BUSCADOR RECOLECTA

In local social migrations, agents move from their initial location looking for a better local social environment. Social migrations processes do not change the number of social agents of a given type (i.e., the empirical distribution of the population) but their spatial location. Although cellular automata seems to appear as a natural approach to model of social migrations, the evolution of the configuration through a cellular automata might induce a new configuration wherein the number of agents of each type might be actually modified. This article provides a characterization of these cellular automata rules such that for any initial empirical distribution, the evolution of the configuration through a cellular automata of such class induces a new configuration with the same empirical distribution as the initial one, as required to model local social migrations. A class of sequences is defined in order to establish a sufficient condition to maintain this invariance property., Support from projects JC2009-00189 and MC238206 is also gratefully acknowledged. J. M. Benito-Ostolaza acknowledges financial support from Project ECO2009-12836 of the Ministry of Science and Innovation of Spain and Project ECO2012-34202 of Ministry of Economy and Competitivity of Spain. Likewise, P. Hernandez and J. Vila thank the Spanish Ministry of Science and Innovation and the European Feder Funds for financial support under project ECO2010-20584 and ECO2013-46550-R as well as the Prometeo Programme Funds PROMETEO/2009/068 and PROMETEOII/2013/019.

This essay deals with the notion and content of freedom of choice proposing a new set up and a new family of measures for this concept which is, indeed, an ethical value of paramount importance in a well ordered and open society. Following some ideas of John StuartMill, we propose that freedom of choice has to be understood not in a single stage of choice, but in the ordered collection of choices that a person can make in her life.We then suggest to represent a life in a tree structure, where each node represents a state of life and the edges between nodes will represent possible decisions in life. In this new framework, we propose a set of axioms that imply the following family of measures of lifetime's freedom of choice: the lifetime's freedom of choice has to be evaluated by a weighted sum of all possible states of life an individual might visit, with weights representing the number of decisions the individual took to reach that state.

We present a model that is closely related to the so-called models of choice under complete uncertainty, in which the agent has no information about the probability of the outcomes. There are two approaches within the said models: the state space-based approach, which takes into account the possible states of nature and the correspondence between states and outcomes; and the set-based approach, which ignores such information, and solves certain diculties arising from the state space-based approach. Kelsey [?] incorporates into a state space-based framework the assumption that the agent has ordinal information about the likelihood of the states. This paper incorporates this same assumption into a set-based framework, thus lling a theoretical gap in the literature. Compared to the set-based models of choice under complete uncertainty we introduce the information about the ordinal likelihood of the outcomes while, compared to Kelsey's approach, we incorporate the advantages of describing uncertainty environments from the set-based perspective. We present an axiomatic study that includes adaptations of some of the axioms found in the related literature and we characterize some rules featuring different combinations of information about the ordinal likelihood of the outcomes and information about their desirability.