Stochastic applications of media theory: Random walks on weak orders or partial orders

Jean Claude Falmagne, Yung Fong Hsu, Fabio Leite, Michel Regenwetter

Research output: Contribution to journalArticlepeer-review


This paper presents the axioms of a real time random walk on the set of states of a medium and some of their consequences, such as the asymptotic probabilities of the states. The states of the random walk coincide with those of the medium, and the transitions of the random walk are governed by a probability distribution on the set of token-events, together with a Poisson process regulating the arrivals of such events. We examine two special cases. The first is the medium on strict weak orders on a set of three elements, the second the medium of strict partial orders on the same set. Thus, in each of these cases, a state of the medium is a binary relation. We also consider tune in-and-out extensions of these two special cases. We review applications of these models to opinion poll data pertaining to the 1992 United States presidential election. Each strict weak order or strict partial order is interpreted as being the implicit or explicit opinion of some individual regarding the three major candidates in that election, namely, Bush, Clinton and Perot. In particular, the strict partial order applications illustrate our notion of a response function that provides the link between theory and data in situations where, in contrast to previous papers, the permissible responses do not span the entire set of permissible states of the medium.

Original languageEnglish (US)
Pages (from-to)1183-1196
Number of pages14
JournalDiscrete Applied Mathematics
Issue number8
StatePublished - Apr 15 2008


  • Media theory
  • Partial orders
  • Random walk
  • Stochastic process
  • Weak orders

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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