COMMENTS ON PAPERS BY ISARD AND SMITH

MICHAEL F. DACEY

Nor~hwestern University

THE ROLE OF A DISCUSSANT

Without question, this work by Isard and Smith is presented as a contribution to the theory of behavior in space. Many months ago I naively agreed--note that I said naive, which is not to be confused with one of Walter's simple people--to comment on their effort, presumably to congratulate, to criticize, to extend or other- wise to evaluate their study. I am hesitant to fulfill this agreement. This hesitance does not mean [ have been intimidated by the lengthy title and its impressive array of pregnant terms. It does reflect my feeling that the theorist working on the spectrum of social sciences concerned, at least, with things, people, and actions in a regional or spatial context is consistently beset by contradictions and uncertainties about the value, merit, and need for his efforts. There are incessant reminders that the theory is always puny relative to the magnitude of problems that society wants and needs to resolve. Moreover, the theory invariably seems inadequate and weak relative to even the limited aspirations of an academic social science theory that is seemingly within range of our capabilities but, as yet, beyond our accomplishments. Conversely, it is invariably a simple matter for a critic to dismiss the available theory as trivial, irrelevant, crude, misleading or, for a multitude of other reasons, unworthy of retention as a viable and useful contribution. The strategies that lead to these conclusions are well known to all of us and, [ suspect, occasionally used by all of us.

The dilemma confronting the critic is what to do in lieu of pat criticism. A com- mon ploy is to describe your own research, which may be (though, not necessarily) relevant to the paper at hand. My ploy is to display some of my thoughts and other mental wonderings that arose as I read or, more accurately, confronted their paper.

THE ROLE OF CHANCE

This paper is geographic in the sense that the concern is with things, people, and actions that are, in principle, mappable. Specifically, it pertains to travel be- havior that is observable and is associated with specific locations in space: the origin and destination of each trip, and possibly, the route connecting these two places. In this sense, the theory purports to describe or explain data that are frequently displayed as a map distribution. Map distributions, by definition, are generated by location processes. Some theoretical location processes are normative and I think I could defend the proposition that the current need is to exploit these types of theories that have direct implications to planning decisions involving land use and trans- portation facilities. The present theory is, however, idiographic in that it describes

The support of the National Science Foundation, Grant GS-2967, is gratefully acknowledged.

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events that actually occur. The formulation of such theories is typically algebraic or probabilistic. While there is no dictum that a theorist must always advocate the same approach, for each statement of a location process he does select one approach over the other and for models that are idiographic and explanatory the selection is between alternatives that in many ways are equally unattractive. The variability in observed data suggests that algebraic models cannot endure a rigorous goodness- of-fit test, whether it is assumptions or conclusions that are matched against data. This failure on empirical tests promotes preference for probabilistic formulations which do include provision for variation in the observations. By and large, social scientists concerned with regional and spatial structures have not adopted this alterna- tive. Because of the strong algebraic orientation of the present models, it is appro- priate to comment briefly on some elements of this neglected alternative.

It evidently is not possible to prove or disprove the assertion that a particular spatial distribution is generated by a location or behavioral process that includes a chance element. Hence, there is considerable freedom in deciding whether an algebraic or probabilistic model is more appropriate to the phenomena and/or more attuned to the predilections of the theorist. Frequently, a decisive factor is the philosophical implications of the role of chance in human decisions and behavior, and most social scientists reject probabilistic formulations because these implications are heretical to cherished doctrines of free will and freedom of choice.

Probabilistic formulations are compatible to the theorist that is willing to agree that location decisions and behavior in space of both individuals and groups are governed by probabilistic laws. Though this view provides immediate access to the extensive theory of stochastic processes, it is an anathema to most social scientists because it suggests, as aptly phrased by Curry [1 ; p. 40], that one is "regarding the earth's surface as governed by the mechanism of a roulette wheel and its development as a permanent floating crap game."

An alternative approach is to adopt the weaker thesis that the observable results of the location decision and actions of individuals and groups appear to the observer as though they are governed by probabilistic laws. This postulate may be more palatable because it can be admitted to a theory without subscription to the preceding postulate that behavior is actually a manifestation of probabilistic laws. A limita- tion of this view is that it emphasizes observations on behavior rather than explana- tion of behavior and to utilize models that treat observed behavior as though it obeyed probabilistic laws is evidently prima facie evidence that models fail to explain the constituents and determinants of human behavior. This defect is critical because of the sharp distinction that is frequently made between models that explain behavior as opposed to those that only replicate the spatial and other consequences of behavior. This attitude is eloquently reflected in the criticism that has been directed by geog- raphers to the use of stochastic models.

Webber [3; p. 27]: " . . . these models are verifiable but they tell us little or nothing about processes. We must recognize these two forms of models--the

DACEY: COMMENTS ON PAPERS BY ISARD AND SMITH 53

process model, and the predictive model--and realize that process and verifiability are :mutually contradictory.. , apart from the normative role, [process models] exist to help us understand reality, not to predict the reality." Guelke [2; p. 42]: "The patterns they [stochastic models] simulate and describe are frequently beyond their competence to explain."

When chance occurs in studies of behavior, it typically enters by two different back doors: by serving as a surrogate for the aspects of behavior that need to be, bat are not yet, incorporated within known and specified deterministic laws and by en- compassing behavior that accompanies inability either to discriminate the effects of alternative decisions or to express a preference for the effects of alternative decisions. The use of probability notions serves primarily as a convenient representation for ignorance of real-world behavior. It permits the social scientist to adopt probabi- listic structures for the study of behavior without a deep commitment to a partic- ular probabilistic interpretation of human behavior. Moreover, the restriction to aspects of behavior that are not known or cannot be known means that chance component is the least interesting aspect of a model that purports to explain location decisions and behavior, and accordingly, receives little or no emphasis in the speci- fication of a model. By this view, probability serves only as a fudge factor that accounts for the discrepancies between observation and theory.

While the implications of these observations on probabilistic models are not conclusive, I think they imply that the regional and spatial social sciences can develop theories that have an internal integrity and are empirically testable with prospects of verifiability only if our theorists shift emphasis away from the deterministic and algebraic model, away from the behavioral approach that seeks to explain and away from the use of probability as a surrogate for ignorance. Seemingly, all that re- mains are stochastic models based on the premise either that behavior is governed by probabilistic laws or the behavior invariably appears to an observer as though it were governed by probabilistic laws.

THE ROLE OF MATHEMATICS

Starting from this premise, additional thoughts accumulated rapidly because gravity and similar models of spatial interaction seemingly belong to a class of intel- lectual concepts that invariably evoke an emotional response. My response is aptly described as enthusiastic detachment. I have tried, unsuccessfully, to entice others (particularly, graduate students) to work on gravity models. At the same time, I have studiously avoided intimate contact with or work on gravity models. Recent- ly, as I was inundated with a steady flow of manuscripts from Isard and Smith, this response was intensified. Certainly, their effort merits a thorough, penetrating as- sessment and I will actively encourage any of you to undertake this task. For my part, even the existence of an impressive mathematical statement does not spark my interest. It may be a deeply ingrained bias of my generation that gravity and similar interaction models are appropriate tools for city planners, highway designers, and

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other engineers that need to resolve immediate practical problems, but they lack the intellectual respectability prerequisite to full acceptance within social science theory. While some theorist from an earlier and, thereby, older generation, such as Isard and Beckmann, did not learn this parable or have chosen to ignore the class distinctions that it implies, most of my contemporaries certainly have maintained a discreet distance between their research and gravity type models. By and large, the col- lective reaction to Allan Wilson's admirable efforts to revitalize gravity models has been-- "If you want to do that sort of t h ing . . . "

Because of this detachment I cannot speak with authority, but it is my impres- sion that the utility of these models for empirical work largely resides in the fact that they "work." Evidently, this means that some variant of a gravity type model frequently can be calibrated to yield values that are acceptably close to observed travel data. The defects evidently are that some data sets defy acceptable approxi- mation by any variant of the gravity model and that the approximations are accept- ably close for applications but are not sufficiently refined to satisfy the standards of most scientific work. In this sense the gravity model is similar to a large number of other regional models, such as the rank-size rule for city sizes and the exponential decay rule for urban population density: they work well if the demand for precision and reliability is not high but they are too crude for acceptance as laws that merit incorporation within social science theories.

Herein lies, I think, one critical constraint on theory development in a regional or spatial context. There are known to us a number of empirical regularities that lack theoretical underpinnings. These regularities, which include gravity, rank- size, and exponential decay rules provide only crude approximations to empirical data. A serious challenge to the would-be theorist is assessment of the level of elaboration and sharpness that is compatible with these crude regularities. Does the gravity model merit the intensive, sophisticated theory developed, first, by Allan Wilson and, now, by Isard and Smith? One speculation is that their refinements pertain to a real world that, regrettably, does not exist. If so, their theory cannot count as much more than an exercise, challenging as it may be, in advanced mathe- matics. I'm not sure that the hypothesis of a messy world is valid, but the chance that it is must inhibit both acceptance and use of theories that encompass sophisti- cated mathematics. These comments should not be misconstrued as an invocation against the integration of higher mathematics into social science theory. The con- tention is that without observations to which they pertain, highly refined results have no greater utility than rough approximations. The art is to identify the level of theoretical precision that is compatible with observations--whether this theory is embodied in sophisticated or elementary mathematics is inconsequential.

THE ROLE OF VERIFICATION I have found it useful to discriminate theoretical contributions by the theorem

testers and the assumption testers. I am a tester of the first kind, which I am fre-

DACEY" COMMENTS ON PAPERS BY ISARD AND SMITH 55

quently informed is an outmoded remnant of classical physics, that accepts that a theory is built from assumptions that are not empirically testable and yields con- sequences some of which are empirically testable. It is a good mathematical theory if there are many steps between the initial, untestable assumptions and the testable conclusions. Preferably, the implications are not obvious consequences of the assumptions, and it is a powerful theory if some of the results are unexpected or unintuitive. Additionally, it is a good empirical theory if the testable conclusions are in accord with observations from the real world. By testable is meant falsi- fiable so that by this approach it is meaningless to speculate on the validity of as- sumptions. Instead, the empirical goodness of a theory depends only on the degree of accord between conclusions and the real world. This contrasts with the approach of the assumption testers who demand of a theory that it be based upon assumptions that are known to be true. Evidently all conclusions that follow from the assump- tions are also true. This approach puts the emphasis on examining the validity of the assumptions rather than verifying the conclusions; it is not necessary that the con- clusions be verifiable and it may be preferable that they are not verifiable. This approach seemingly dominates the theoretical literature in geography. After one or two initial studies that follow the mode of assumptions followed by conclusion, subsequent studies have a format that, to me, is perplexing. A typical study notes that a prior study was based upon assumptions I to n. Evidence is then presented to show that one or more assumptions are not in accord with empirical data. Alterna- tive assumptions are then identified and evidence is presented that indicates ac- cordance with the data. The paper ends with enumeration of a new and, presumably, improved set of assumptions. Invariably, the new assumptions are more complex and less intuitive than the ones they replace. To one who accepts the classical approach of assumptions first, followed by preliminary lemmas and ending with major theorems, this emphasis upon assumptions, with entire papers that involve only assumptions, is indeed curious. The current paper is in the tradition of as- sumption testers, though at the initial, embryonic stage in which a statement of impli- cation follows the assumptions. It is characteristic of this tradition that most subse- quent studies will concentrate on evaluation and refinement of the assumptions given by both Isard and Smith. Despite my qualms, the justification for this ap- proach is compelling. Models are constructed to explain behavior. The explana- tion resides not in the observed behavior but in its underlying rationale. This rationale is encompassed within the assumptions. Hence, the assumptions must not only be true but they are also the most interesting component of the model.

The feature of this approach that confuses me is the need for model construc- tion. Evidently, the ideal model contains only statements that are known to have empirical validity. The model codifies this intelligence and is augmented only as new empirical facts become known. Though a symbolic notation may be useful for expressing these facts, the deductive power of mathematics evidently plays no funda- mental role in extending our understanding of behavior. Though theorems of

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existence, uniqueness, and so forth, may be welcome appendages, their contribution to understanding behavior is minor.

THE ROLE OF GEOGRAPHY

If this paper were given at a meeting of the Association of American Geographers, it would undoubtedly headline a section titled: Behavioral Geography. It is inter- esting to note that the Pennsylvania group of regional scientists is moving into this arena at the time that it is being vacated by geographers who evidently have decided the approach was not productive, or at least, failed to satisfy the aspirations of its advocates who, not too long ago, were numerous, optimistic, and vocal. This movement replaces the trend of the past several decades in which geography has lagged behind hard-core regional science in adoption of intellectual innovations. Currently, American geography seems to lack a dominating intellectual thrust that is exciting and stimulating to its proponents and challenging and irritating to its opponents. In fact, at this time geography is a dull, uninteresting field quiescently waiting for the stimulus provided by emergence of a new intellectual frontier or reemergence of prematurely discarded research focus. Possibly, a potentially signif- icant contribution of this study is to rekindle interest in behavioral geography-- heaven forbid !

REFERENCES [1] Curry, L. "Chance and Landscape," in J. W. House, ed., Northern Geographical Essays

in Honor of G. H. J. Daysh. Newcastle-upon-Tyne: Oriel Press, 1966. [2] GueIke, L. "Problems of Scientific Explanation in Geography," Canadian Geographer,

Vol. 15 (1971), pp. 38-53. [3] Webber, M.J. "Empirical Verifiability of Classical Central Place Theory," Geographical

Analysis, Vol. 3 (1971), pp. 15-28.