GRTJ - Grup de Recerca en Teoria de Jocs
http://hdl.handle.net/2117/3429
Sun, 29 May 2016 07:49:36 GMT2016-05-29T07:49:36ZSome advances in the theory of voting systems based on experimental algorithms
http://hdl.handle.net/2117/87345
Some advances in the theory of voting systems based on experimental algorithms
Freixas Bosch, Josep; Molinero Albareda, Xavier
In voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker cite{TaZw92} establishes the equivalence between weighted voting games and $k$-trade robust games for each positive integer $k$. Moreover, they also construct, in cite{TaZw95}, a succession of games $G_k$ based on magic squares which are $(k-1)$-trade robust but not $k$-trade robust, each one of these games $G_k$ has $k^2$ players. The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to they are: a weighted voting game or a game which is $(k-1)$-trade robust but not $k$-trade robust for all values of $k$. As a consequence it will we showed the existence of games with less than $k^2$ players which are $(k-1)$-trade robust but not $k$-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.
Thu, 26 May 2016 08:32:43 GMThttp://hdl.handle.net/2117/873452016-05-26T08:32:43ZFreixas Bosch, JosepMolinero Albareda, XavierIn voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker cite{TaZw92} establishes the equivalence between weighted voting games and $k$-trade robust games for each positive integer $k$. Moreover, they also construct, in cite{TaZw95}, a succession of games $G_k$ based on magic squares which are $(k-1)$-trade robust but not $k$-trade robust, each one of these games $G_k$ has $k^2$ players. The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to they are: a weighted voting game or a game which is $(k-1)$-trade robust but not $k$-trade robust for all values of $k$. As a consequence it will we showed the existence of games with less than $k^2$ players which are $(k-1)$-trade robust but not $k$-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.The cost of getting local monotonicity
http://hdl.handle.net/2117/86881
The cost of getting local monotonicity
Freixas Bosch, Josep; Kurz, Sascha
Committees with yes-no-decisions are commonly modeled as simple games and the ability of a member to influence the group decision is measured by so-called power indices. For a weighted game we say that a power index satisfies local monotonicity if a player who controls a large share of the total weight vote does not have less power than a player with a smaller voting weight. In (Holler, 1982) Manfred Holler introduced the Public Good index. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback (Felsenthal & Machover, 1998, 221 ff.)or as an advantage (Holler & Napel 2004). In this paper we consider a convex combination of the two indices and require the validity of local monotonicity. We prove that the cost of obtaining it is high, i.e., the achievable new indices satisfying local monotonicity are closer to the Banzhaf index than to the Public Good index. All these achievable new indices are more solidary than the Banzhaf index, which makes them as very suitable candidates to divide a public good. As a generalization we consider convex combinations of either: the Shift index, the Public Good index, and the Banzhaf index, or alternatively: the Shift Deegan-Packel, Deegan-Packel, and Johnston indices.
Tue, 10 May 2016 14:22:58 GMThttp://hdl.handle.net/2117/868812016-05-10T14:22:58ZFreixas Bosch, JosepKurz, SaschaCommittees with yes-no-decisions are commonly modeled as simple games and the ability of a member to influence the group decision is measured by so-called power indices. For a weighted game we say that a power index satisfies local monotonicity if a player who controls a large share of the total weight vote does not have less power than a player with a smaller voting weight. In (Holler, 1982) Manfred Holler introduced the Public Good index. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback (Felsenthal & Machover, 1998, 221 ff.)or as an advantage (Holler & Napel 2004). In this paper we consider a convex combination of the two indices and require the validity of local monotonicity. We prove that the cost of obtaining it is high, i.e., the achievable new indices satisfying local monotonicity are closer to the Banzhaf index than to the Public Good index. All these achievable new indices are more solidary than the Banzhaf index, which makes them as very suitable candidates to divide a public good. As a generalization we consider convex combinations of either: the Shift index, the Public Good index, and the Banzhaf index, or alternatively: the Shift Deegan-Packel, Deegan-Packel, and Johnston indices.Minimal representations for majority games
http://hdl.handle.net/2117/86215
Minimal representations for majority games
Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
This paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.
Wed, 27 Apr 2016 07:22:54 GMThttp://hdl.handle.net/2117/862152016-04-27T07:22:54ZFreixas Bosch, JosepMolinero Albareda, XavierRoura Ferret, SalvadorThis paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.On the complexity of exchanging
http://hdl.handle.net/2117/86068
On the complexity of exchanging
Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, María José
We analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of j given losing coalitions into a set of j winning coalitions. We also look at the problem of turning winning coalitions into losing coalitions. We analyze the problem when the simple game is represented by a list of wining, losing, minimal winning or maximal loosing coalitions.
Thu, 21 Apr 2016 13:57:53 GMThttp://hdl.handle.net/2117/860682016-04-21T13:57:53ZMolinero Albareda, XavierOlsen, MartinSerna Iglesias, María JoséWe analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of j given losing coalitions into a set of j winning coalitions. We also look at the problem of turning winning coalitions into losing coalitions. We analyze the problem when the simple game is represented by a list of wining, losing, minimal winning or maximal loosing coalitions.Components with higher and lower risk in a reliability system
http://hdl.handle.net/2117/84179
Components with higher and lower risk in a reliability system
Freixas Bosch, Josep; Pons Vallès, Montserrat
A new reliability importance measure for components in a system, that we
call Representativeness measure, is introduced. It evaluates to which extent the performance of a component is representative of the erformance of the whole system. Its relationship with Birnbaum’s measure is analyzed, and the ranking of components given by both measures are compared. These rankings happen to be equal when all components have the same reliability but different in general. In contrast with Birnbaum’s, the Representativeness reliability importance measure of a component does depend on its reliability.
Thu, 10 Mar 2016 19:15:02 GMThttp://hdl.handle.net/2117/841792016-03-10T19:15:02ZFreixas Bosch, JosepPons Vallès, MontserratA new reliability importance measure for components in a system, that we
call Representativeness measure, is introduced. It evaluates to which extent the performance of a component is representative of the erformance of the whole system. Its relationship with Birnbaum’s measure is analyzed, and the ranking of components given by both measures are compared. These rankings happen to be equal when all components have the same reliability but different in general. In contrast with Birnbaum’s, the Representativeness reliability importance measure of a component does depend on its reliability.Power in voting rules with abstention: an axiomatization of a two components power index
http://hdl.handle.net/2117/84162
Power in voting rules with abstention: an axiomatization of a two components power index
Freixas Bosch, Josep; Lucchetti, Roberto
In order to study voting situations when voters can also abstain and the output is binary, i.e., either approval or rejection, a new extended model of voting rule was defined. Accordingly, indices of power, in particular Banzhaf’s index, were considered. In this paper we argue that in this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We also provide an axiomatization for both indices, and from this a characterization as well of the standard Banzhaf index (the sum of the former two) is obtained. Some examples are provided to show how the indices behave.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-016-2124-5
Thu, 10 Mar 2016 15:58:37 GMThttp://hdl.handle.net/2117/841622016-03-10T15:58:37ZFreixas Bosch, JosepLucchetti, RobertoIn order to study voting situations when voters can also abstain and the output is binary, i.e., either approval or rejection, a new extended model of voting rule was defined. Accordingly, indices of power, in particular Banzhaf’s index, were considered. In this paper we argue that in this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We also provide an axiomatization for both indices, and from this a characterization as well of the standard Banzhaf index (the sum of the former two) is obtained. Some examples are provided to show how the indices behave.Exponential decay in nonsimple thermoelasticity of type III
http://hdl.handle.net/2117/83497
Exponential decay in nonsimple thermoelasticity of type III
Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
This paper deals with the model proposed for nonsimple materials
with heat conduction of type III.We analyze rst the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.
This is the peer reviewed version of the following article: Magaña, A., and Quintanilla, R. (2016) Exponential decay in nonsimple thermoelasticity of type III. Math. Meth. Appl. Sci., 39: 225–235. doi: 10.1002/mma.3472, which has been published in final form at http://dx.doi.org/10.1002/mma.3472. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
Fri, 26 Feb 2016 13:13:35 GMThttp://hdl.handle.net/2117/834972016-02-26T13:13:35ZMagaña Nieto, AntonioQuintanilla de Latorre, RamónThis paper deals with the model proposed for nonsimple materials
with heat conduction of type III.We analyze rst the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.Manipulation in games with multiple levels of output
http://hdl.handle.net/2117/80825
Manipulation in games with multiple levels of output
Freixas Bosch, Josep; Parker, Cameron
In (j,k)-games each player chooses amongst j ordered options and there are k possible outcomes. In this paper, we consider the case where players are assumed to prefer some outcomes to others, and note that when k>2 the players have an incentive to vote strategically. In doing so, we combine the theory of cooperative game theory with social choice theory, especially the theory of single-peaked preferences. We define the concept of a (j,k)-game with preferences and what it means for it to be manipulable by a player. We also consider Nash equilibriums with pure strategies for these games and find conditions that guarantee their existence.
Wed, 16 Dec 2015 16:44:35 GMThttp://hdl.handle.net/2117/808252015-12-16T16:44:35ZFreixas Bosch, JosepParker, CameronIn (j,k)-games each player chooses amongst j ordered options and there are k possible outcomes. In this paper, we consider the case where players are assumed to prefer some outcomes to others, and note that when k>2 the players have an incentive to vote strategically. In doing so, we combine the theory of cooperative game theory with social choice theory, especially the theory of single-peaked preferences. We define the concept of a (j,k)-game with preferences and what it means for it to be manipulable by a player. We also consider Nash equilibriums with pure strategies for these games and find conditions that guarantee their existence.A method to calculate generalized mixed modified semivalues: application to the Catalan Parliament (legislature 2012-2016)
http://hdl.handle.net/2117/80018
A method to calculate generalized mixed modified semivalues: application to the Catalan Parliament (legislature 2012-2016)
Giménez Pradales, José Miguel; Puente del Campo, María Albina
We focus on generalized mixed modified semivalues, a family of coalitional values. They apply to games with a coalition structure by combining a (induced) semivalue in the quotient game, but share within each union the payoff so obtained by applying different (induced) semivalues to a game that concerns only the players of that union. A computation procedure in terms of the multilinear extension of the original game is also provided and an application to the Catalan Parliament (legislature 2012-2016) is shown
The final publication is available at Springer via http://dx.doi.org/10.1007/s11750-014-0356-6”.
Fri, 27 Nov 2015 16:23:44 GMThttp://hdl.handle.net/2117/800182015-11-27T16:23:44ZGiménez Pradales, José MiguelPuente del Campo, María AlbinaWe focus on generalized mixed modified semivalues, a family of coalitional values. They apply to games with a coalition structure by combining a (induced) semivalue in the quotient game, but share within each union the payoff so obtained by applying different (induced) semivalues to a game that concerns only the players of that union. A computation procedure in terms of the multilinear extension of the original game is also provided and an application to the Catalan Parliament (legislature 2012-2016) is shownIdentifying optimal components in a reliability system
http://hdl.handle.net/2117/78945
Identifying optimal components in a reliability system
Freixas Bosch, Josep; Pons Vallès, Montserrat
The first step in a reliability optimization process is to
make a reliability assessment for each component in the system. If
this assessment is made in a qualitative way, by grouping together
components with the same reliability, and establishing a prevalence
order among groups, is there a way to decide which components
have the greatest Birnbaum measure without computing the exact
value of this measure? In this paper, three relations between com-
ponents are introduced and studied, and it is proved that they are
useful for selecting the components that have the biggest effect on
the system reliability in the sense of Birnbaum. An algorithm that
uses the results in the paper to select these important components
is also provided.
Mon, 09 Nov 2015 17:12:18 GMThttp://hdl.handle.net/2117/789452015-11-09T17:12:18ZFreixas Bosch, JosepPons Vallès, MontserratThe first step in a reliability optimization process is to
make a reliability assessment for each component in the system. If
this assessment is made in a qualitative way, by grouping together
components with the same reliability, and establishing a prevalence
order among groups, is there a way to decide which components
have the greatest Birnbaum measure without computing the exact
value of this measure? In this paper, three relations between com-
ponents are introduced and studied, and it is proved that they are
useful for selecting the components that have the biggest effect on
the system reliability in the sense of Birnbaum. An algorithm that
uses the results in the paper to select these important components
is also provided.