The Competitiveness of Nations

in a Global Knowledge-Based Economy

H.H. Chartrand

April 2002

Milton Friedman

Essays in Positive Economics

Part I - The Methodology of Positive Economics (b - cont'd)

Web Page 1 Introduction, 3; I. The Relationship between Positive and Normative Economics, 3; II. Positive Economics, 7; III. Can a Hypothesis be Tested by the Realism of Its Assumptions?, 16; IV. The Significance and Role of the "Assumptions" of a Theory, 23; A. The Use of "Assumptions" in Stating a Theory, 24; B. The Use of "Assumptions" as an Indirect Test of a Theory, 26; Web Page (c) V. Some Implications for Economic Issues, 30; VI. Conclusions, 39.

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            We may start with a simple physical example, the law of falling bodies.  It is an accepted hypothesis that the acceleration of a body dropped in a vacuum is a constant - g, or approximately 32 feet per second per second on the earth - and is independent of the shape of the body, the manner of dropping it, etc.  This implies that the distance traveled by a falling body in any specified time is given by the formula s = gt2, where s is the distance traveled in feet and t is time in seconds.  The application of this formula to a compact ball dropped from the roof of a building is equivalent to saying that a ball so dropped behaves as if it were falling in a vacuum.  Testing this hypothesis by its assumptions presumably means measuring the actual air pressure and deciding whether it is close enough to zero.  At sea level the air pressure is about 15 pounds per square inch.  Is 15 sufficiently close to zero for the difference to be judged insignificant?  Apparently it is, since the actual time taken by a compact ball to fall from the roof of a building to the ground is very close to the time given by the formula.  Suppose, however, that a feather is


dropped instead of a compact ball.  The formula then gives wildly inaccurate results.  Apparently, 15 pounds per square inch is significantly different from zero for a feather but not for a ball.  Or, again, suppose the formula is applied to a ball dropped from an airplane at an altitude of 30,000 feet.  The air pressure at this altitude is decidedly less than 15 pounds per square inch.  Yet, the actual time of fall from 30,000 feet to 20,000 feet, at which point the air pressure is still much less than at sea level, will differ noticeably from the time predicted by the formula - much more noticeably than the time taken by a compact ball to fall from the roof of a building to the ground.  According to the formula, the velocity of the ball should be gt and should therefore increase steadily.  In fact, a ball dropped at 30,000 feet will reach its top velocity well before it hits the ground.  And similarly with other implications of the formula.

The initial question whether 15 is sufficiently close to zero for the difference to be judged insignificant is clearly a foolish question by itself.  Fifteen pounds per square inch is 2,160 pounds per square foot, or 0.0075 ton per square inch.  There is no possible basis for calling these numbers “small” or “large” without some external standard of comparison.  And the only relevant standard of comparison is the air pressure for which the formula does or does not work under a given set of circumstances.  But this raises the same problem at a second level.  What is the meaning of “does or does not work”?  Even if we could eliminate errors of measurement, the measured time of fall would seldom if ever be precisely equal to the computed time of fall.  How large must the difference between the two be to justify saying that the theory “does not work”?  Here there are two important external standards of comparison.  One is the accuracy achievable by an alternative theory with which this theory is being compared and which is equally acceptable on all other grounds.  The other arises when there exists a theory that is known to yield better predictions but only at a greater cost.  The gains from greater accuracy, which depend on the purpose in mind, must then be balanced against the costs of achieving it.

This example illustrates both the impossibility of testing a


theory by its assumptions and also the ambiguity of the concept “the assumptions of a theory.”  The formula s = gt2 is valid for bodies falling in a vacuum and can be derived by analyzing the behavior of such bodies.  It can therefore be stated: under a wide range of circumstances, bodies that fall in the actual atmosphere behave as if they were falling in a vacuum.  In the language so common in economics this would be rapidly translated into: the formula assumes a vacuum.  Yet it clearly does no such thing.  What it does say is that in many cases the existence of air pressure, the shape of the body, the name of the person dropping the body, the kind of mechanism used to drop the body, and a host of other attendant circumstances have no appreciable effect on the distance the body falls in a specified time.  The hypothesis can readily be rephrased to omit all mention of a vacuum: under a wide range of circumstances, the distance a body falls in a specified time is given by the formula s = gt2.  The history of this formula and its associated physical theory aside, is it meaningful to say that it assumes a vacuum?  For all I know there may be other sets of assumptions that would yield the same formula.  The formula is accepted because it works, not because we live in an approximate vacuum - whatever that means.

The important problem in connection with the hypothesis Is to specify the circumstances under which the formula works or, more precisely, the general magnitude of the error in its predictions under various circumstances.  Indeed, as is implicit in the above rephrasing of the hypothesis, such a specification is not one thing and the hypothesis another.  The specification is itself an essential part of the hypothesis, and it is a part that is peculiarly likely to be revised and extended as experience accumulates.

In the particular case of falling bodies a more general, though still incomplete, theory is available, largely as a result of attempts to explain the errors of the simple theory, from which the influence of some of the possible disturbing factors can be calculated and of which the simple theory is a special case.  However, it does not always pay to use the more general theory because the extra accuracy it yields may not justify the extra cost of using it, so the question under what circumstances the simpler theory works “well enough” remains important.  Air pressure

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is one, but only one, of the variables that define these circumstances; the shape of the body, the velocity attained, and still other variables are relevant as well.  One way of interpreting the variables other than air pressure is to regard them as determining whether a particular departure from the “assumption” of a vacuum is or is not significant.  For example, the difference in shape of the body can be said to make 15 pounds per square inch significantly different from zero for a feather but not for a compact ball dropped a moderate distance.  Such a statement must, however, be sharply distinguished from the very different statement that the theory does not work for a feather because its assumptions are false.  The relevant relation runs the other way: the assumptions are false for a feather because the theory does not work.  This point needs emphasis, because the entirely valid use of “assumptions” in specifying the circumstances for which a theory holds is frequently, and erroneously, interpreted to mean that the assumptions can be used to determine the circumstances for which a theory holds, and has, in this way, been an important source of the belief that a theory can be tested by its assumptions.

Let us turn now to another example, this time a constructed one designed to be an analogue of many hypotheses in the social sciences.  Consider the density of leaves around a tree.  I suggest the hypothesis that the leaves are positioned as if each leaf deliberately sought to maximize the amount of sunlight it receives, given the position of its neighbors, as if it knew the physical laws determining the amount of sunlight that would be received in various positions and could move rapidly or instantaneously from any one position to any other desired and unoccupied position. 14  Now some of the more obvious implications of this hypothesis are clearly consistent with experience: for example, leaves are in general denser on the south than on the north side of trees but, as the hypothesis implies, less so or not at all on the northern

14. This example, and some of the subsequent discussion, though independent in origin, is similar to and in much the same spirit as an example and the approach in an important paper by Armen A. Alchian, “Uncertainty, Evolution, and Economic Theory,” Journal of Political Economy, LVIII (June, 1950), 211-21.


slope of a hill or when the south side of the trees is shaded in some other way.  Is the hypothesis rendered unacceptable or invalid because, so far as we know, leaves do not “deliberate” or consciously “seek,” have not been to school and learned the relevant laws of science or the mathematics required to calculate the “optimum” position, and cannot move from position to position?  Clearly, none of these contradictions of the hypothesis is vitally relevant; the phenomena involved are not within the “class of phenomena the hypothesis is designed to explain”; the hypothesis does not assert that leaves do these things but only that their density is the same as if they did.  Despite the apparent falsity of the “assumptions” of the hypothesis, it has great plausibility because of the conformity of its implications with observation.  We are inclined to “explain” its validity on the ground that sunlight contributes to the growth of leaves and that hence leaves will grow denser or more putative leaves survive where there is more sun, so the result achieved by purely passive adaptation to external circumstances is the same as the result that would be achieved by deliberate accommodation to them.  This alternative hypothesis is more attractive than the constructed hypothesis not because its “assumptions” are more “realistic” but rather because it is part of a more general theory that applies to a wider variety of phenomena, of which the position of leaves around a tree is a special case, has more implications capable of being contradicted, and has failed to be contradicted under a wider variety of circumstances.  The direct evidence for the growth of leaves is in this way strengthened by the indirect evidence from the other phenomena to which the more general theory applies.

The constructed hypothesis is presumably valid, that is, yields “sufficiently” accurate predictions about the density of leaves, only for a particular class of circumstances.  I do not know what these circumstances are or how to define them.  It seems obvious, however, that in this example the “assumptions” of the theory will play no part in specifying them: the kind of tree, the character of the soil, etc., are the types of variables that are likely to define its range of validity, not the ability of the leaves to do complicated mathematics or to move from place to place.

20 Index

A largely parallel example involving human behavior has been used elsewhere by Savage and me. 15  Consider the problem of predicting the shots made by an expert billiard player.  It seems not at all unreasonable that excellent predictions would be yielded by the hypothesis that the billiard player made his shots as if he knew the complicated mathematical formulas that would give the optimum directions of travel, could estimate accurately by eye the angles, etc., describing the location of the balls, could make lightning calculations from the formulas, and could then make the balls travel in the direction indicated by the formulas.  Our confidence in this hypothesis is not based on the belief that billiard players, even expert ones, can or do go through the process described; it derives rather from the belief that, unless in some way or other they were capable of reaching essentially the same result, they would not in fact be expert billiard players.

It is only a short step from these examples to the economic hypothesis that under a wide range of circumstances individual firm behave as if they were seeking rationally to maximize their expected returns (generally if misleadingly called “profits”) 16 and had full knowledge of the data needed to succeed in this attempt; as if, that is, they knew the relevant cost and demand functions,

15. Milton Friedman and L. J. Savage, “The Utility Analysis of Choices Involving Risk,” Journal of Political Economy, LVI (August, 1948), 298. Reprinted in American Economic Association, Readings in Price Theory (Chicago: Richard D. Irwin, Inc., 1952), pp. 57-96.

16. It seems better to use the term “profits” to refer to the difference between actual and “expected” results, between ex post and ex ante receipts.  “Profits” are then a result of uncertainty and, as Alchian (op. cit., p. 212), following Tintner, points out, cannot be deliberately maximized in advance.  Given uncertainty, individuals or firms choose among alternative anticipated probability distributions of receipts or incomes.  The specific content of a theory of choice among such distributions depends on the criteria by which they are supposed to be ranked.  One hypothesis supposes them to be ranked by the mathematical expectation of utility corresponding to them (see Friedman and Savage, “The Expected-Utility Hypothesis and the Measurability of Utility,” op. cit.).  A special case of this hypothesis or an alternative to it ranks probability distributions by the mathematical expectation of the money receipts corresponding to them.  The latter is perhaps more applicable, and more frequently applied, to firms than to individuals.  The term “expected returns” is intended to be sufficiently broad to apply to any of these alternatives.

The issues alluded to in this note are not basic to the methodological issues being discussed, and so are largely by-passed in the discussion that follows.


calculated marginal cost and marginal revenue from all actions open to them, and pushed each line of action to the point at which the relevant marginal cost and marginal revenue were equal.  Now, of course, businessmen do not actually and literally solve the system of simultaneous equations in terms of which the mathematical economist finds it convenient to express this hypothesis, any more than leaves or billiard players explicitly go through complicated mathematical calculations or falling bodies decide to create a vacuum.  The billiard player, if asked how he decides where to hit the ball, may say that he “just figures it out” but then also rubs a rabbit’s foot just to make sure; and the businessman may well say that he prices at average cost, with of course some minor deviations when the market makes it necessary.  The one statement is about as helpful as the other, and neither is a relevant test of the associated hypothesis.

            Confidence in the maximization-of-returns hypothesis is justified by evidence of a very different character.  This evidence is in part similar to that adduced on behalf of the billiard-player hypothesis - unless the behavior of businessmen in some way or other approximated behavior consistent with the maximization of returns, it seems unlikely that they would remain in business for long.  Let the apparent immediate determinant of business behavior be anything at all - habitual reaction, random chance, or whatnot.  Whenever this determinant happens to lead to behavior consistent with rational and informed maximization of returns, the business will prosper and acquire resources with which to expand; whenever it does not, the business will tend to lose resources and can be kept in existence only by the addition of resources from outside.  The process of “natural selection” thus helps to validate the hypothesis - or, rather, given natural selection, acceptance of the hypothesis can be based largely on the judgment that it summarizes appropriately the conditions for survival.

An even more important body of evidence for the maximization-of-returns hypothesis is experience from countless applications of the hypothesis to specific problems and the repeated failure of its implications to be contradicted.  This evidence is extremely hard to document; it is scattered in numerous memo-


randums, articles, and monographs concerned primarily with specific concrete problems rather than with submitting the hypothesis to test.  Yet the continued use and acceptance of the hypothesis over a long period, and the failure of any coherent, self-consistent alternative to be developed and be widely accepted, is strong indirect testimony to its worth.  The evidence for a hypothesis always consists of its repeated failure to be contradicted, continues to accumulate so long as the hypothesis is used, and by its very nature is difficult to document at all comprehensively.  It tends to become part of the tradition and folklore of a science revealed in the tenacity with which hypotheses are rather than in any textbook list of instances in which the thesis has failed to be contradicted.




Up to this point our conclusions about the significance of the “assumptions” of a theory have been almost entirely negative: we have seen that a theory cannot be tested by the “realism” of its “assumptions” and that the very concept of the “assumptions” of a theory is surrounded with ambiguity.  But, if this were all there is to it, it would be hard to explain the extensive use of the concept and the strong tendency that we all have to speak of the assumptions of a theory and to compare the assumptions of alternative theories.  There is too much smoke for there to be no fire.

In methodology, as in positive science, negative statements can generally be made with greater confidence than positive statements, so I have less confidence in the following remarks on the significance and role of “assumptions” than in the preceding remarks.  So far as I can see, the “assumptions of a theory” play three different, though related, positive roles: (a) they are often an economical mode of describing or presenting a theory, (b) sometimes facilitate an indirect test of the hypothesis by its implications, and (c), as already noted, they are sometimes a convenient means of specifying the conditions under which the theory is expected to be valid.  The first two require more extensive discussion.



The example of the leaves illustrates the first role of assumptions.  Instead of saying that leaves seek to maximize the sunlight they receive, we could state the equivalent hypothesis, without any apparent assumptions, in the form of a list of rules for predicting the density of leaves: if a tree stands in a level field with no other trees or other bodies obstructing the rays of the sun, then the density of leaves will tend to be such and such; if a tree is on the northern slope of a hill in the midst of a forest of similar trees, then... ; etc.  This is clearly a far less economical presentation of the hypothesis than the statement that leaves seek to maximize the sunlight each receives.  The latter statement is, in effect, a simple summary of the rules in the above list, even if the list were indefinitely extended, since it indicates both how to determine the features of the environment that are important for the particular problem and how to evaluate their effects.  It is more compact and at the same time no less comprehensive.

More generally, a hypothesis or theory consists of an assertion that certain forces are, and by implication others are not, important for a particular class of phenomena and a specification of the manner of action of the forces it asserts to be important.  We can regard the hypothesis as consisting of two parts: first, a conceptual world or abstract model simpler than the “real world” and containing only the forces that the hypothesis asserts to be important; second, a set of rules defining the class of phenomena for which the “model” can be taken to be an adequate representation of the “real world” and specifying the correspondence between the variables or entities in the model and observable phenomena.

These two parts are very different in character.  The model is abstract and complete; it is an “algebra” or “logic.”  Mathematics and formal logic come into their own in checking its consistency and completeness and exploring its implications.  There is no place in the model for, and no function to be served by, vagueness, maybe’s, or approximations.  The air pressure is zero, not “small,” for a vacuum; the demand curve for the product of a competitive

24 Index

producer is horizontal (has a slope of zero), not “almost horizontal.”

The rules for using the model, on the other hand, cannot possibly be abstract and complete.  They must be concrete and in consequence incomplete - completeness is possible only in a conceptual world, not in the “real world,” however that may be interpreted.  The model is the logical embodiment of the half-truth, “There is nothing new under the sun”; the rules for applying it cannot neglect the equally significant half-truth, “History never repeats itself.”  To a considerable extent the rules can be formulated explicitly - most easily, though even then not completely, when the theory is part of an explicit more general theory as in the example of the vacuum theory for falling bodies.  In seeking to make a science as “objective” as possible, our aim should be to formulate the rules explicitly in so far as possible and continually to widen the range of phenomena for which it is possible so.  But, no matter how successful we may be in this attempt, there inevitably will remain room for judgment in applying the rules.  Each occurrence has some features peculiarly its own, not covered by the explicit rules.  The capacity to judge that these are or are not to be disregarded, that they should or should not affect what observable phenomena are to be identified with what entities in the model, is something that cannot be taught; it can be learned but only by experience and exposure in the “right” scientific atmosphere, not by rote.  It is at this point that the “amateur” is separated from the “professional” in all sciences and that the thin line is drawn which distinguishes the “crackpot” from the scientist.

A simple example may perhaps clarify this point.  Euclidean geometry is an abstract model, logically complete and consistent.  Its entities are precisely defined - a line is not a geometrical figure “much” longer than it is wide or deep; it is a figure whose width and depth are zero.  It is also obviously “unrealistic.”  There are no such things in “reality” as Euclidean points or lines or surfaces.  Let us apply this abstract model to a mark made on a blackboard by a piece of chalk.  Is the mark to be identified with a Euclidean line, a Euclidean surface, or a Euclidean solid?


Clearly, it can appropriately be identified with a line if it is being used to represent, say, a demand curve.  But it cannot be so identified if it is being used to color, say, countries on a map, for that would imply that the map would never be colored; for this purpose, the same mark must be identified with a surface.  But it cannot be so identified by a manufacturer of chalk, for that would imply that no chalk would ever be used up; for his purposes, the same mark must be identified with a volume.  In this simple example these judgments will command general agreement.  Yet it seems obvious that, while general considerations can be formulated to guide such judgments, they can never be comprehensive and cover every possible instance; they cannot have the self-contained coherent character of Euclidean geometry itself.

In speaking of the “crucial assumptions” of a theory, we are, I believe, trying to state the key elements of the abstract model.  There are generally many different ways of describing the model completely - many different sets of “postulates” which both imply and are implied by the model as a whole.  These are all logically equivalent: what are regarded as axioms or postulates of a model from one point of view can be regarded as theorems from another, and conversely.  The particular “assumptions” termed “crucial” are selected on grounds of their convenience in some such respects as simplicity or economy in describing the model, intuitive plausibility, or capacity to suggest, if only by implication, some of the considerations that are relevant in judging or applying the model.



In presenting any hypothesis, it generally seems obvious which of the series of statements used to expound it refer to assumptions and which to implications; yet this distinction is not easy to define rigorously.  It is not, I believe, a characteristic of the hypothesis as such but rather of the use to which the hypothesis is to be put.  If this is so, the ease of classifying statements must reflect unambiguousness in the purpose the hypothesis is designed to serve.  The possibility of interchanging theorems and axioms in


an abstract model implies the possibility of interchanging “implications” and “assumptions” in the substantive hypothesis corresponding to the abstract model, which is not to say that any implication can be interchanged with any assumption but only that there may be more than one set of statements that imply the rest.

For example, consider a particular proposition in the theory of oligopolistic behavior.  If we assume (a) that entrepreneurs seek to maximize their returns by any means including acquiring or extending monopoly power, this will imply (b) that, when demand for a “product” is geographically unstable, transportation costs are significant, explicit price agreements illegal, and the number of producers of the product relatively small, they will tend to establish basing-point pricing systems. 17  The assertion (a) is regarded as an assumption and (b) as an implication because we accept the prediction of market behavior as the purpose of the analysis.  We shall regard the assumption as acceptable if we find that the conditions specified in (b) are generally associated with basing-point pricing, and conversely.  Let us now change our purpose to deciding what cases to prosecute under the Sherman Antitrust Law’s prohibition of a “conspiracy in restraint of trade.”  If we now assume (c) that basing-point pricing is a deliberate construction to facilitate collusion under the conditions specified in (b), this will imply (d) that entrepreneurs who participate in basing-point pricing are engaged in a “conspiracy in restraint of trade.”  What was formerly an assumption now becomes an implication, and conversely.  We shall now regard the assumption (c) as valid if we find that, when entrepreneurs participate in basing-point pricing, there generally tends to be other evidence, in the form of letters, memorandums, or the like, of what courts regard as a “conspiracy in restraint of trade.”

Suppose the hypothesis works for the first purpose, namely, the prediction of market behavior.  It clearly does not follow that it will work for the second purpose, namely, predicting whether there is enough evidence of a “conspiracy in restraint of trade”

17. See George J. Stigler, “A Theory of Delivered Price Systems,” American Economic Review, XXXIX. (December, 1949), 1143-57.


to justify court action.  And, conversely, if it works for the second purpose, it does not follow that it will work for the first.  Yet, in the absence of other evidence, the success of the hypothesis for one purpose- in explaining one class of phenomena - will give us greater confidence than we would otherwise have that it may succeed for another purpose - in explaining another class of phenomena.  It is much harder to say how much greater confidence it justifies.  For this depends on how closely related we judge the two classes of phenomena to be, which itself depends in a complex way on similar kinds of indirect evidence, that is, on our experience in other connections in explaining by single theories phenomena that are in some sense similarly diverse.

To state the point more generally, what are called the assumptions of a hypothesis can be used to get some indirect evidence on the acceptability of the hypothesis in so far as the assumptions can themselves be regarded as implications of the hypothesis, and hence their conformity with reality as a failure of some implications to be contradicted, or in so far as the assumptions may call to mind other implications of the hypothesis susceptible to casual empirical observation. 18  The reason this evidence is indirect is that the assumptions or associated implications generally refer to a class of phenomena different from the class which the hypothesis is designed to explain; indeed, as is implied above, this seems to be the chief criterion we use in deciding which statements to term “assumptions” and which to term “implications.”  The weight attached to this indirect evidence depends on how closely related we judge the two classes of phenomena to be.

Another way in which the “assumptions” of a hypothesis can facilitate its indirect testing is by bringing out its kinship with other hypotheses and thereby making the evidence on their validity relevant to the validity of the hypothesis in question.  For example, a hypothesis is formulated for a particular class

18. See Friedman and Savage, “The Expected-Utility Hypothesis and the Measurability of Utility,” op. cit., pp. 466-67, for another specific example of this kind of indirect test.


of behavior.  This hypothesis can, as usual, be stated without specifying any “assumptions.”  But suppose it can be shown that it is equivalent to a set of assumptions including the assumption that man seeks his own interest.  The hypothesis then gains indirect plausibility from the success for other classes of phenomena of hypotheses that can also be said to make this assumption; at least, what is being done here is not completely unprecedented or unsuccessful in all other uses.  In effect, the statement of assumptions so as to bring out a relationship between superficially different hypotheses is a step in the direction of a more general hypothesis.

This kind of indirect evidence from related hypotheses explains in large measure the difference in the confidence attached to a particular hypothesis by people with different backgrounds.  Consider, for example, the hypothesis that the extent of racial or religious discrimination in employment in a particular area or industry is closely related to the degree of monopoly in the industry or area in question; that, if the industry is competitive, discrimination will be significant only if the race or religion of employees affects either the willingness of other employees to work with them or the acceptability of the product to customers and will be uncorrelated with the prejudices of employers. 19  This hypothesis is far more likely to appeal to an economist than to a sociologist.  It can be said to “assume” single-minded pursuit of pecuniary self-interest by employers in competitive industries; and this “assumption” works well in a wide variety of hypotheses in economics bearing on many of the mass phenomena with which economics deals.  It is therefore likely to seem reasonable to the economist that it may work in this case as well.  On the other hand, the hypotheses to which the sociologist is accustomed have a very different kind of model or ideal world, in which single-minded pursuit of pecuniary self-interest plays a much less important role.  The indirect evidence available to the sociologist on

19. A rigorous statement of this hypothesis would of course have to specify how “extent of racial or religious discrimination” and “degree of monopoly”are to be judged.  The loose statement in the text is sufficient, however, for present purposes.


this hypothesis is much less favorable to it than the indirect evidence available to the economist; he is therefore likely to view it with greater suspicion.

Of course, neither the evidence of the economist nor that of the sociologist is conclusive.  The decisive test is whether the hypothesis works for the phenomena it purports to explain.  But a judgment may be required before any satisfactory test of this kind has been made, and, perhaps, when it cannot be made in the near future, in which case, the judgment will have to be based on the inadequate evidence available.  In addition, even when such a test can be made, the background of the scientists is not irrelevant to the judgments they reach.  There is never certainty in science, and the weight of evidence for or against a hypothesis can never be assessed completely “objectively.”  The economist will be more tolerant than the sociologist in judging conformity of the implications of the hypothesis with experience, and he will be persuaded to accept the hypothesis tentatively by fewer instances of “conformity.”


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