Media theory
type: Item
instance of: scholarly article
title: Media theory
zbMATH Open document ID: 1026.20056
DOI: 10.1016/S0166-218X(01)00235-9
author: R. Smith
published in: Discrete Applied Mathematics
publication date: 2002-08-29T00:00:00Z
review text: 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.
reviewed by: Xie Xiang-Yun
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 91D10
zbMATH DE Number: 1792336
zbMATH Keywords: semigroups
zbMATH Keywords: partial orders
zbMATH Keywords: wellgradedness
zbMATH Keywords: random walks
zbMATH Keywords: opinion polls
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1792336