Mathematical Sociology

This paper studies the conditions that improve bargaining power using threats and promises. We develop a model of strategic communication, based on theconflict game with perfect information, in which a noisycommitment messageis sent by a better-informed sender to a receiver who takes an action that determines the welfare of both. Our model captures different levels of aligned-preferences, for which classical games such asstag hunt,hawk-dove, andprisoner’s dilemmaare particular cases. We characterise the Bayesian perfect equilibrium with nonbinding messages undertruth-telling beliefsandsender’s bargaining powerassumptions. Through our equilibrium selection we show that the less conflict the game has, the more informative the equilibrium signal is and less credibility is necessary to implement it.

The concept that we live in small world networks connected by
short paths has proved fascinating. These networks, however, do
not typically emerge as linear responses to individual-level changes;
rather, subtle changes in relations produce extraordinarily different
macrolevel outcomes. Similarly, nuances in how we conceptualize,
define, and measure relations can lead to widely different network
characterizations. The author demonstrates this variability using a
spectrum of interaction types and argue that the dependence of
results on subtleties in definition or measurement makes theoretical
interpretation difficult. He offers an index to calculate how much
inaccuracy or imprecision relational definitions or data-gathering
techniques can tolerate before results yield utterly different
interpretations.

This paper is motivated by a distinctive appreciation of the difficulties posed by quantitative observational inquiry into complex social and economic systems. It develops ordinary and piecewise indices of joint and incremental informational association that enable robust approaches to a common problem in social inquiry: grappling with associations between a quantity of interest and two distinct sets of co-variates taking values over large numbers of individuals. The distinct analytical usefulness of these indices is illustrated with their application to inquiry into the systemic economic effects of patterns of discrimination by social identity in the U.S. economy.

The research framework of this study is related to the problem of why and how the population´s beliefs born, develop and, finally extinct. In previous work, the kinetics of the groups that remain constant in their empire's nationalistic ideologies was developed. Now, this research tries to calculate how beliefs diminish until disappearing. Founded in basic historical data of two ideologies, Christianism and Sovietism, the aim of this work is to establish that the populations increase is inversely proportional to the difference between that population and the maximum Nm that could reach, dN / (Nm - N), and the elapsed time 1dt, where1 is a coefficient greater than zero. As an eternal duration is impossible, a decrement factor Nmexp (-2t) is introduced. This produces a differential equation that can be interpreted mechanically as the initial impulse that pushes and made it works. The conclusion can be desegregated in three parts: first, in terms of formal equations; second, in soc...

The research framework of this study is related to the problem of why and how the population´s beliefs born, develop and, finally extinct. In previous work, the kinetics of the groups that remain constant in their empire's nationalistic ideologies was developed. Now, this research tries to calculate how beliefs diminish until disappearing. Founded in basic historical data of two ideologies, Christianism and Sovietism, the aim of this work is to establish that the populations increase is inversely proportional to the difference between that population and the maximum Nm that could reach, dN / (Nm - N), and the elapsed time 1dt, where1 is a coefficient greater than zero. As an eternal duration is impossible, a decrement factor Nmexp (-2t) is introduced. This produces a differential equation that can be interpreted mechanically as the initial impulse that pushes and made it works. The conclusion can be desegregated in three parts: first, in terms of formal equations; second, in soc...

The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a 'functorial' mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the 'theory of categories,' a branch of modern algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach.

Las migraciones humanas han sido, y son , uno de los principales factores del cambio social y desarrollo humano. Actualmente, un fenomeno migratorio internacional caracteriazado por la diversidad de origenes, idiomas y culturas se asientan en las ciudades , generando una serie de situaciones y demandas desconocidas en Euskadi hasta la fecha. Ante este nuevo panorama de cambio social acelerado, explicar el modo en que los procesos sociales toman cuerpo en el espacio urbano se hace indispensable. El objeto de estudio de este proyecto forma parte de ese gran campo de "lo urbano", que se enmarca en la disciplina de la sociologia urbana y tambien de la sociologia de las migraciones: estudiar y analizar las pautas de localizacion socio-residencial de las personas inmigrantes extranjeras en el Area Metropolitana de Bilbao.La tradicion sociologica de este tipo de estudios es antigua, comenzo en la Escuela de Chicago en los anos 30 con Park y sus discipulos. Bajo la maxima de que &...