In order to formalize the act of agreement between two individuals, the concept of consensus functional equation, for a bi-variate map defined on an abstract choice set, is introduced. Then, and in a purely choice-theoretical framework, we relate the solutions of this equation to the notion of a...

It is shown that any completely preordered topological real algebra admits a continuous utility representation which is an algebra-homomorphism (i.e., it is linear and multiplicative). As an application of this result, we provide an algebraic characterization of the projective (dictatorial)...

This paper proposes a comprehensive, path-independent decomposition formula of changes into ceteris paribus effects and interaction effects. The formula implies a reassessment of sequential decomposition methods that are widely used in the literature and that are restrictive in how they treat...

How do individuals shape societies? How do societies shape individuals? This paper develops a framework for studying the connections between micro and macro phenomena. The framework builds on two ingredients widely used in social science − population and variable. Starting with the simplest...

This paper proposes a new unified theory of sociobehavioral forces. The goal of the new theory is to integrate theories describing five sociobehavioral processes - comparison (including justice and self-esteem), status, power, identity, and happiness - bringing under a single theoretical...

The last three decades the accumulation of quantitative research evidence has led to the development of systematic methods for combining information across samples of related studies. Although a few methods have been described for accumulating research evidence over time, meta-analysis is widely...

The goal of scientific work is to understand more and more by less and less. In this effort, theoretical unification plays a large part. There are two main types of theoretical unification – unification of different theories of the same field of phenomena and unification of theories of...

This paper proposes a new model of wage determination and wage inequality. In this model, wage-setters set workers' wages; they do so either directly, as when individuals vote in a salary committee, or indirectly, as when political parties, via the myriad of social, economic, fiscal, and other...

Social scientists study two kinds of inequality: inequality between persons (as in income inequality) and inequality between subgroups (as in racial inequality). This paper analyzes the mathematical connections between the two kinds of inequality. The paper proceeds by exploring a set of...

This paper develops the mathematical foundations of comparison, referential, and relative (CRR) processes. The key ingredients are: (1) three kinds of terms; and (2) two kinds of relations. Combining the three terms - absolute amount, relative amount, and relative rank - with the two kinds of...