17 research outputs found
Computing Tournament Solutions using Relation Algebra and REL VIEW
We describe a simple computing technique for the tournament choice problem. It rests upon a relational modeling and uses the BDD-based computer system RelView for the evaluation of the relation-algebraic expressions that specify the solutions and for the visualization of the computed results. The Copeland set can immediately be identified using RelView's labeling feature. Relation-algebraic specifications of the Condorcet non-losers, the Schwartz set, the top cycle, the uncovered set, the minimal covering set, the Banks set, and the tournament equilibrium set are delivered. We present an example of a tournament on a small set of alternatives, for which the above choice sets are computed and visualized via RelView. The technique described in this paper is very flexible and especially appropriate for prototyping and experimentation, and as such very instructive for educational purposes. It can easily be applied to other problems of social choice and game theory.Tournament, relational algebra, RelView, Copeland set, Condorcet non-losers, Schwartz set, top cycle, uncovered set, minimal covering set, Banks set, tournament equilibrium set.
A relation-algebraic approach to simple games
Simple games are a powerful tool to analyze decision - making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational specifications for solving some basic problems of them. In particular, we test certain fundamental properties of simple games and compute specific players and coalitions. We also apply relation algebra to determine power indices. This leads to relation-algebraic specifications, which can be evaluated with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. In order to demonstrate the visualization facilities of RelView, we consider an example of the Catalonian Parliament after the 2003 election.Relation algebra ; RelView ; simple game ; winning coalition ; swinger ; dominant player ; central player ; power index
Applying relational algebra and RelView to measures in a social network
We present an application of relation algebra to measure agents' 'strength' in a social network with influence between agents. In particular, we deal with power, success, and influence of an agent as measured by the generalized Hoede-Bakker index and its modifications, and by the influence indices. We also apply relation algebra to determine followers of a coalition and the kernel of an influence function. This leads to specifications, which can be executed with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. As an example we consider the present Dutch parliament.RelView; relation algebra; social network; Hoede-Bakker index; influence index
Social networks: Prestige, centrality, and influence (Invited paper)
We deliver a short overview of di erent centrality measures and influence concepts in social networks, and present the relation-algebraic approach to the concepts of power and influence. First, we briefly discuss four kinds of measures of centrality: the ones based on degree, closeness, betweenness, and the eigenvector-related measures. We consider centrality of a node and of a network. Moreover, we give a classi cation of the centrality measures based on a topology of network flows. Furthermore, we present a certain model of influence in a social network and discuss some applications of relation algebra and RelView to this model.social network ; centrality ; prestige ; influence ; relation algebra ; RelView
A relation-algebraic approach to simple games
International audienceSimple games are a powerful tool to analyze decision - making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational specifications for solving some basic problems of them. In particular, we test certain fundamental properties of simple games and compute specific players and coalitions. We also apply relation algebra to determine power indices. This leads to relation-algebraic specifications, which can be evaluated with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. In order to demonstrate the visualization facilities of RelView, we consider an example of the Catalonian Parliament after the 2003 election
Solving Hard Control Problems in Voting Systems via Integer Programming
Voting problems are central in the area of social choice. In this article, we
investigate various voting systems and types of control of elections. We
present integer linear programming (ILP) formulations for a wide range of
NP-hard control problems. Our ILP formulations are flexible in the sense that
they can work with an arbitrary number of candidates and voters. Using the
off-the-shelf solver Cplex, we show that our approaches can manipulate
elections with a large number of voters and candidates efficiently
07431 Abstracts Collection -- Computational Issues in Social Choice
From the 21st to the 26th of October 2007, the Dagstuhl Seminar 07431
on ``Computational Issues in Social Choice\u27\u27 was held
at the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their recent
research, and ongoing work and open problems were discussed.
The abstracts of the talks given during the seminar are collected in this paper.
The first section summarises the seminar topics and goals in general.
Links to full papers are provided where available
Entwurf funktionaler Implementierungen von Graphalgorithmen
Classic graph algorithms are usually presented and analysed
in imperative programming languages.
Imperative programming languages are well-suited for the description of
a program flow,
in which the order in which the operations are performed is important.
One common example of such a description is the successive,
typically destructive modification of objects.
This kind of iteration often occurs in the context of graph algorithms
that deal with a certain kind of optimisation.
In functional programming,
the order of execution is abstracted
and problem solutions are described
as compositions of intermediate solutions.
Additionally,
functional programming languages are referentially transparent
and thus destructive updates of objects are discouraged.
The development of purely functional graph algorithms begins with the
decomposition of a given problem into simpler problems.
In many cases
the solutions of these partial problems can be used to solve
different problems as well.
What is more,
this compositionality allows exchanging functions
for more efficient or more comprehensible versions with little effort.
An algebraic approach with a focus on relation algebra as defined by Tarski
is used as an intermediate step in this dissertation.
One advantage of this approach is the formality of the resulting specifications.
Despite their formality,
the resulting expressions are still readable,
because the algebraic operations have intuitive interpretations.
Another advantage is that the specification is executable,
once the necessary operations are implemented.
This dissertation presents the basics of the algebraic approach in the
functional programming language Haskell.
Using this foundation,
some exemplary graph-theoretic problems are solved in the presented
framework.
Finally,
optimisations of the presented implementations are discussed
and pointers are provided to further problems
that can be solved using the above methods.Klassische Graphalgorithmen werden üblicherweise in imperativen
Programmiersprachen
beschrieben und analysiert.
Imperative Programmiersprachen eignen sich gut,
um Programmabläufe zu beschreiben,
in welchen die Reihenfolge der Operationen
wichtig ist.
Dies betrifft insbesondere die schrittweise,
in der Regel destruktive Veränderung von Objekten,
wie sie häufig im Falle von Optimierungsproblemen
auf Graphen vorkommt.
In der funktionalen Programmierung abstrahiert man von einer festen
Berechnungsreihenfolge und beschreibt Problemlösungen als
Kompositionen von Teillösungen.
Ferner sind funktionale Programmiersprachen referentiell transparent,
sodass destruktive Veränderungen nur bedingt möglich sind.
Die Entwicklung rein funktionaler Graphalgorithmen setzt bei der Zerlegung
der bestehenden Probleme in einfachere Probleme an.
Oftmals können Lösungen dieser Teilprobleme auch in anderen
Situationen eingesetzt werden.
Darüber hinaus erlaubt es diese Kompositionalität,
einzelne Funktionen mit wenig Aufwand durch effizientere
oder verständlichere Fassungen
auszutauschen.
Als Zwischenschritt in der Entwicklung wird in dieser Dissertation
ein algebraischer Ansatz basierend auf der Relationenalgebra im Sinne von Tarski
verwendet.
Ein Vorteil dieses Ansatzes ist die
Formalität der entstehenden Spezifikationen.
Trotz ihrer Formalität bleiben die entstehenden Ausdrücke oft
leserlich,
weil die algebraischen Operationen
anschauliche Interpretationen zulassen.
Ein weiterer Vorteil ist,
dass Spezifikationen ausführbar werden,
sobald bestimmte Basisoperationen implementiert sind.
In dieser Dissertation werden Grundlagen einer Implementierung
des algebraischen Ansatzes in der
funktionalen Programmiersprache Haskell behandelt.
Ausgehend hiervon werden exemplarisch einige
Probleme der Graphentheorie gelöst.
Schließlich werden Optimierungen der vorgestellten Implementierungen
und weitere Probleme,
welche mit den obigen Methoden lösbar sind, diskutiert