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

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 ...

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Jean-Claude Falmagne, Yung-Fong Hsu, Fabio Leite, Michel Regenwetter
• Keywords: DAM 2008, Random Walk, Strict Partial Order, Strict Weak Order