ANALYSIS OF SPATIAL BEHAVIOR BY REVEALED SPACE PREFERENCEстатья из журнала
Аннотация: ABSTRACT In the study of spatial behavior we are interested in finding the rules for spatial choice which, when applied to any unique distribution of spatial opportunities, are capable of generating spatial behavior patterns similar to those observed. Behavioral postulates in geographical theories should incorporate these rules rather than descriptive statistics of actual behavior in a spatial system, since the latter are incorporating knowledge of the same spatial system that the theory hopes to generate and, in so doing, to explain. The concept of revealed space preferences is proposed as the organizing concept for finding these rules. This concept is similar to that of revealed preference in the theory of consumer demand. If spatial choice is viewed as a comparison and evaluation of alternative spatial opprtunities against a personal preference function, then, from any consistent statement of preferences from the paired comparison of spatial opportunities, it ought to be possible to derive a unique ranking of those spatial opportunities. Such a ranking is graphically portrayed on the familiar indifference surface. This article evaluates one method of finding this preference structure (indifference surface) by generating hypothetical spatial behavior patterns in accordance with a known ranking of spatial opportunities and shows that it is possible to find that ranking from the spatial behavior patterns. A mathematical proof shows why this is possible and also indicates the circumstances in which the proposed model is valid and those where it is weak. Notes 1 L. Curry, "Central Places in the Random Spatial Economy,"Journal of Regional Science, Vol. 7, No. 2 (Supplement, 1967), p. 218. 2 Curry, op. cit., footnote 1, p. 218. 3 J. Nystuen, "A Theory and Simulation of Intraurban Travel," Chapter 3 in W. L. Garrison and D. F. Marble (Eds.), Quantitative Geography, Part I (Evanston, Illinois: Northwestern University, Studies in Geography, No. 13, 1967). 4 B. J. L. Berry, "A Synthesis of Formal and Functional Regions Using A General Field Theory of Spatial Behavior," in B. J. L. Berry and D. F. Marble, Spatial Analysis (Prentice-Hall, 1968), Part VI, Chapter 3, p. 420. 5 Curry, op. cit., footnote 1, p. 219. 6 D. F. Marble and J. D. Nystuen"An Approach to the Direct Measurement of Community Mean Information Fields,"Papers and Proceedings, The Regional Science Association, Vol. 11 (1963), p. 105. 7 Several authors have emphasized the role of the distribution of opportunities in influencing behavior in space: S. A. Stouffer, "Intervening Opportunities: A Theory Relating Mobility and Distance,"American Socilogical Review, Vol. 5 (1940); D. F. Bramhall, "Gravity, Potential and Spatial Interaction Models," in W. Isard (Ed.), Methods of Regional Analysis: An Introduction to Regional Science (New York: John Wiley and Sons, 1960), Chapter 11, pp. 538–44; C. Clark and G. H. Peters"The Intervening Opportunities Method of Traffic Analysis,"Traffic Quarterly, Vol. 19 (1965), pp. 101 19; C. Clark, "Trip Distribution in Oslo,"Traffic Quarterly, Vol. 22 (1968), pp. 259 70. 8 J. Wolpert, "Behavioral Aspects of the Decision to Migrate,"Papers, The Regional Science Association, Vol. 15 (1965), pp. 159 72. 9 T. Hagerstrand, "On Monte Carlo Simulation of Diffusion," Chapter 1 in Garrison and marble, op. cit., footnote 3. 10 Marble and Nystuen, op. cit., footnote 6, p. 99. 11 W. Christaller (C. W. Baskin, trans.), Central Places in Southern Germany (Englewood Cliffs, N. J.: Prentice-Hall, 1966). It is common for writers who review Christaller's Central Place Theory to describe his definition of the Range of a Good (p. 22, p. 43, pp. 49–58), and then review his theoretical derivation of central place patterns (pp. 49–58). However, it has never been made clear that there is no formal relation between the two in Christaller's work. In his theoretical derivation, Christaller used the more simple spatial behavioral postulate that the consumer patronizes the nearest center offering the required good. The consequences of substituting for this behavioral postulate, the more complex and ill-defined concept of the range of a good have not yet been described. For example, if we agree with Christaller that, "the range of a good is greater when it is offered in a larger central place than when it is offered in a smaller central place," (p. 50), then one consequence would be unsymmetrical tributary areas around centers thus giving varying sized tributary areas even for towns of the same order—since towns of the same order have neighbors of different orders depending on their location on in the central place system. Herein lies a paradox, for towns of the same order, by definition, imply towns with similar sized tributary areas in an area with a spatially uniform surface of propensity to purchase. Yet, if we apply Christaller's definition of range we are inevitably drawn to the conclusion that centers of the same order do not have similar sized tributary areas. Christaller obviously made his simplifying behavioral postulate to escape from this dilemma. We include this footnote to illustrate the relevance of the spatial behavioral postulate to central place theory. 12 H. S. Houthaker, "The Present State of Consumption Theory: A Survey Article,"Econometrica, Vol. 29 (1961). 13 P. A. Samuelson, "Consumption Theory in Terms of Revealed Preference,"Economica, Vol. 15 (1948), pp. 243 53. 14 K. E. Boulding, Economic Analysis (New York: Harper and Row, 1955), 3rd edition, Chapter 36, "Indifference Curves and the Theory of Optimum Choice." For other studies of revealed preference theory and its relation to consumer demand see: R. G. D. Allen, "The Nature of Indifference Curves,"Review of Economic Studies, Vol. I (1933), pp. 110–21; W. Edwards, "The Theory of Decision-Making,"Phychological Bulletin, Vol. 51 (1954), pp. 380 417; N. Georgescu-Roegen, "The Theory of Choice and the Constancy of Economic Laws,"Quarterly Journal of Economics, Vol. 64 (1950), pp. 125 38; N. Georgescu-Roegen, "The Pure Theory of Consumer's Behavior,"ibid., Vol. 5 (1936); Houthaker, op. cit., footnote 12. 15 W. Leontief, "Introduction to a Theory of the Internal Structure of Functional Relationships,"Econometrica, Vol. 15 (1947), pp. 361 73. 16 Houthaker, op. cit., footnote 12, p. 718. 17 R. Malm, G. Olsson, and O. Wärneryd, "Approaches to Simulations of Urban Growth,"Geografiska Annaler, Series B, Vol. 48 (1966), p. 10. 18 G. Rushton, Spatial Pattern of Grocery Purchases by the Iowa Rural Population, (Iowa City: University of Iowa, Bureau of Business and Economic Research, Studies in Business and Economics, New Series No. 9, 1966), pp. 21–62; G. Rushton, R. G. Golledge and W. A. V. Clark, "Formulation and Test of a Normative Model for the Sptial Allocation of Grocery Expenditures by a Dispersed Population,"Annals, Association of American Geographers, Vol. 57 (1967), pp. 389 400. 19 In this study a random sample of 480 households drawn from a universe of all farm households living outside towns in Iowa was used. Píj could be measured directly in a computer subroutine since compatible x, y location coordinates existed for all towns in Iowa with a 1960 population greater than fifty-five and for the 480 sample households. 20 Rushton, Golledge and Clark, op. cit., footnote 18, p. 396. 21 I would like to acknowledge and to thank Mr. Michael Goodchild of McMaster University who developed this proof. 22 H. M. Walker and J. Lev, Statistical Inference (New York: Holt, Rinehart and Winston, 1953), p. 272. 23 S. Siegel, Nonparametric Statistics (New York: McGraw-Hill, 1956), p. 226. 24 This approach is described in G. Rushton, "The Scaling of Locational Preferences," in K. Cox and R. G. Golledge (Eds.), Problems of Spatial Behavior: A Symposium (Evanston, Ill.: Department of Geography, Northwestern University, to be forthcoming in 1969).
Год издания: 1969
Авторы: Alexander M. Rush
Издательство: American Association of Geographers
Источник: Annals of the Association of American Geographers
Ключевые слова: Regional Economics and Spatial Analysis, Consumer Retail Behavior Studies, Regional Economic and Spatial Analysis
Открытый доступ: closed
Том: 59
Выпуск: 2
Страницы: 391–400