plan aufgibt die Abstimmung zu attackieren.
Diese Arbeit befasst sich mit strategischem Vorgehen in eingeschränkten Abstimmungen in dem Sinne, dass die vorgegebenen Abstimmungen kombinatorischen Einschränkungen unterliegen. Ziel ist es herauszufinden, wie sich die Komplexität des strategischen Handelns von dem sehr eingeschränkten zu dem generellen Fall ändert
Egalitarian judgment aggregation
Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance with respect to gender or ethnicity in committee elections. Yet, the egalitarian approach has received little attention in judgment aggregation—a powerful framework for aggregating logically interconnected issues. We make the first steps towards filling that gap. We introduce axioms capturing two classical interpretations of egalitarianism in judgment aggregation and situate these within the context of existing axioms in the pertinent framework of belief merging. We then explore the relationship between these axioms and several notions of strategyproofness from social choice theory at large. Finally, a novel egalitarian judgment aggregation rule stems from our analysis; we present complexity results concerning both outcome determination and strategic manipulation for that rule.publishedVersio