Media theory
Let \(\varepsilon\) be a finite set of states. A token (of information) is a function \(\tau\colon S\mapsto S\tau\) mapping \(\varepsilon\) into itself. Let \(\mathcal J\) be a set of tokens on \(\varepsilon\). The pair \((\varepsilon,{\mathcal J})\) is called a token system. A token system is called a medium if it satisfies some axioms [\textit{J.-Cl. Falmagne}, J. Math. Psychol. 41, No. 2, 129-143 (1997; Zbl 1072.91654)]. This paper focuses on a particular semigroup of transformations of a set of states, that is, a medium. The authors list examples of media arising in combinatorics, and gather new results dealing with particular subclasses of media called oriented media, which was suggested by some examples in first section of this paper. In the final section, the authors summarize, in a stochastic framework, the results of an application of media theory to some polling data concerning the 1992 US Presidential Election [Psychol. Rev. 106, No. 2, 362-384 (1992)]. Media theory is a good application branch of the algebraic theory of semigroups.
scientific article; zbMATH DE number 1792336
scientific article