GRTJ - Grup de Recerca en Teoria de Jocs
http://hdl.handle.net/2117/3429
Thu, 25 May 2017 01:45:56 GMT2017-05-25T01:45:56ZUsing the multilinear extension to study some probabilistic power indices
http://hdl.handle.net/2117/104580
Using the multilinear extension to study some probabilistic power indices
Freixas Bosch, Josep; Pons Vallès, Montserrat
We consider binary voting systems modeled by a simple game, in which voters vote independently of each other, and the probability distribution over coalitions is known. The Owen’s multilinear extension of the simple game is used to improve the use and the computation of three indices defined in this model: the decisiveness index, which is an extension of the Banzhaf index, the success index, which is an extension of the Rae index, and the luckiness index. This approach leads us to prove new properties and inter-relations between these indices. In particular it is proved that the ordinal equivalence between success and decisiveness indices is achieved in any game if and only if the probability distribution is anonymous. In the anonymous case, the egalitarianism of the three indices is compared, and it is also proved that, for these distributions, decisiveness and success indices respect the strength of the seats, whereas luckiness reverses this order.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10726-016-9514-6
Wed, 17 May 2017 14:32:45 GMThttp://hdl.handle.net/2117/1045802017-05-17T14:32:45ZFreixas Bosch, JosepPons Vallès, MontserratWe consider binary voting systems modeled by a simple game, in which voters vote independently of each other, and the probability distribution over coalitions is known. The Owen’s multilinear extension of the simple game is used to improve the use and the computation of three indices defined in this model: the decisiveness index, which is an extension of the Banzhaf index, the success index, which is an extension of the Rae index, and the luckiness index. This approach leads us to prove new properties and inter-relations between these indices. In particular it is proved that the ordinal equivalence between success and decisiveness indices is achieved in any game if and only if the probability distribution is anonymous. In the anonymous case, the egalitarianism of the three indices is compared, and it is also proved that, for these distributions, decisiveness and success indices respect the strength of the seats, whereas luckiness reverses this order.On alpha-roughly weighted games
http://hdl.handle.net/2117/103235
On alpha-roughly weighted games
Freixas Bosch, Josep; Kurz, Sascha
Very recently Gvozdeva, Hemaspaandra, and Slinko (2011) h
ave introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of weighted voting games or roughly weighted voting games. Their third class C aconsists of all simple games
permitting a weighted representation such that each winnin
g coalition has a weight of at least 1 and each losing coalition a weight of at most a. We continue their work and contribute some new results on the possible values of a for a given number of voters.
Mon, 03 Apr 2017 15:53:36 GMThttp://hdl.handle.net/2117/1032352017-04-03T15:53:36ZFreixas Bosch, JosepKurz, SaschaVery recently Gvozdeva, Hemaspaandra, and Slinko (2011) h
ave introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of weighted voting games or roughly weighted voting games. Their third class C aconsists of all simple games
permitting a weighted representation such that each winnin
g coalition has a weight of at least 1 and each losing coalition a weight of at most a. We continue their work and contribute some new results on the possible values of a for a given number of voters.The complexity of testing properties of simple games
http://hdl.handle.net/2117/103171
The complexity of testing properties of simple games
Freixas Bosch, Josep; Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, María José
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea'' votes yield passage of the issue at hand. A collection of ``yea'' voters forms a winning coalition.
We are interested on performing a complexity analysis of problems on such games depending on the game representation. We consider four natural explicit representations, winning, loosing, minimal winning, and maximal loosing. We first analyze the computational complexity of obtaining a particular representation of a simple game from a different one. We show that some cases this transformation can be done in polynomial time while the others require exponential time. The second question is classifying the complexity for testing whether a game is simple or weighted. We show that for the four types of representation both problem can be solved in polynomial time. Finally, we provide results on the complexity of testing whether a simple game or a weighted game is of a special type. In this way, we analyze strongness, properness, decisiveness and homogeneity, which are desirable properties to be fulfilled for a simple game.
Fri, 31 Mar 2017 15:48:07 GMThttp://hdl.handle.net/2117/1031712017-03-31T15:48:07ZFreixas Bosch, JosepMolinero Albareda, XavierOlsen, MartinSerna Iglesias, María JoséSimple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea'' votes yield passage of the issue at hand. A collection of ``yea'' voters forms a winning coalition.
We are interested on performing a complexity analysis of problems on such games depending on the game representation. We consider four natural explicit representations, winning, loosing, minimal winning, and maximal loosing. We first analyze the computational complexity of obtaining a particular representation of a simple game from a different one. We show that some cases this transformation can be done in polynomial time while the others require exponential time. The second question is classifying the complexity for testing whether a game is simple or weighted. We show that for the four types of representation both problem can be solved in polynomial time. Finally, we provide results on the complexity of testing whether a simple game or a weighted game is of a special type. In this way, we analyze strongness, properness, decisiveness and homogeneity, which are desirable properties to be fulfilled for a simple game.Weighted voting, abstention and multiple levels of approval
http://hdl.handle.net/2117/103170
Weighted voting, abstention and multiple levels of approval
Freixas Bosch, Josep; Zwicker, William S.
In this paper we introduce the class of simple games with several ordered levels of approval in the input and in the output – the ( j,k) simple games – and propose a definition for weighted games in this context. Abstention is treated as a level of input approval intermediate to votes of yes and no. Our main theorem provides a combinatorial characterization, in terms of what we call grade trade robustness, of weighted ( j,k) games within the class of all ( j,k) simple games. We also introduce other subclasses of ( j,k) simple games and classify several examples. For example, we show the existence of a weighted representation for the UNSC, seen as a voting system in which abstention is permitted.
Research partially supported by Grant 1999BEAI400096 of the Commissioner for Universities and Research of the Catalonia Generalitat and by Grant BFM 2000–0968 of the Spanish Ministry of Science and Technology. The authors would like to thank Larry Becker, Clifford Brown, Vin Moscardelli, and Fred Jonas for their assistance. Extensive remarks by Moshé Machover as well as comments by an anonymous referee greatly improved the manuscript.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00355-003-0212-3.
Fri, 31 Mar 2017 15:30:18 GMThttp://hdl.handle.net/2117/1031702017-03-31T15:30:18ZFreixas Bosch, JosepZwicker, William S.In this paper we introduce the class of simple games with several ordered levels of approval in the input and in the output – the ( j,k) simple games – and propose a definition for weighted games in this context. Abstention is treated as a level of input approval intermediate to votes of yes and no. Our main theorem provides a combinatorial characterization, in terms of what we call grade trade robustness, of weighted ( j,k) games within the class of all ( j,k) simple games. We also introduce other subclasses of ( j,k) simple games and classify several examples. For example, we show the existence of a weighted representation for the UNSC, seen as a voting system in which abstention is permitted.
Research partially supported by Grant 1999BEAI400096 of the Commissioner for Universities and Research of the Catalonia Generalitat and by Grant BFM 2000–0968 of the Spanish Ministry of Science and Technology. The authors would like to thank Larry Becker, Clifford Brown, Vin Moscardelli, and Fred Jonas for their assistance. Extensive remarks by Moshé Machover as well as comments by an anonymous referee greatly improved the manuscript.Ability to separate situations with a priori coalition structures by means of symmetric solutions
http://hdl.handle.net/2117/102517
Ability to separate situations with a priori coalition structures by means of symmetric solutions
Giménez Pradales, José Miguel
We say that two situations described by cooperative games are inseparable by a family of solutions, when they obtain the same allocation by all solution concept of this family. The situation of separability by a family of linear solutions reduces to separability from the null game. This is the case of the family of solutions based on marginal contributions weighted by coef¿cients only dependent of the coalition size: the semivalues. It is known that for games with four or more players, the spaces of inseparable games from the null game contain games different to zero-game. We will prove that for ¿ve or more players, when a priori coalition blocks are introduced in the situation described by the game, the dimension of the vector spaces of inseparable games from the null game decreases in an important manner.
Wed, 15 Mar 2017 13:33:58 GMThttp://hdl.handle.net/2117/1025172017-03-15T13:33:58ZGiménez Pradales, José MiguelWe say that two situations described by cooperative games are inseparable by a family of solutions, when they obtain the same allocation by all solution concept of this family. The situation of separability by a family of linear solutions reduces to separability from the null game. This is the case of the family of solutions based on marginal contributions weighted by coef¿cients only dependent of the coalition size: the semivalues. It is known that for games with four or more players, the spaces of inseparable games from the null game contain games different to zero-game. We will prove that for ¿ve or more players, when a priori coalition blocks are introduced in the situation described by the game, the dimension of the vector spaces of inseparable games from the null game decreases in an important manner.Effect of a science communication event on students’ attitudes towards science and technology
http://hdl.handle.net/2117/102416
Effect of a science communication event on students’ attitudes towards science and technology
Torras Melenchón, Núria; Grau Vilalta, Maria Dolors; Font Soldevila, Josep; Freixas Bosch, Josep
Tue, 14 Mar 2017 08:15:19 GMThttp://hdl.handle.net/2117/1024162017-03-14T08:15:19ZTorras Melenchón, NúriaGrau Vilalta, Maria DolorsFont Soldevila, JosepFreixas Bosch, JosepA new procedure to calculate the Owen value
http://hdl.handle.net/2117/102250
A new procedure to calculate the Owen value
Puente del Campo, María Albina; Giménez Pradales, José Miguel
In this paper we focus on games with a coalition structure. Particularly, we deal with the Owen value, the coalitional value of the Shapley value, and we provide a computational procedure to calculate this coalitional value in terms of the multilinear extension of the original game.
Thu, 09 Mar 2017 19:07:48 GMThttp://hdl.handle.net/2117/1022502017-03-09T19:07:48ZPuente del Campo, María AlbinaGiménez Pradales, José MiguelIn this paper we focus on games with a coalition structure. Particularly, we deal with the Owen value, the coalitional value of the Shapley value, and we provide a computational procedure to calculate this coalitional value in terms of the multilinear extension of the original game.Measuring satisfaction in societies with opinion leaders and mediators
http://hdl.handle.net/2117/101810
Measuring satisfaction in societies with opinion leaders and mediators
Molinero Albareda, Xavier; Riquelme Csori, F.; Serna Iglesias, María José
An opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:
Wed, 01 Mar 2017 16:19:14 GMThttp://hdl.handle.net/2117/1018102017-03-01T16:19:14ZMolinero Albareda, XavierRiquelme Csori, F.Serna Iglesias, María JoséAn opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:Decisiveness indices are semiindices: addendum
http://hdl.handle.net/2117/98770
Decisiveness indices are semiindices: addendum
Freixas Bosch, Josep; Pons Vallès, Montserrat
In the paper Decisiveness indices are semiindices (Freixas and Pons, 2016) it was shown that any decisiveness index obtained from an anonymous probability distribution is a semiindex, and that the converse is not true. In this note we characterize the semiindices which are indices of decisiveness.
Thu, 22 Dec 2016 15:36:17 GMThttp://hdl.handle.net/2117/987702016-12-22T15:36:17ZFreixas Bosch, JosepPons Vallès, MontserratIn the paper Decisiveness indices are semiindices (Freixas and Pons, 2016) it was shown that any decisiveness index obtained from an anonymous probability distribution is a semiindex, and that the converse is not true. In this note we characterize the semiindices which are indices of decisiveness.On the construction of high dimensional simple games
http://hdl.handle.net/2117/97663
On the construction of high dimensional simple games
Olsen, Martin; Kurz, Sascha; Molinero Albareda, Xavier
Voting is a commonly applied method for the aggregation
of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., “yes” and “no”, every voting system can be
described by a (monotone) Boolean function : f0; 1gn ! f0; 1g.
However, its naive encoding needs 2n bits. The subclass of threshold
functions, which is sufficient for homogeneous agents, allows
a more succinct representation using n weights and one threshold.
For heterogeneous agents one can represent as an intersection of k
threshold functions. Taylor and Zwicker have constructed a sequence
of examples requiring k 2 n2 ¿1 and provided a construction guaranteeingk ¿ n bn=2c 2 2n¿o(n). The magnitude of the worst case situation was thought to be determined by Elkind et al. in 2008, but the analysis unfortunately turned out to be wrong. Here we uncover a relation to coding theory that allows the determination of the minimum number k for a subclass of voting systems. As an application, we give a construction for k 2n¿o(n), i.e., there is no gain from a representation complexity point of view.
Thu, 01 Dec 2016 19:18:00 GMThttp://hdl.handle.net/2117/976632016-12-01T19:18:00ZOlsen, MartinKurz, SaschaMolinero Albareda, XavierVoting is a commonly applied method for the aggregation
of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., “yes” and “no”, every voting system can be
described by a (monotone) Boolean function : f0; 1gn ! f0; 1g.
However, its naive encoding needs 2n bits. The subclass of threshold
functions, which is sufficient for homogeneous agents, allows
a more succinct representation using n weights and one threshold.
For heterogeneous agents one can represent as an intersection of k
threshold functions. Taylor and Zwicker have constructed a sequence
of examples requiring k 2 n2 ¿1 and provided a construction guaranteeingk ¿ n bn=2c 2 2n¿o(n). The magnitude of the worst case situation was thought to be determined by Elkind et al. in 2008, but the analysis unfortunately turned out to be wrong. Here we uncover a relation to coding theory that allows the determination of the minimum number k for a subclass of voting systems. As an application, we give a construction for k 2n¿o(n), i.e., there is no gain from a representation complexity point of view.