New Entropy Models in the Social Sciences. 1. Elementary Residential-Location Models

Abstract

This paper is concerned with the development of new entropy models for use in the social sciences and, in particular, with residential location in a spatial-interaction context. The inconsistencies and limitations inherent in some of the existing spatial-interaction entropy models used to describe activities taking place in urban and regional systems are first discussed, and new location models that have none of these inconsistencies are then developed. The new models describe the location of households about a city centre and, more generally, about a given distribution of jobs. The models take due account, in a consistent fashion, of any zonal-capacity constraints. The use of the models is illustrated with suitable data.

Energy laws in human travel behaviour

“…For example, they have transfered the gravity law to fit migration rates and origindestination matrices of streams of persons or goods [14]. Moreover, in order to derive more appropriate mathematical relations for these, they have applied entropy principles [15,16]. In fact, some of the most common decision models such as the so-called multinomial logit model [17] can be derived from entropy principles [18].…”

Intraurban Residential Migration: An Entropy Maximizing Approach*

“…Let these be X j and p" respectively, then Equation (41) of the last section may be written as Equation (43) represents not only a concise formulation of the model but also a generalization to include every possible set of variables that may be considered as affecting the residential migration process. It has the same form as Equation (20) of Dacey and Norcliffe [7] and in a sense is a generalization of their model, although slightly different approaches have been utilized in deriving the equations.…”

“…Consequently, one can see an analogy between this and the probability urn model where one is faced with a situation of drawing balls from an urn containing N A balls of one type and N B of the other (Webber [25]). A useful analogy in statistical mechanics is the FermiDirac distribution where molecules obey Pauli's exclusion principle according to which the number of molecules in a quantum state is either zero or unity (Dacey and Norcliffe [7], Fisk …”

On planning and forecasting the location of retail and service activity

“…Contributions to this area were made, among others, by Fisk and Brown (1975), Dacey and NorclifTe (1976), Snickars and Weibull ( 1977), Batty ( 1978), Lesse et al ( 1978), Brotchie et al (1979) and Roy and Lesse (1981). Some of these ideas were applied to shopping models in Roy (1981).…”