"The History of the Prediction Paradox," presented at the Annual Meeting of the International Society for the History of the Behavioral and Social Sciences, Akron, OH (May 10, 1970)
by Gordon Welty
Wright State University
Dayton, OH 45435 USA
We will trace today the history of the prediction paradox from Professor Oskar Morgenstern's first rigorous formulation up to the present. The prediction paradox is defined for that situation where an infinite series of reciprocally conjectural reactions and counter-reactions between two or more actors occurs. These reactions occur when the calculation of the outcomes of one agent's future behavior includes expectations of the future behavior of other actors, and vice versa./1/
Two points follow: (a) A prediction naively made of the behavior of another agent will in general be false or irrefutable, since the other's acts are based in part on the behavior of the predictor. The other's acts, the purported subject of the prediction, will thus take into account the prediction itself, which thereby in general becomes self-fulfilling or suicidal. On the other hand, (b) a theory of social behavior which accommodates this regress of conjectural reactions is explicitly a dynamic theory.
Morgenstern first articulated the paradox in his book on Economic Forecasting in 1928./2/ We should not suppose that Morgenstern was the first to recognize the problem: for instance, Frank Knight of Chicago noted in 1925 that the social scientist is faced with an unusual problem: the human being, whom the social scientist seeks to understand control, likewise seeks understanding and control of others, including the scientist himself. Knight asks, "Who is the controller and who the controlled? Who is the potter and who the pot?"/3/ We will return to Knight in a moment.
It is important to notice the importance of rigorous formulation of a problem to its solution. Suppes has noted that negative proofs, or impossibility theorems, are inherently more difficult of proof than other theorems./4/ As we shall see, the prediction paradox has been taken as being suggestive of the impossibility of rigorous research, hence can be considered a conjecture of impossibility. Thus it becomes crucial to know just what is being conjectured as impossible.
We will turn to the analytical problems, after we have presented three case studies illustrating the development of awareness of the problems in the prediction paradox.
Excellent examples of reflexive predictions are available in the study of race relations. A classic case is given by the historian, James Johnson in 1930./5/ He described the influx of Blacks into Harlem, and the repercussions.
In the early part of the 20th century, Blacks began to purchase houses along Lenox Avenue in Harlem. Their entry into formerly white neighborhoods took on, in the eyes of the whites, the appearance of an invasion. Johnson continues that the whites "felt that Negroes as neighbors ... lowered the values of their property."/6/
The suggestion is being made that the housing market was conceived of as follows by the whites. Consider this diagram:
We have drawn a vertical supply curve (S) because the supply of houses is considered by the homeowner to be quite inelastic in the short run. The homeowners supposed that the value of property declined in the face of the influx of Blacks. This is reflected by a downward shift of the demand curve, from D to D'.
Thus it was predicted by realtors and homeowners that the price of houses would decline, as illustrated on the ordinate. In Chicago's Hyde Park area, they supposed that the prices of their houses had decreased to one-third of the original, when the Blacks entered Hyde Park./7/
Johnson relates how the whites in Harlem "began to flee. They took fright, they became panic-stricken, they ran amuk." After noting that the reasoning of the homeowners was unsound, he went on "these people did not stop to reason, they did not stop to ask why they did what they were doing, or what would happen if they didn't do it." The prediction of lowered prices, though based on false premises, became a reality. Johnson is graphic. "The stampeded whites actually deserted house after house and block after block. Then prices dropped; they dropped lower than the bottom ..."/8/
There is an explanation of the decline in value implicit in Johnson's discussion which is more plausible than that of the homeowners. If we suppose that the demand curve is a composite of a demand curve of Blacks and whites, and that for housing in a given neighborhood in transition, the demand by Blacks absorbs any decline in demand by whites, then it follows that the demand curve is fixed.
The decline in price, expected by the white homeowners and noted by Johnson, would be explained by a shift in the supply curve from S to S', as illustrated in the following diagram:
We observe the effect, the change in price, is the same as that registered in Figure I.
The shift of the supply curve can be understood as a reaction of the white homeowner to the informal prediction, by an "authority" on the housing market such as a realtor, that the price of housing would decline in that neighborhood. Acting on this expectation, and the belief that this price change signalled a decline in value of the houses, the homeowners rush to sell. The local market is glutted and the price falls.
Thus the prediction is true by virtue of its being uttered alone, rather than its theoretic merit. This classic illustration while showing at least implicitly, theoretical sophistication, has very little of methodological import. In other fields, recognition of the methodological problem commenced. For instance, there was the recognition of the related paradox of the Hawthorne effect. We make reference, as an example, to the famous Hawthorne studies. Since Cook's vast research /9/ more than amply covers investigations of the Hawthorne effect up to 1967, we will only note a few highlights of the early studies.
The initial studies at Hawthorne were to examine the rather pedestrian problem of the relationship of lighting to industrial output. They ran from 1924 to 1927. The major findings were two. It was recognized that the problems of experimental control were great, and that the response of output to systematic variation of illumination was curious. Output appeared to be monotonically increasing, quite independent of the illumination and its variation./10/
At this point, the Western Electric Company decided to undertake more extensive research in a special and isolated room where it was assumed that problems of control could be eliminated. This research, from 1927 to 1932, provided the base of a radical change in industrial relations,/11/ as well as the conception of the practice of research.
Roethlisberger and Dickson reported on this research that the "results were puzzling to the investigators, for they were not what they had expected. The general upward trend in output . . . was astonishing (and) perplexing."/12/ They continued that "five hypotheses or interpretations were suggested" to explain the monotonic increase of output. Three of these hypotheses related the change in output to experimental conditions which (1) improved working conditions, (2) relieved cumulative fatigue, and (3) relieved monotony. A fourth hypothesis supposed the increases could be attributed to increased wage incentives./l3/
The first factor, that of improved working conditions, was dismissed on the basis of Whitehead's earlier work./14/ The next three, relating to fatigue, monotony, and incentives, were rejected by Roethlisberger and Dickson as not explaining the increase./15/ The investigators turned instead to an argument that, rather than a controlled experiment, the Relay Assembly Test Room had become a "social situation which needed to be described and understood as a system of interdependent elements."/16/ A fifth hypothesis then supposed that "the experimental periods had been essentially carriers of social value."/17/ In essence, the establishment of a social system to test any hypothesis about the relationship of lighting to output was sufficient in itself to increase output. Hence, given the hypothesis predicting that "increased lighting causes increased output," this hypothesis, by its testing circumstance, is guaranteed of proving true in its consequent. Output would necessarily increase, hence the hypothesis was self-fulfilling.
Roethlisberger and Dickson conclude that "the results from a research point of view were negative."/18/ This was because "the experiment they had planned to conduct was quite different from the experiment they had actually performed."/19/ The failure of the Hawthorne studies from a research standpoint can be at the very least a stark illustration of the increasing interest in the social context of research. As Cook has noted, "It should not be assumed that the report of the Hawthorne studies prompted this concern directly."/20/ Rather a recognition of reactive behavior, based in a number of areas of research, was beginning to coalesce into a received opinion among research practitioners that there were substantial and perhaps insurmountable problems at the basis of the study of human behavior.
By 1944, we find Otto Neurath noting the impredictability, within empirical social science, of human behavior./21/ By this time, the methodological problems were clearly seen.
The pessimistic judgment on the possibility of social science research received its greatest support from yet another area of investigation, namely that of public opinion and attitude research. Several resounding predictive failures of polls in the early thirties, such as the 1936 fiasco of the Literary Digest in forecasting the presidential election, caused practitioners to devote more care to eliminating sampling biases and interviewer biases.
But these refinements of method were apparently to little avail. In 1948, the major public opinion pollsters failed to correctly predict the outcome of the Dewey-Truman presidential campaign. At issue was more than the failure of prediction. It was suggested that because of the forecast of Dewey's impending victory, Republicans stayed home on election day, thus falsifying the forecast. Similarly, because of or perhaps in spite of the expectation of Truman's impending loss, Democrats turned out, and by means of an "underdog effect" assured Truman's victory./22/
Rensis Likert argued of public opinion measurement that no matter how wrong were Gallup, Roper, etc in 1948, "it would be as foolish to abandon this field as it would be to give up any scientific inquiry which, because of faulty methods and analysis, produced inaccurate results."/23/ Likert saw the failure of prediction as a shortcoming of the practice of the researchers, not as a portent of the impossibility of research. But there were other views. Perhaps the most searching comment was that of no less than Elmer Roper, who noted the "dangers to our science when the measurement of public opinion begins to influence the very opinion it is seeking to measure."/24/ Roper concludes with, "To my mind, a very strong case can be made against polling." Here the methodological point is in the fore: the predictions in social science are reflexive, hence perhaps social science should be abandoned.
Having traced the development of the problem, let us turn to its analysis. Professors Emile Grunberg, Franco Modigliani and Herb Simon, working closely at Carnegie Institute of Technology, proved that under plausible conditions, prediction hence social science was possible in the reflexive case./25/
There is a behavior under study. There is a modification of that behavior, due to the realization of the actor that he is being studied. The behavior under study is predicted by a continuous real-valued function x. It is a plausible assumption that the modification of behavior can be described by a continuous real-valued reaction function R.
R is defined for the closed interval 0 £ x £ 1. Also, R is bounded above and below, vis. 0 £ R £ 1. Thus we have constrained R to the unit interval. These constraints would appear to be met in most social situations. We can depict the reaction function as follows:
We will now give a differential calculus proof of the existence of at least one value of x which is the correct prediction of the behavior under study.
Construct a function P such that p(x) = R(x) - x
There are then three cases:
a) R(0) = 0
b) R(l ) = 1
c) 0 < R(x) < 1
In cases (a) and (b), we have trivially a behavior following the actor's modification which has the same value as the predicted value. Thus for R(0) = 0 or R(l ) = 1, correct prediction can occur. In case (c) we have a function which is positive at one endpoint, negative at the other endpoint, and continuous through the interval. By a corollary of Rolle's Theorem, this function vanishes somewhere between the endpoints. Where P(x) = 0, we have R(x) = x, which is again the correctly predicted value. We can graphically depict this case as:
Thus we see that sufficient and plausible conditions can be given whereby correct prediction of a behavior can occur, whether or not the actor whose behavior is under study is aware of his social role of "subject."
The formal properties of this prediction situation are as follows. In the metalanguage, or at the linguistic level where we can discuss the language of the behavioral model which is being applied in the prediction situation, we might say that there are n independent factors which affect the experimental outcome.
One of these n factors is the subjects' response to the realization that he is being studied. A model with n - l factors is hence underdetermined. There are less variables than equations and this sort of equation set cannot in general be uniquely solved. Thus the model must include a reaction function.
As Simon has pointed out, again in the metalanguage, this requires that an asymmetrical relationship exists between the behavior of the experimenter and the behavior of the subject./26/ That is to say, while the experimenter must know the subject's reaction function, vice versa cannot be true. In light of current work by Rosenthal/27/ and Friedman,/28/ it is perhaps fruitful to consider any scientist engaged in prediction as a potential manipulator of his subject matter. In any case, as we have seen, the question of whether public predictions are inherently invalid must be answered in the negative.
The reaction function, a behavioral parameter such as it is, transforms the methodological problem into one of sociology or of social psychology. With the resolution of the argument about the possibility of nomothetic behavioral research, the problem becomes one of specifying under what conditions and to what extent the subject reacts to the role of "subject."/29/
There are reasons to believe that a comprehensive and predictive theory of behavior must be dynamic. The concepts of latent function and unforeseen social consequences were attempts on the part of Richard Merton, another figure in the history of the prediction paradox, to make a contribution to the theoretical development./30/
The "sociologizing" of research is at present a vaguely articulated discussion, exampled mainly by the Continental Wissensoziologie. On the other hand, the "social psychologizing" of the research context was clearly anticipated by Kurt Lewin./31 / In social engineering projects, he recognized that the inclusion of feedback loops for project control necessitated explicit consideration of the project manager in the research scheme. What obtains outside the laboratory can only be accomodated in a field theory of behavior.
We find on a review of the literature since 1954 that a good deal of confusion still accompanies the prediction paradox, especially among those scholars who purport to discuss methodological issues. There seem to be two groups.
First, there are those writers who accept the possibility proof as methodologically conclusive. Illustrative is Professor Roger Buck's 1963 discussion of reflexive predictions. While he purports a "consideration of the social scientist's methodological problem,"/32/ we find him confusing the logical argument with the dynamic theory.
It is interesting to notice his psychologistic language, including such phrasing as "Suspecting that his prediction may be reflexive, what should the social scientist do?"/33/ Of course, the scientist involved in the conjectural reactions of the reflexive subject will seek, by a series of reciprocally conjectural counter-reactions, to establish the asymmetric relationship we noted above. Whether he will or not is a theoretic problem of social psychology or the sociology of science.
But Buck thinks he is engaging in methodological considerations. Further, Buck notes that in a given series of conjectural reactions and counter-reactions, an infinite series is generated. This again is a theoretic problem of social psychology, which Buck unwittingly acknowledges by noting "Whether or not any particular series will generate such a convergence and thus tend towards equilibrium, depends on the slopes of the curves involved."/34/ Such a dependency is an empirical matter. Thus again the logical problem of the possibility of prediction is confused with the substantive problem of what happens among interrelated actors.
But Buck thought he was engaging in methodological discourse: he concludes "How serious, then, is the methodological problem for the social scientist? In my view, not very!"/35/
On the other extreme, there are the writers who do not appreciate the purely formal nature, and hence the remarkable extension of the possibility proof. A good example here is Professor Daniel Stufflebeam. He addresses the problem of the use of research designs in the social space characterized by feedback loops. Examples here would be research in an organization through time.
If the problems encountered in the employment of designs were simply the practical ones enumerated for example, by Stanley Seashore,/36/ they could in principal be overcome by diligence and adequate resources. Stufflebeam has proposed, however, that there is a logical incompatibility between the application of design and the dynamic study of organizations. The first premise of this logical argument is that if preliminary research findings are disseminated during the research cycle, in simplest terms, between pre- and post-measures, then the management may use these findings to modify operations or organization during the cycle. This sort of modification practice, to achieve organizational improvement, so the argument goes, will corrupt the design and render the research meaningless. The other premise of the logical argument is that the researcher either is ethically prescribed to publish the preliminary findings, or else is under a monetary sanction to do so. From these premises, the conclusion of incompatibility is drawn./37/
As most research designs are developed within the framework of the linear model, the preceding analysis of the prediction paradox is relevant here. Also recall our comments on Lewin and his conception of this problem in organizational research.
That there is still a good bit of concern for the prediction paradox is unquestionable. For instance, Senator John Pastore noted that, because of an "increasing concern" for the effect on an election outcome of predictions based on computer projections "it was suggested in 1964 that an 8 o'clock eastern standard time declaration of a winner could catch 23 States still voting with an electoral strength of 216 out of 538 total."/38/ This concern continued up to the Senate hearings of July 19, 1967, when the following exchange, typical of the overall hearings, took place between Dr. Warren Miller, of the Survey Research Center at the University of Michigan, and Senator Robert Griffin. First, Dr. Miller: "...our own experience starting in 1948, running particularly through 1964, is that in no instance do we have any evidence that we as research scholars have been given additional problems because the polls have made an impact on people and have changed their behavior ..."
Next, Senator Griffin: "...my understanding as a politician and a candidate tells me that the bandwagon psychology is important in campaigning and that if you can get the public to believe that you are going to be a winner or that you are winning ... this has an impact on potential voters. ...and if during a campaign, I can find a poll and get it published that shows that I am ahead or that I am gaining, that is helpful to me. Do you challenge that?" Dr. Miller again: "I suspect I do fundamentally, Senator."/39/
Thus we suggest that the tide has turned. While in the received opinion the prediction paradox is still a consideration, it appears that it has been sufficiently resolved to permit the scholar to continue his work.
l. Oskar Morgenstern, "Volkommene Voraussicht und wirtschaftliches Gleichgewicht," Zeitschrift fur Nationalokonomie, VI:3 (1935), pp. 337- 357. Translated by George Stigler as "Perfect Foresight and Economic Equilibrium," now available in Research Memorandum No. 55, Princeton University, Econometric Research Program (April 30, 1963), pp. 37-67.
2. Oskar Morgenstern, Wirtschaftsprognose, Wien: Julius Springer (1928), pp. 92-l06.
3. Frank H. Knight, "Economic Psychology and The Value Problem," Quarterly Journal of Economics, Vol. 39 (1925). Reprinted in Ethics of Competition and other Essays, New York: Harpers (1935), pp. 89-90. Cf. also his Risk, Uncertainty and Profit, London (1933), Preface, pp. xxxiii-xxv. We should note that Stigler undertook the translation of Morgenstern at Knight's request.
4. Patrick Suppes, "The Desirability of Formalism in Science," Journal of Philosophy, Vol. 68 (1968), pp. 659-664.
5. James Weldon Johnson, Black Manhattan, New York: Knopf (1930), pp.147-155.
6. Johnson, op. cit., p. 150
7. Chicago Commission on Race Relations, The Negro in Chicago, Chicago: University of Chicago Press (1922), pp. 116ff.
8. Johnson op. cit., p. 150.
9. Desmond L. Cook, The Impact of the Hawthorne Effect in Experimental Designs in Educational Research, Columbus: Ohio State University (1967).
10. G. A. Pennock, "Industrial Research at Hawthorne," The Personnel Journal,Vol. 8 (1929), pp. 296-313.
11. Illustrative is Elton Mayo's Human Problems of an Industrial Civilization, New York: Macmillan (1933).
12. F. J. Roethlisberger and William J. Dickson, Management and the Worker, Cambridge: Harvard University Press (1939), p. 86.
13. Roethlisberger and Dickson, op.cit., pp. 87-88.
14. T. N. Whitehead, The Industrial Worker, Cambridge: Harvard University Press (1938).
15. They dismiss the factor of fatigue at op. cit., p. 127; that of monotony, ibid; and incentives at p. 160.
16. Roethlisberger and Dickson op. cit.., p. 183.
17. ibid., p. 88
18. Roethlisberger and Dickson op. cit., p. 184.
19. op.cit., p. 183
20. Cook, op. cit., p. 5.
21. Otto Neurath, "Foundations of the Social Sciences," International Encyclopedia of Unified Science, Vol. II:1 (1944), pp. 28-29.
22. On the 1948 presidential polls, cf. "Opinion Polls and the 1948 U. S. Presidential Election: A Symposium," International Journal of Opinion and Attitude Research, Vol. 2 (1948), pp. 309-328 and ibid, Vol. 3 (1949), pp. 451-591.
23. Rensis Likert, "Public Opinion Polls," Scientific American, Vol. 179 (1948), pp. 7-11.
24. Elmo Roper, "Some Comments on Election Polls," International Journal of Opinion and Attitude Research, Vol. 3 (1949), p. 2.
25. Cf. E. Grunberg and F. Modigliani, "The Predictability of Social Events," Journal of Political Economy 62:6 (1954) pp. 465-478; Herbert A. Simon, "Bandwagon and Underdog Effects of Election Predictions," Public Opinion Quarterly (1954) pp. 245-253.
26. Herbert Simon, "Causal Ordering and Identifiability," in A. Ando, F. M. Fisher and H. A. Simon. Essays on the Structure of Social Science Models, Cambridge: MIT Press (1963) p. 21.
27. Robert Rosenthal, Experimenter Effects in Behavioral Research, New York: Appleton-Century-Crofts (1966).
28. Neil Friedman, Social Nature of Psychological Research, New York: Basic Books (1967).
29. Cf. Grunberg and Modigliani op. cit. p. 471; Robert Rosenthal, op. cit, p. 319, considers the converse question: to what extent does the experimenter project his role of "experimenter?"
30. Cf. R. K. Merton, "Unanticipated Consequences of Purposive Social Action," American Sociological Review (1936) and his Social Theory and Social Structure, New York: Free Press (1957).
31. Kurt Lewin, "Frontiers of Group Dynamics," Human Relations Vol. I (1948). Cf. also Richard Jung's "Socializing Organizations as Ejective Channels," presented at the Ohio Valley Sociological Society, 1962 Annual Meeting, East Lansing, Michigan (May 4, 1962).
32. Roger C. Buck, "Reflexive Predictions," reprinted in The Nature and Scope of Social Science, ed. L. I. Krimerman, New York: Appleton-Century-Crofts (1969) p. 157. Cf. also E. Grunberg and F. Modigliani, "Reflexive Prediction," Philosophy of Science Vol. 32: 2 (1965) pp. 173-174.
33. Buck ibid.
34. Buck op. cit., p. 158. .
35. Buck op.cit., p. 159.
36. S. E. Seashore, "Field Experiments with Formal Organizations," Human Organization (1964) p. 165.
37. Cf. Gordon Welty, "Use of Experimental Designs in the Decision-Making Feedback Process," Journal of Experimental Education Vol. 37:2 (1968) p. 89.
38. Report of the Committee on Commerce, "Predictions and Projections of Election Results," 90th Congress, Senate Report No. 561, Washington, D. C.: U. S. Government Printing Office (1967), p. 1.
39. Hearings before the Subcommittee on Communication, "Projections - Predictions of Election Results and Political Broadcasting," 90th Congress, 1st Session. Washington, D. C.: U. S. Government Printing Office (1967), p. 220.
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