Media Theory

University Of California-Irvine, Irvine CA

Investigators

Abstract

Abstract Falmagne, Jean-Claude E. University of California, Irvine SES-9986269 Whereas considerable research has been devoted to the study of individual preferences, both from empirical and theoretical standpoints, the evolution of preferences over time has been given only scant attention. The proposed research focuses on this question. Various classes of preference relations (total orders, partial orders, semiorders, biorders, etc.) are regarded as special cases of the abstract concept of a "medium", i.e., a particular kind of semigroup of transformations on a set of states. The research will develop the algebraic and stochastic aspects of media theory, and will apply the results to substantial data, such as the evolution of opinions regarding candidates in an important election. The study of opinions and their evolution over time is a natural concern in a democratic country. It is important to develop scientific tools capable of faithfully interpreting the judgements expressed by the members of a community regarding critical issues. The aim of the research is to make such tools not only available, but also easy to use. The results will provide, among other benefits, more accurate techniques for the analysis of opinion polls.