Competition and Succession in the Dynamics of Scientific Revolution
Jason Wittenberg John D. Sterman
Department of Political Science Sloan School of Management
Massachusetts Institute of Technology Massachusetts Institute of Technology
Cambridge, MA 02139 Cambridge, MA (02139
jwittenb@athena.mitedu jsterman@mitedu
Abstract
‘What is the relative importance of internal versus contextual forces in the birth and death of scientific theories?
Elaborating on the analysis of a model of multiple paradigm competition and scientific development already developed
by Wittenberg and Sterman, we find that situational factors present when a paradigm is launched largely determine a
Beradign's peobeblicy of reg to dominance, Stronger paradigms that survive the emergence phase live longer than
won oowmgpers, Oa Gal 1 ee SpaL Op LACS BSE RE DE ERED
Introduction
‘The publication of Thomas S: Kuhn's Structure of Scientific Revolutions heralded a radically new conception of
science. In the traditional view science applies universally-accepted norms of logical inquiry and scientific develop-
ment is seen as the uncontested triumph of ever more truthful and encompassing images of reality. In contrast, Kuhn
argued that new theories replace old ones rather than build upon them, revolutionizing science's very image of itself
(1970: 84-85). For Kuhn scientific development is fraught with errors, blind alleys, and intense competition among
competing world-views. Progress is understood less as a steady accumulation of truths than “as a succession of
tradition-bound periods punctuated by non-cumulative breaks" (Kuhn 1970: 208). se
The idea that social, historically contingent factors might play a role in scientific development equal to that of a
theory’s intellectual content has elated social scientists and historians as much as it has infuriated many philosophers
and scientists: For many social researchers Kuhn's theory legitimated resistance to the century-old attempt to make
the study of society, politics and culture more ‘scientific’. For many scientists and philosophers Kuhn's attempt to
historicize the scientific process was at best reckless and at worst heresy. Yet whether as prophecy or apostasy, his
ideas continue to stimulate interest in the nature of truth and the source of scientific commitment. Even. the most
ardent believer in scientific rationality must marvel at how "bad" explanations sometimes catch on while “good” ones
languish for lack of interest. Even the most determined critic of Kuhn's theory must wonder how the Aristotelian
paradigm, so demonstrably 'wrong' from the point of view of a Newtonian, could have dominated scientific thought
for well over a millennium. Why is‘it that some paradigms last for centuries while others quickly wither? How do
factors internal to a paradigm and contextual forces interact to shape and constrain the development of new paradigms?
Purpose
‘We address these questions with a formal dynamic modél of paradigm competition. The model is based on Sterman's
(1985).model of Kuhn's theory, -which portrayed how internal factors could produce the collective behavior Kuhn
identified as characteristic of scientific development. Wittenberg (1992) criticized this model for having excluded con-
textual -and contingent ¢lements suchas the’existence of competitor paradigms. Building upon this criticism,
Wittenberg and Sterman (1992) extended the model to allow for expiicit paradigm competition while still preserving
the complex intemal structure of the paradigm in Sterman's original model. In this paper we use the model to inves-
tigate the relative importance of internal and contextual factors in determining the fate of new paradigms.
Although this model remains inspired by Kuhn's work we do not claim to have fully captured his theory. Translating
the theory from its qualitative, highly abstract written form into an internally consistent, formal model has involved
many simplifications. Indeed, making explicit the causal connections that we and others readers of Kuhn routinely
take for granted has required the introduction of conjectures Kuhn might even disagree with (Wittenberg ibid.; but see
also Sterman 1992, Radzicki 1992 and Barlas 1992.) Nonetheless, formalization has advantages. Most discussions of
Kuhn's theory are based on ambiguous mental models, and Kuhn's work itself is textual, rich with ambiguity, multi-
ple meanings, and implicit assumptions. More importantly, Kuhn offers no calculus by which one. can assess
‘whether the dynamics he describes can be produced by the causal factors he postulates. Formalization helps to surface
auxiliary assumptions so they can be debated and tested. We see formalization as complementary to the work of
and historians of science attempting to empirically verify theories of scientific change (e.g. Donovan,
Laudan and Landan, 1988). Kuhn's theory is also one example of a broader class of theories of revolutionary change.
We thank Frank Sulloway and Anjali Sastry for helpful comments.
SYSTEM DYNAMICS '93 573
The model may provide insights into how revolutionary upheavals occurs in other domains such. as the social
sciences (see Kuhn, 1970: 208-209; Gersick, 1991, Tushman and Anderson 1986, Sastry, 1992). Finally, the model
applies nonlinear dynamics to sociological phenomena, It describes path-dependent processes in which new paradigms
are endogenously and stochastically generated. Our results may thus contribute to the growing literature on evolu-
tionary behavior (see Anderson, Arrow & Pines (1988); Bruckner, Ebeling and Scharnhorst (1989); Ebeling (1991);
Bruckner, Ebeling and Schamhorst (1990); Radzicki and Sterman (1993).)
A Theory of Paradigm Development
Rather than summarize Kuhn's theory here, we assume familiarity with Kuhn's work and the many interpretations and
alternatives to it (e.g. Lakatos and Musgrave 1970). An important aspect of Kuhn's theory for purposes of modeling
is the life cycle-of a paradigm. Kuhn describes a sequence of four stages: emergence, normal science, crisis, and revo-
lution (followed by the emergence of a new paradigm). The emergence phase is characterized by the absence of com-
monly-accepted beliefs or standards governing scientific activity. Conflict among paradigm-candidates is thus rooted
in incompatible metaphysical beliefs and logics of inquiry. Such conduct characterized electrical research before
Franklin and his successors provided the field with a paradigm (Kuhn 1970: 13-15). Once a theory attracts nearly
every scientist in the field — thereby becoming a dominant paradigm — normal science begins, Now scientists cease to
debate fundamental issues, and, convinced that their paradigm is the proper way to characterize reality, proceed to
apply it to nature's puzzles, When clashes between theory and reality do occur, they are more often than not resolved.
in favor of theory. Thus, for example, by the early twentieth century physics had become so identified with Newton's
Principia that no one questioned Newton's theory even though there were persistent discrepancies between it and ob-
servations concerning the speed of sound and the motion of Mercury (Kuhn 1970: 81). A paradigm enters crisis when
enough unsolved puzzles are recognized as important anomalies. Increasing numbers of scientists will devote their
time to solving these anomalies rather than other puzzles, and some will propose radical solutions. A revolution
‘occurs when a new paradigm based on such a radical idea is adopted, and science is reconstructed from new fundamen-
tals, Einstein's theory of relativity is.a well-known example of a revolutionary theory, in which. basic notions of
‘space and time were fundamentally reconceptualized. Obviously: the timing, character, and context of each stage differ
from case to case. For example, a dominant paradigm in crisis may quickly be replaced, or crisis may deepen for
decades as new theories fail to sprout or flower. The social, political and cultural context, as well as chance factors
(the existence of an Einstein, Bohr or Keynes) may strongly condition the character and timing of the dynamics.
A Model of Paradigm Development
‘We construct a multi-paradigm model in which the structure of Sterman's original (1985) model is replicated for each
of the competitor paradigms, and additional structure is added to specify how the paradigms interact. The 1985.paper
provides a complete description and documentation of the model structure for each paradigm; here we only outline that
structure. The model creates a simulated ecology of interacting paradigms, each representing a community of practi-
tioners; recruitment and defection from that community; and the intellectual activities of the members such as formu-
lating and solving nature's puzzles, recognizing and trying to reconcile anomalies, and conceiving new theories. The
model simulates the attitudes .and beliefs of the practitioners within each paradigm through constructs such as
“confidence in the paradigm’ and the time required to perceive: phenomena which challenge the theory such as‘anoma-
lies. The essence of the dynamic hypothesis is the notion that the average difficulty of the puzzles to be solved by the
paradigm increases as the cumulative number of puzzles solved grows, This ‘paradigm depletion’ represents the idea
that cach par ‘digm is a limited model of reality which may apply well in. the domain of phenomena it was originally
formulated to explain, but will be harder and harder to apply as scientists extend it to new domains. Newtonian
mechanics worked brilliantly for macroscopic, slow masses, but was harder to apply successfully. to the domains of
the very small or very fast. Specifically, the average difficulty of new puzzles to be solved, D, is given by
D=(SP/C)Y qa)
where SP is the cumulative number of solved puzzles, C, the nominal solved puzzle reference, determines the intrin-
sic capability of each paradigm, and 7 is the rate.at which difficulty rises with cumulative progress (y=1 here). Small
values of C mean paradigm’s intrinsic explanatory power is weak — the difficulty of new puzzles rises rapidly as
normal science proceeds. Large values indicate a powerful paradigm, one that can explain a great deal before it
becomes harder to apply. As the difficulty of puzzles grows, puzzle-solving may slow and more unsolved puzzles
may become recognized as anomalies. If the stock of anomalies grows too large, the confidence practitioners have in
the truth or utility of the paradigm may fall. The collapse of confidence is self-reinforcing: anomalies destroy confi-
deace, and falling confidence increases the ability and willingness of practitioners to see the gaps in the theory.
‘The focal point of the model is a construct called ‘confidence’. Confidence captures the basic beliefs of practitioners
regarding regarding the epistemological status of their paradigm-— is it seen as a provisional model or revealed truth?
574 SYSTEM DYNAMICS '93
Encompassing logical, cultural, and emotional factors, confidence determines how anomalies are perceived, how prac-
titioners allocate research effort, and recruitment to and defection from the paradigm. It is defined between 0 (absolute
conviction the paradigm is false, nonsensical) through .5 (maximum uncertainty as to its truth) to.1 (absolute.convic-
tion the paradigm is truth). Pressures leading confidence to change arise both from within a paradigm and from com-
parisons with other paradigms, Confidence rises when puzzle-solving progress is high and when anomalies are low.
‘The impact of anomalies and progress is mediated by the level of confidence itself. Extreme levels of confidence:
hinder rapid changes in confidence because practitioners, utterly committed, resist any. evidence contrary to their
beliefs. Practitioners with only lukewarm commitment, lacking firm reasons to accept or reject the paradigm, are far
more likely to change their confidence in the face of anomalies.
‘The external factors affecting confidence encompass the way in which practitioners in one paradigm view the accom-
plishments of other paradigms. We distinguish between the dominant paradigm, defined as that paradigm which has
set the norms of inquiry and commands the allegiance of the most practitioners and alternative paradigms, the upstart
contenders. Confidence in a competing paradigm tends to increase if its anomalies are less than those of the dominant
Pade ee as measured ‘by Cumulative solved puzzles.-Confidence tends to
if the dominant paradigm has fewer anomalies or more solved puzzles. Alternative paradigms compare them-
petit with one another as well as with the dominant paradigm. Confidence in’an alternative paradign to tends to
decrease if it has more anomalies or fewer solved puzzles than the most successful of the other alternatives.
According to Kuhn, normal science is puzzle-solving. In the model, the rate at which scientists formulate and solve
these puzzles, depends .on.the number of practitioners, the fraction of their time devoted to puzzle solving, and the
intrinsic difficulty of the puzzles. Under normal conditions a puzzle, once formulated and attacked, will be solved in
fairly short order, adding to the cumulative stockpile of knowledge generated by the paradigm. But as the intrinsic
difficulty. of puzzles grows, a growing number will resist solution long enough to be recognized.as anomalies,
Anomaly recognition is a subtle psychological process. Confidence determines the degree to which practitioners are
conditioned to see. reality as consistent with their paradigm. Increases in confidence will slow the recognition of
anomalies since practitioners become increasingly blinded by the paradigm and thus take a longer time to recognize
the problems that do arise as anomalies. Anomalies may sometimes be resolved into the theory, thus ending a poten-
tial threat to the paradigm. The rate at which anomalies are resolved depends on the number of practitioners in sanc-
tioned. research, the. fraction of those involved in anomaly resolution, and the average difficulty. of anomalies.
Anomalies are assumed to be more difficult to solve.than puzzles, and as the difficulty of puzzles increases, the diffi-
culty of anomalies rises as well. The fraction of practitioners involved.in anomaly resolution depends on the balance
between the number of anomalies and the acceptable number. The acceptable number of anomalies is the number that
can be tolerated without losing confidence in the paradigm. If the number of anomalies increases, additional scientists
are drawn into anomaly resolution in an attempt to solve the major outstanding problems challenging the.theory. For
example; the Michelson-Morley experiment drew forth many efforts to reconcile Newtonian theory with the observed
constancy of the speed of light with respect to relative motion.
‘The.population of practitioners committed to each paradigm is endogenous, increasing with recruitment and decreas-
ing with retirement of elder scientists and defection of others to competing paradigms. We assume for simplicity that
the total population of scientists in all_paradigms is constant: scientists who leave one paradigm enter another; and
entry of young scientists is balanced by retirement of the-old. The assumption of constant total population simpli-
fies the interpretation of the results but is in no way essential to the main conclusions; it can easily be relaxed in
future versions. Practitioners defect based on their confidence relative to the confidence of those in the dominant.
paradigm, The greater the (negative) discrepancy between a challenger's confidence and confidence in the dominant
paradigm, the larger the proportion of the challenger's practitioners that will defect. Recruitment is proportional to a
Pparadigm’s relative attractiveness and its total number of practitioners. The greater a paradigm’s attractiveness, the
gfeater the proportion of defectors it will recruit. Attractiveness‘is proportional to the number of practitioners since.
paradigms are assumed to get more funding, train more students, and have a larger voice in tenure and other peer-
career decisions than small paradigms. Attractiveness also depends on the confidence of the paradigm’s practitioners.
Here confidence measures the excitement, enthusiasm, and progress flowing from’a successful endeavor~ scientists are
naturally drawn to outstanding examples of achievement.
‘We model the. creation of a new paradigm as a stochastic event whose probability depends upon the distribution of
practitioner activities in the currently dominant paradigm. Practitioners may toil in normal science (puzzle-solving),
anomaly resolution (the attempt to reconcile Anomalies with the current paradigm), and other activities (described by
Kuhn as including philosophical reconsideration of the paradigm and other activities not sanctioned by the dominant
paradigm). In general, each of these activities may result in the creation of a new paradigm, but the probability that a
new paradigm is created as a result of a practitioner year of effort devoted to each activity may differ. Thus:
SYSTEM DYNAMICS '93 575
\
i
PAt = Pps‘PPSt + ParPARt + PosPOAr @
practitioners in the dominant paradigm engaged in other activities i )
probability of creating a new paradigm per practitioner year of effort in puzzle-solving
probability of creating a new paradigm per practitioner year of effort in anomaly resolution
= probability of creating a new paradigm per practitioner year of effort in other activities
Following Kuhn, we assume that normal science is unlikely to produce new paradigms, focused as it is on solving
puzzles within the context of the existing paradigm. Other activities are more likely to produce a new paradigm,
while effort devoted to anomaly resolution is most likely to result in the creation of radical new theories. Thus Par >
Pos > Pps- In the model, the distribution of effort among these three activities is endogenous. Thus the probability
that a new paradigm will be created in any time period is endogenous and will vary.as practitioner effort changes in
response to the changing health of the dominant paradigm. Once a new paradigm is launched, we assume it begins
with a small number of practitioners (five), a confidence level equal to..5 (neutral), a very small stock of solved
puzzles and no initial anomalies. The newly launched paradigm must then compete against other existing paradigms
and will succeed or fail to the extent it can (1) solve puzzles and resolve anomalies such that confidence in'that
paradigm grows; and (2) prove more attractive than other paradigms against which it might’be competing. During a
period of crisis the probability of creating a new paradigm may rise and remain high long enough for more than one
new paradigm to be launched. In this case many practitioners in the dominant paradigm abandon puzzle-solving, and
newly created paradigms will vie for ascendancy not only against the dominant paradigm but against ore another.
Exploring the Dynamics of Paradigm Development
‘The results presented in Wittenberg and Sterman (1992) confirm that consideration of competing paradigms does not
alter the essential dynamics of the paradigm life cycle as laid out in Sterman (1985). Readers are referred to'the former
paper for a complete description of this replic Figures 1a and 1b illustrate a simulation with fully endogenous
competition among paradigms. Paradigm 1 is initialized in the midst of normal science, and new paradigms are
launched stochastically, with’a probability depending upon the vitality of the dominant paradigm. We allow the
intrinsic puzzle-solving capability ‘of each paradigm to differ. Specifically, the rate. at which puzzle-solving becomes
difficult as solved puzzles accumulate (the paradigm’s inherent potential,C) is chosen randomly Sots a lognormal
distribution. Otherwise all paradigms have identical structure and parameters.
Figure 1 shows 1400 years of a simulation. The simulation yields a succession of dominant paradigms in: which the
initial paradigm gives way to successors whose life cycles vary in their length, timing and character.’ What is most:
interesting is not what the figures display but what they conceal. Not all new theories succeed.. Beneath the appar-
ently orderly succession of paradigms lies considerable turmoil. As evident in figure 1a, paradigms 2-4, 7, 9-12, 15,
17-18 never become dominant. Many new theories face early extinction. Figures 1a and 1b illustrate what Kuhn
calls the invisibility of revolutions, where the linear and cumulative character of normal science portrayed in the text-
books conceals the messy, uncertain and contentious character of actual scientific practice (Kuhn 1970: 136-143).
‘The simulation replicates the ‘punctuated equilibrium’ pattem described by-Kuhn.
‘Does the fate of a new paradigm depend on its intrinsic potential to explain nature or on situational ‘contingencies.
surrounding its birth? Does “truth” eventually triumph as better theories defeat inferior ones, or is timing every-
thing? Consider paradigms 8 and 9, launched around years 199 and 203, respectively. Although they emerge only
about 4 years apart, during the crisis of paradigm 5, they suffer very different fates: paradigm 8 comes to dominate the
field, while paradigm 9 eventually perishes. "Here the contingency of outcomes on situational factors is decisive.
Significantly, paradigm:8 does not succeed because of its head start in attracting practitioners: between years 212 and
215 it-actually has the same number as paradigiy,9. Nor is paradigm 8's success a result of superior explanatory
power: paradignt 9 has a potential 13% greater than paradigm 8. The difference in their destinies lies in their levels of
confidence. Consider the year 212. Paradigm 8, though equal in size to paradigm 9, is more attractive to adherents of
crisis-ridden paradigm 5 because its adherents, having had a 4 year lead over paradigm 9 in solving puzzles, have been
able to consolidate and articulate their paradigm more coherently and persuasively than their chief rivals. The small
advantage held by paradigm 8 is amplified as succéss begets success through the many positive loops surrounding
the emergence process (figure 2). Paradigm 8 eventually dominates science, while paradigm 9 slowly fades into
obscurity. If it is remembered at all,’ it is viewed as a blind alley, foolish error, or curiosity:
576 SYSTEM DYNAMICS '93
Practitioners in Paradigms 1 through 19
Random Potential Explanatory Power
Fraction of Practitioners
Committed to Paradigm
0 200 400 600 800 1000 1200 1400
Years.
Figure. la
& Confidence in Paradigms 1 Through 19
| Random Potential ane Power
se! '
& 5 £
7 @o. 14 1%
=8 pt nace F
£§ | E
8 € E
go E
5 (1) 200 400 600 800 1000 4200 1400
°o Years
Figure 1b
The simulation illustrates the subtle interplay between endogenous feedback processes and contextual, situational
factors in determining the dynamics and succession of paradigms. The basic life cycle of paradigms is determined by
the feedback loop structure of the system as discussed above. Figure 2 shows some of the positive feedback loops
that act to differentiate competing paradigms (the many negative loops are not shown). These positive feedbacks
boost confidence and rapidly produce a focused community from a promising but incoherent new idea. They give a
Paradigm with an initial advantage ‘an edge in recruitment of new members, leading to still greater advantage. These
‘same loops are responsible for the resistance of the dominant paradigms to challenges, as high confidence suppresses
the creation and progress of any new theories. Once a dominant paradigm begins to experience depletion of the root
metaphor which defines it these same loops accelerate the collapse. The prevalence of positive feedback processes in
the dynamics means that historical contingencies such as the number of practitioners in the dominant paradigm, their
confidence level, the number of solved puzzles and anomalies of the dominant paradigm, as well as the number of
competing Paradigms and their membership, confidence, and accomplishments strongly condition the fate of new
paradigms. While it is obvious that the creation of a new theory is intrinsically unpredictable, the simulation shows
clearly that the likelihood any given new paradigm grows to dominance or rapidly becomes extinct is strongly con-
tingent on the environment into which it is launched — an environment which in turn depends on the history of the
paradigms which precede it. The prevalence of positive feedback processes in paradigm development means that the
evolution of the system as a whole is strongly path-dependent.
SYSTEM DYNAMICS '93. 577
toA
Figure 2. Some of the positive feedback loops captured in the model which create path-dependent behavior. These
loops rapidly differentiate paradigms which might initially be quite similar, and can amplify small fluctuations in
local conditions to macroscopic significance. For clarity the negative loops in the system are not shown.
To characterize the role of intrinsic and contingent factors quantitatively, we now present the pooled results of 57
2000-year model runs. The only parameters varied were the paradigm's intrinsic explanatory power and the random
number seed affecting the launch of new paradigms. In order to eliminate initial transients and end effects the first and
last five paradigms of each simulation are eliminated from the analysis. There are 350 dominant paradigms and 676
never-dominant paradigms in the sample. Most of the runs were made withy randomly selected intrinsic capability,
C. In some runs all paradigms had identical intrinsic capabilities, with C=200, 300 or 400.
To assess the relative impact of intrinsic explanatory power versus contextual factors on the probability a paradigm
+ becomes dominant we ran a LOGIT model with three explanatory variables: intrinsic capability (C), the confidence
in the dominant paradigm at the time the new paradigm is launched (CP4°™), and the number of competitor ~
paradigms (not including the dominant paradigm) that new paradigm faces when launched (Table 1). Using a single
(ordinal) variable for number of competitors implies that moving from one competitor to two has the same effect on
the probability of dominance as moving from two to three. We thus treat the number of competitors as a categorical
variable, constructing dummy variables for situations of 1, 2, 3 and 4 competitors. Thus, COMPET;=1 if the num-
ber of competitors equals i at the time each paradigm is founded, and zero otherwise.
4
P,(Dom) = 1/(1+ exp(—(b, + b,C+ b,CP2™ + 2” {COMPET; ))) 7 @)
is
where the t subscript indicates that the probability is calculated at the launch time of the new paradigm.
| Indep Variable Estimated Coeff. Standard Error t-statistic
Constant 5.44 0.52 10.42*
c . 6.860-4 4340-4 1.58
Cpdom 7.27 0.55 -13.19*
COMPET) 1.43 0.23 ; 6.17%
COMPET2 4.99 0.52 i -9.54*
COMPET3 =13.52 50.00 0.27
COMPET4 14.65 147,91 -9.91e-2
* P<0.05 Number of observations = 1026
Table 1
578 SYSTEM DYNAMICS '93
LOGIT. models are more difficult to evaluate than standard regression models because we have no actual probabilities
of dominance with which to compare our predicted values: in the model paradigms either become dominant or do not.
We thus compare the actual distribution of non-dominant and dominant paradigms with the distribution predicted by
the model. Here a predicted probability of dominance greater than 50% is interpreted as a prediction of dominance. If
this probability is less than or equal to 50% it is considered a prediction of failure. Table 2 displays a 2x2 matrix of
how well the model predicted actual successes and failures.
Predicted
Non-dominant Dominant Total
Actual Non-dominant 641 35 676
Dominant 135 215 350
Total : 776 250 1026
A, =0.51 © f
Table 2.
For any paradigm picked at random our best guess of whether it was dominant or non-dominant (without knowing
the values of C, CP4°m and COMPET;) would be that it was non-dominant, since fully 66% of all paradigms never
dominate. The statistic 4, = 1-((errorsimodel)/(errorsino model) measures how much the model improves the :accu-
racy in predicting whether a paradigm becomes dominant compared to the chance error rate. Using these explanatory
variables reduces the error rate by half, a substantial improvement,
The values of the individual coefficients illustrate the relative weakness of intrinsic capability in comparison with
the contextual factors in determining whether a paradigm becomes dominant. Although the magnitudes of the esti-
mated C and CP4OM coefficients can not be directly compared because they are measured in different units, we can.
still get a sense of their relative impact. The maximum value C can take is 800, so its maximum ‘input into the
LOGIT equation is (.000686)(800)=0.55. The value CP4™ would have to take to offset the impact of C = 0.55 is
0.55/7.27 = .08. Thus whenever CP4°™>0.08, its contribution to a new paradigm's probability of dominance
exceeds the greatest contribution C could ever make. Given that only a little over 7% of all paradigms are launched
with. CP4°™<0,1, the influence of CP4°m will outweigh that of C in most cases. Figure 3 best illustrates the rela-
tive importance of the contextual factors CP¢°™ and the number of competitors compared to intrinsic capability.
Prob(Dom) at: Launch Time as Predicted
1 Internal
2
ny
a
Predicted Probability
of Dominance
2°
a
T ee: ba ton mcs
Ositidence Qi 4vne pongignt Paragigen
(Confidence Units)
Figure 3
SYSTEM DYNAMICS '93 579
‘The values along the y-axis of figure 3 are the predicted probabilities of paradigm dominance generated by the LOGIT
in equation 1. The value along the x-axis-is confidence in the dominant paradigm at the time the new paradigm is
launched. Each point in the plot represents the probability of dominance of a particular paradigm, as predicted by its
intrinsic capability, the number of competitors it faces at birth (excluding the dominant paradigm), and the confi-
dence of the dominant paradigm it faces. The smooth curves plot the predicted probability of dominance as
varies over the [0,1] interval, for each number of competitors and assuming intrinsic capability takes on its mean
value Cayg = 371.4; that is:
P,(Dom) = 1 / (1 + exp(-(6.44 + .000686Cavg - 7.27CP4™ + w;))). 4
For paradigms launched into a field with only the dominant paradigm, the probability of dominance is given by the
curve in the upper-right. Curves are also.displayed for settings with one and two other competitors, The curve for
four competitors has probabilities ~ 0. For all but the smallest values of CP4™, the greater the number of com-
Petitors, the less likely a new paradigm becomes dominant. Likewise, the greater the value of CP¢°™, the less likely
a new paradigm is to become dominant. The regression results and figure 3 show the number of competitors exist-
ing at the time a new paradigm is created strongly influences its fate. Latecomers are not likely to succeed. When
CPdom is between about 0.1 and 0,6 a new paradigm stands a better than even chance of becoming dominant if it
faces.a total of two.competitors or less, and will likely fail if there-are three or more competitors. When CP4°m is
between about 0.6 and 0.8 the.new paradigm is more than likely to become dominant if it faces only the dominant
paradigm, likely to fail if it faces two competitors, and almost sure to die if faces three or more competitors.
Figure 3 also underscores the virtual irrelevance of internal factors in determining a paradigm's probability of domi-
nance. The data fall very close to the predicted values. Departures from these curves represent the added impact of
intrinsic capability as a predictor of dominance. Capability has an effect approaching that of the number of competi-
tors only when CP4m is very low or very high, and in all cases the overall magnitude is quite small.
‘Thus the likelihood a new paradigin rises to dominance is overwhelmingly determined by historical contingencies
and only weakly influenced by its intrinsic explanatory power (its “truth”). The relative importance of inherently
unpredictable situational factors is not particularly sensitive to the parameters. Rather it is a consequence of the
many positive feedbacks by which paradigms bootstrap themselves from doubt to normal science (figure 2).
While context determines the likelihood a given new theory will rise to dominance, how do internal and contextual
factors interact to determine how long successful paradigms dominate their field? “Do intrinsically powerful
paradigms remain dominant longer than their weaker counterparts? Although intrinsic capability exercises a much
greater influence over the duration of domination than it does over the probability of dominance, the effect is still
highly conditioned on the environment during the critical period of paradigm emergence. Figure 4 shows a
paradigm's duration of domination as a function of its intrinsic capability. Note that not all values of intrinsic capa-
bility have occurred equally. There are far-more paradigms with intrinsic capabilities of 200, 300, 400 than there are
with other capabilities because in several of the simulations we required all paradigms to have the same potential
power. The cluster of paradigms with a capability of 800 reflects an arbitrarily-set limit on the potential we assign to
new paradigms. This limit in no way changes the model's qualitative behavior. Not displayed in the plot is one
paradigm with a duration of domination of 913 years and all the paradigms that never rise to dominance.
Although intrinsically more powerful paradigms do tend to experience longer periods of domination than their weaker
counterparts, the effect of this increased potential is far from uniform. Figure 4 reveals two qualitatively different
modes of behavior, each distinguishable by the degree to which internal factors appear to influence paradigm devel-
opment. These two modes illustrate the tension within every paradigm between the psychological forces binding
Practitioners to a particular world-view and the ‘rational’ doubts that inevitably arise as a paradigm's root metaphor
begins to fail. Contextual forces during the period of paradigm emergence largely determine which of these two
internal factors is more influential in a paradigm's development. In mode 1, where duration of dominance increases
relatively steeply with intrinsic capability, psychological forces predominate. These paradigms emerge when confi-
dence in the dominant paradigm is relatively high (> 0.8). Most scientists are still satisfied with the dominant
paradigm, slowing defections to the new paradigm. During this time, however, the few adherents of the new
paradigm are able to solidify the foundations of their theory. Because they are few in number, they are not able to
solve puzzles so rapidly that the limits of their paradigm are reached. Anomalies grow very slowly as increasingly
confident practitioners solve relatively easy puzzles. Their confidence rises. By the time practitioners in the domi-
nant paradigm finally do become disaffected, the initial adherents will have articulated the new paradigm well enough
580 SYSTEM DYNAMICS '93,
to provide an attractive and viable alternative. With high confidence to focus research on the puzzle solving of nor-
mal science the new paradigm is poised to fulfill its intrinsic potential.
Internal Determinants of
Duration of Domination
Duration of Domination
(Years)
0 200. 400 600. 800 1000
Intrinsic Explanatory Power
Figure 4
‘Rational’ factors predominate in the development of paradigms in mode 2. These paradigms emerge when confidence
in the dominant paradigm is already quite low (usually < 0.4): The new contender enters a field in which practitioners
are doubting the dominant paradigm, but still have not found a more attractive alternative. Thus, as uncertain as the
new paradigm is, it nonetheless quickly wins new members. The rapid influx of new practitioners means the rate of
puzzle solving will be high. ‘The underlying metaphor defining the paradigm will be extended rapidly into new
terrain, and the average difficulty of puzzles. starts to rise, increasing the number of puzzles likely to be seen‘as
anomalies. Further, the influx of new practitioners occurs at a time when confidence is low, meaning basic dis-
agreements about the methods, data, and criteria of validity for the theory still persist. "Without normal science,
without the acculturation and perceptual filters provided by the world view of a well-articulated paradigm, anomalies
and disagreements arise at an alarmingly high rate. Practitioners quickly begin doubting the new paradigm, and con-
fidence can fall. Falling confidence causes people to perceive anomalies still more readily, further decreasing con-
fidence. The new perdign rapidly disouegrates, Ws fugh intunsic polenta! largely unrealized.
Conclusion
The present work extends Wittenberg and Sterman's (1992) analysis of paradigm creation and competition. Results
show that the importance of situational contingencies found in the earlier work is robust over many runs of the model
and widely varying values of intrinsic explanatory power. The confidence of practitioners in the old paradigm and the
number of other new competitors determine whether a new theory will rise to dominance or quickly perish. The
eclipse of potentially strong paradigms by inherently weaker ones is thus not a pathological outcome, but rather a
normal part of scientific progress as we have modeled it.
‘The interplay between inherent potential and historical contingency is quite subtle. A paradigm’s inherent potential —
its logical force and power to explain nature — does influence its future development: of those paradigms that manage
to survive their initial years, those that are more powerful will remain dominant longer, on average, than those that
are weaker. But the impact of intrinsic capability on the duration of dominance for any given paradigm is mediated by
the competitive conditions in the emergence period. In particular, weak competitive environments make it more
likely a new paradigm will rise to inance, but condemn even pore paradigms to early deaths as they are
extended too far and-too fast, anomalies and destroying confidence prematurely. On the other hand, though
competition reduces the likelihood of survival, competition gives those that do survive time to bootstrap themselves
into normal science, insulating them against mere disconfirmation, and thus persisting until the anomalies that do
cause revolution, in Kuhn’s words, “penetrate existing knowledge to the core.”
Most important, however, competition does not:serve to weed out the weak paradigms so the strong may grow. On
the contrary, competition decimates the strong and weak alike - we found that intrinsic capability has but a weak
T
SYSTEM DYNAMICS '93 581
effect on survival. The infant mortality rate for paradigms seems to depend almost entirely on the environmental
conditions at the time of birth. This is a sobering conclusion, since we can never know the micro-level contingen-
cies of history that can prove decisive; here favoring an intrinsically weak paradigm, there killing an intrinsically
‘strong theory (see Gould 1990 for a similar view applied to the evolution of life). These characteristics of the compe-
tition among paradigms are consequences of the powerful positive feedback processes operating within and among
paradigms, These positive loops can amplify microscopic perturbations in the environment — the unobservable, local
conditions of science, society, and self faced by the creator of a new theory — until they reach macroscopic signifi-
cance. Such dynamics are the hallmark of nonlinear, self-organizing evolutionary systems.
We do not claim the model encompasses the full scope of sociological, intellectual, cultural, and other factors that
impinge on activities as basic to society as scientific theory-building, nor even that it captures all the subtleties of
Kuhn's theory. Plainly it does neither. Rather, we seek to demonstrate that it is both desirable and possible to cap-
ture in a formal model some of the causal hypotheses embodied in written theories of scientific endeavor that are
alleged by their authors to produce the dynamics as those authors see them. The process of formalizing such
hypotheses demands a discipline that surfaces inconsistencies, implicit assumptions, glosses and errors in the mental
simulations authors necessarily perform to infer the dynamics of science from their theories of its structure. Such an
endeavor is worthwhile as a complement to historical studies and other analyses. As in Sterman (1985) and
Wittenberg and Sterman (1992), complete documentation of the model is available; we invite others to replicate,
critique, revise, and extend the model in order to model and test views of scientific activity that differ from ours.
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