TY - JOUR

T1 - Stochastic applications of media theory

T2 - Random walks on weak orders or partial orders

AU - Falmagne, Jean Claude

AU - Hsu, Yung Fong

AU - Leite, Fabio

AU - Regenwetter, Michel

N1 - Funding Information:
We are grateful to the editors and two anonymous referees for their service and critical comments. Falmagne's work in this area was supported by NSF Grant No. SES-9986269 to J.-C. Falmagne at UCI.

PY - 2008/4/15

Y1 - 2008/4/15

N2 - 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.

AB - 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.

KW - Media theory

KW - Partial orders

KW - Random walk

KW - Stochastic process

KW - Weak orders

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U2 - 10.1016/j.dam.2007.04.032

DO - 10.1016/j.dam.2007.04.032

M3 - Article

AN - SCOPUS:40849116257

VL - 156

SP - 1183

EP - 1196

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 8

ER -