Quaternary dichotomous voting rules

In this paper we provide a general model of "quaternary" dichotomous voting rules (QVRs), namely, voting rules for making collective dichotomous decisions (to accept or reject a proposal), based on vote profiles in which four options are available to each voter: voting ("yes", "no" or "abstaining") or staying home and not turning out. The model covers most of actual real-world dichotomus rules, where quorums are often required, and some of the extensions considered in the literature. In particular, we address and solve the question of the representability of QVRs by means of weighted rules and extend the notion of "dimension" of a rule.

Majorities with a quorum

Based on a general model of "quaternary" voting rule, sensitive to voters' choices between four different options (abstaining, voting "yes", voting "no" and staying home), we systematically study different types of majority and quorum. The model allows for a precise formulation of majority rules and quorum constraints. For such rules four types of majority can be defined. We also consider four types of quorum. Then we study the possible combinations of a majority system with a type of quorum and provide examples from rules actually used in parliaments.

Network formation under institutional constraints

We study the effects of institutional constraints on stability, efficiency and network formation. An exogenous "societal cover" consisting of a collection of possibly overlapping subsets covering the set of players specifies the social organization in different groups or "societies". It is assumed that a player may imitiate links only with players that belong to at least one society that she also belongs to, thus restricting the feasible strategies and networks. In this setting, we examine the impact of such societal constraints on stable/efficient architectures and on dynamics. We also study stability and stochastic stability in the presence of decay.network, stability, dynamics, decay, stochastic stability

Majorities with a quorum

Based on a general model of "quaternary" voting rule, sensitive to voters' choices between four different options (abstaining, voting "yes", voting "no" and staying home), we systematically study different types of majority and quorum. The model allows for a precise formulation of majority rules and quorum constraints. For such rules four types of majority can be defined. We also consider four types of quorum. Then we study the possible combinations of a majority system with a type of quorum and provide examples from rules actually used in parliaments.This research is supported by the Spanish Ministerio de Ciencia e Innovación under projects SEJ2006-05455 and ECO2009-11213, co-funded by ERDF, and from the Basque Government's funding to Grupo Consolidado GIC07/146-IT-377-07

Preferences, actions and voting rules

In this paper we address several issues related to collective dichotomous decision-making by means of quaternary voting rules, i.e., when voters may choose between four actions: voting yes, voting no, abstaining and not turning up - which are aggregated by a voting rule into a dichotomous decision: acceptance or rejection of a proposal. In particular we study the links between the actions and preferences of the actors. We show that quaternary rules (unlike binary rules, where only two actions -yes or no- are possible) leave room for manipulability (i.e., strategic behaviour). Thus a preference profile does not in general determine an action profile. We also deal with the notions of success and decisiveness and their ex ante assessment for quaternary voting rules, and discuss the role of information and coordination in this context.

Efficiency of weighted networks

In this paper, we address the question of the efficiency of weighted networks in a setting where nodes derive utility from their direct and indirect connections. Under rather general conditions, based on a set of assumptions about the value that connections in a weighted network generate, and about link-formation technology, we prove that any network is dominated by a special type of nested split graph weighted network. These conditions include some of the models in the literature, which are seen as particular cases of this general model.This research is supported by the Spanish Ministerio de Economía y Competitividad under projects ECO2015-66027-P and ECO2015- 67519-P (MINECO/FEDER). Both authors also bene t from Basque Government Departamento de Educación, Política Lingüística y Cultura funding for Grupos Consolidados IT869-13 and IT568-13

A Marginalist Model of Network Formation

We develop a network-formation model where the quality of a link depends on the amount invested in it and is determined by a link-formation "technology" , an increasing strictly concave function which is the only exogenous ingredient in the model. The revenue from the investments in links is the information that the nodes receive through the network. Two approaches are considered. First, assuming that the investments in links are made by a planner, the basic question is that of the efficient investments, either relative to a given infrastructure (i.e. a set of feasible links) or in absolute terms. It is proved that efficient networks belong to a special class of weighted nested split graph networks. Second, assuming that links are the result of investments of the node-players involved, there is the question of stability in the underlying network-formation game, be it restricted to a given infrastructure or unrestricted. Necessary and sufficient conditions for stability of the complete and star networks, and nested split graph networks in general, are obtained.This research is supported by the Spanish Ministerio de Economía y Competitividad under projects ECO2015-66027-P and ECO2015-67519-P (MINECO/FEDER). Both authors also bene t from the Basque Government Departa-mento de Educación, Política Lingüística y Cultura funding for Grupos Consolidados IT869-13 and IT568-13

Information, stability and dynamics in networks under institutional constraints

In this paper we study the effects of institutional constraints on stability, efficiency and network formation. More precisely, an exogenous "societal cover" consisting of a collection of possibly overlapping subsets that covers the whole set of players and such tha no set in this collection is contained in another specifies the social organization in different groups or "societies". It is assumed that a player may initiate links only with players that belong to at leats one society that s/he also belongs to, thus restricting the feasible strategies and networks. In this way only the players in the possiby empty "societal core", i.e., those that belong to all societies, may initiate links with all individuals. In this setting the part of the current network within each connected component of the cover is assumed to be common knowledge to all players in that component. Based on this two-ingredient model, network and societal cover, we examine the impact of societal constraints on stable/efficient architectures and on dynamics.This research is supported by the Spanish Ministerio de Ciencia e Innovación under projects ECO2009-11213 and ECO2009-07939, co-funded by ERDF. Both authors also benefit from the Basque Government's funding to Grupos Consolidados GIC07/146-IT-377-07 and GIC07/22-IT-223-07

Efficiency of weighted networks

In this paper, we address the question of the efficiency of weighted networks in a setting where nodes derive utility from their direct and indirect connections. Under rather general conditions, based on a set of assumptions about the value that connections in a weighted network generate, and about link-formation technology, we prove that any network is dominated by a special type of nested split graph weighted network. These conditions include some of the models in the literature, which are seen as particular cases of this general model.This research is supported by the Spanish Ministerio de Economía y Competitividad under projects ECO2015-66027-P and ECO2015- 67519-P (MINECO/FEDER). Both authors also bene t from Basque Government Departamento de Educación, Política Lingüística y Cultura funding for Grupos Consolidados IT869-13 and IT568-13

Efficiency vs. Stability in a Mixed Network Formation Model

Documentos de TrabajoThe purpose of this paper is twofold. First, the incomplete results relative to effciency in a transitional model introduced in a previous paper, distinguishing two types of links, strong or doubly-supported and weak or singly-supported, are completed with a full-characterization. Second, as it turns out, effcient structures are stable only for a small range of values of the parameters within the much wider range where they are effcient. This motivates the study of the impact on stability of allowing players to negotiate bilaterally the shares of the cost of doubly-supported links.Spanish Ministerio de Economía y Competitividad under proycts ECO2012-31626 and ECO2012-31346. Basque Government Departamento de Educación, Política Lingüística y Cultura funding for Grupos Consolidados IT869-13 and IT568-1