Accidental Atheists? Agent-Based Explanations
for the Persistence of Religious Regionalism
LAURENCE R. IANNACCONE
MICHAEL D. MAKOWSKY
This article outlines a new approach to the study of religious commitment. Starting with a variant on Schelling’s
classic model of mobility and segregation, we develop a multi-agent religion simulation (MARS) that incorporates
insights from theories of religious choice, social influence, and preference formation. Compared to standard
statistical methods, MARS does a better job of linking individual choices and collective outcomes. In particular,
it demonstrates that stable regional patterns require a balanced combination of attachment to personal identity
and adaptation to the social environment.
Imagine the following magic trick: A statistician grabs a pair of urns, one with red balls and
one with blue. He shakes the first urn and pours some of its red balls into the second urn, then
shakes the second urn and pours some of its red-blue mixture back into the first. He continues this
mixing process 10 or 20 times, and then finally tips over both urns so as to reveal their current
contents. To everyone’s surprise, the first urn contains only red balls and the second only blue.
He then repeats his trick starting with a 60-40 red-blue mix of balls in the first urn and a 20-80
mix in the second, but no matter when we look, the color ratio in each urn never changes.
Short of special props or slight of hand, one really would need magic to pull this off. Yet, a
similar sort of magic characterizes religious regionalism in America and throughout the world.
Visualize the American population as three hundred million “balls” —red if they regularly attend
church and blue otherwise. The balls are distributed unevenly across regional “urns,” with high
proportions of religious “reds” in the Southeast and high proportions of nonreligious “blues” in
the Pacific West. Each year, millions of these balls move from urn to urn.1 And yet, year after
year the regions maintain their distinctive character. Despite massive nonstop mixing, the South
remains relatively religious while the West remains relatively irreligious.
Researchers have studied mobility and regionalism for decades, using numerous data sets
and increasingly sophisticated statistics. But their work does more to confirm the magic than
to explain it. Thus Smith et al. (1998:504) conclude that “[s]omething about merely ‘being’
in the South . . . leads one to have a stronger religious commitment [and] detectable religious
homogenization has still not occurred.” Welch (1983:179) likewise observes that “[e]ven after
statistical adjustment [for different demographics and different rates of mobility], the Western
church membership trough is still quite marked.” And Finke (1989) shows that the American
West has remained relatively “unchurched” for at least 150 years.2
This article seeks to resolve the puzzle of religious regionalism, but it also seeks to do
much more. We introduce a new multi-agent (MA) framework that helps scholars and students
explore a wide range of generalizations about social dynamics and religious outcomes. Relative
to regression and most other standard multivariate statistical methods, MA simulation does a far
better job showing how macro-level outcomes emerge from micro-level forces and actions.
Correspondence should be addressed to Laurence Iannaccone at Larry@EconZone.com
Laurence R. Iannaccone is Koch Professor of Economics at George Mason University, Fairfax, VA 22030. E-mail:
Larry@EconZone.com
Michael Makowsky is a Ph. D. candidate and Earhart Fellow in the Department of Economics at George Mason University,
Fairfax, VA 22030. E-mail: MMakowsk@gmu.edu
For appendices and MARS software, see
Journal for the Scientific Study of Religion (2007) 46(1):1–16
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Our Multi-Agent Religion Simulation (MARS) traces the magic of persistent regionalism
back to the combined impact of personal experience and social conformity. If newcomers routinely
adapt to their new social environment, then a region can remain “blue” despite a large influx of
“reds.” As newcomers change their colors, the West acquires “accidental” atheists and the South
gains “accidental” enthusiasts. As we shall show, however, getting from this plausible story to a
workable theory is much harder than it seems—in part because social forces strong enough to
capture newcomers tend also to tip entire regions toward a single shared “color.”
Multi-agent methods are relatively new to the social sciences and almost entirely new to the
study of religion.3 Because regionalism provides a good introduction to MA models of religion,
we have built a website to complement this article (www.MARSmodels.com). The site already
includes a technical appendix to the article, web-based “applets,” a user’s guide, and the MARS
program written in NetLogo (Wilensky 1999). Readers can verify the claims in our article by rerunning the simulations and altering their parameters. They can then move on to the full MARS
model and explore a much broader range of phenomena, including commitment, conversion,
conformity, social networks, religious capital, and denominational growth.
THE PARADOX OF PERSISTENT REGIONALISM
The paradox of persistent mobility and persistent regionalism defies easy resolution. America
has long been a nation of people on the move, both geographically and socially, and there can
be no doubt that internal mobility does tend to induce homogeneity. The logic is so compelling
that scholars of the 1950s and 1960s viewed religious convergence as a done deal. Will Herberg
(1960:38–39) aptly summarized the consensus in his widely read book, Protestant, Catholic, Jew,
which described America as a “triple melting pot” where regional, ethnic, and sectarian differences had become “distinctly secondary” and the three major religious traditions had themselves
converged toward a shared “American way of life.”
By the late 1960s, however, scholars could no longer ignore the evidence for persistent
regional cultures, especially in the South (Glenn and Simmons 1967; Reed 1972; Halvorson,
Newman, and Nielsen 1978). Subsequent studies have confirmed the remarkable stability of
America’s religious landscape (Finke 1989; Newman and Halvorson 1984; Smith, Sikkink, and
Bailey 1998; Stump 1984; Wuthnow and Christiano 1979).4 But despite these and many other
studies of both migration and regionalism, the underlying puzzle persists.5 The standard analytical
methods hit a wall long ago. Little has changed since the early 1980s, when Welch (1983:179)
complained that “explanations of regional distinctiveness tend to be post hoc or excessively
historicist” and that “well-specified models” are “relatively rare.” In fact, “relatively rare” is too
generous. “Nonexistent” comes closer to the truth.
To do better we must overcome two problems. First, we must find a way to model the
interacting effects of multiple factors, all of which influence a person’s religious beliefs and
behavior. Prior research is witness to the importance of social ties, denominational affiliation, prior
religious experience, and personal demographic attributes. Second, we must somehow model a
complete social landscape comprising individual actors (with distinct histories, locations, and
personal attributes) whose interactions over space and time shape the landscape and are in turn
shaped by it.
In the sociology of religion, the standard response to such problems is multiple regression
and other multivariate statistical methods. Armed with a large national survey, or better yet a
large longitudinal survey, the researcher statistically relates the religiosity of individuals to their
age, gender, race, religious background, migration history, current location, social network, and
more. After sifting through many different effects, the researcher identifies the most “significant”
predictors of religiosity. For well-executed examples of this approach see Stump (1984, 1986) or
Smith (1998). A typical result has the form,
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Rit = a + b ∗ (demographics) + c ∗ (denomination) + d ∗ (migration) + e ∗ (region),
whereRit denotes the religiosity of individual i at time t. The “demographics” variables usually
include age, gender, race, education, and marital status; “denomination” indicates the respondent’s denominational affiliation. “Migration” captures the respondent’s migration history, and
the “region” variables indicate where the respondent currently resides.
Estimation procedures along these lines produce fairly consistent results. The region coefficients invariably show that the South remains relatively religious, the West relatively irreligious,
the Midwest and Northeast somewhere in between, and Utah is a bastion of (Mormon) religiosity.
Residential mobility tends to reduce religious activity, ceteris paribus. This effect is, however,
complicated by social conformity—whereby religiosity tends to rise among people who migrate
from less religious areas to more religious areas and tends to fall when moving in the opposite
direction. Finally, the regressions almost always yield standard denominational and demographic
effects (including positive, statistically significant effects associated with being older, female,
African American, married, and affiliated with a conservative Protestant denomination).
WHY THE STANDARD METHODS FAIL
The statistical pitfalls associated with regression and other multivariate statistical methods
are well known: misspecification; omitted variables; endogeneity; abuse of statistical significance;
and so forth. In this case, however, the standard problems are of secondary concern.6 For the sake
of argument, let us therefore assume that our data and statistical methods are not tainted by any
standard statistical flaws. Even then, the published results tell us almost nothing about the social
dynamics that give rise to persistent religious regionalism.
To see why, consider first the regression coefficients for “region” effects. These simply confirm
what we already knew: the observed regional differences are large, stable, and not reducible
to individual-level attributes. Consider next the “migration” effects. Residential mobility tends
by itself to reduce religious involvement, but the net effect of a move depends also on whether the
individual enters a region of higher or lower religiosity. At best, these results suggest that social ties
influence individual religiosity—another fact that we already know.7 As for the demographic and
denominational effects, these simply mirror the results obtained from hundreds of other surveys.
The problems persist even when we include more direct measures of social characteristics.
Consider, for example, the effect of augmenting our regressions with measures of regional religiosity such as the average R in the respondent’s current region. The estimated equation now
becomes
Rit = a + b ∗ (demographics) + · · · + e ∗ (region) + f ∗ R̄it .
t
For the sake of argument let us assume that after including the R i variable, all other “regions”
become statistically insignificant. Such a result might seem to warrant publication, inasmuch as it
t
fully “explains” regional differences in terms of the social effect R i , plus mobility, demographics,
and so forth.
But consider the matter more closely. Our improved model has introduced a potentially serious
t
specification problem because the right-hand averages, R i , depend upon the left-hand levels,Rit .
The average Rs will be influenced by the same unobserved “error” terms that influence individualRs, thereby violating the OLS independence assumption, and thus biasing estimated coefficients,
significance levels, goodness of fit, and so forth. If this seems like a minor technicality, note that
the same statistical problem seriously biased numerous regression results published throughout
the 1990s on religious pluralism versus religious adherence (Voas, Olson, and Crockett 2002). For
a thorough analysis of the underlying statistical issues, see Moutlon (1990) and Manski (1993,
1995).
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The problem also persists in the face of larger data sets. As the sample approaches the entire
population, the average R values exactly equal the average of the corresponding individual Rs,
and estimation becomes impossible due to perfect collinearity. Better measures of social influence
can likewise make matters worse. When average R for an entire region is replaced by average R in
the respondent’s neighborhood the statistical bias grows. The smaller the social circle, the more
likely it is that any unobserved effect influencing average religiosity tends also to directly affect
the individual’s religiosity. TheRit error term becomes increasingly correlated with R̄it , and hence
the regression results increasingly overstate the size and significance of the average R social effect
while possibly invalidating all other coefficient estimates as well. Something is seriously wrong
when methods of inquiry become less valid as the data become more complete and detailed.8
The fundamental problem really is not statistical at all, though it certainly creates statistical
hazards. The problem is that we lack a coherent model linking individual behavior to aggregate
outcomes and vice versa. Regression and its more sophisticated cousins will never get us where we
need to go because they bypass the links we need to address. Regression reduces the macro-micro
link to regional averages or dummy variables. This reduction contradicts what we already know
about social influence, namely, its operation through close social ties that depend on personspecific social networks.9 The fundamental feature of social influence, documented in scores
of case studies since the 1960s, is its variability. People are heavily influenced by their close
friends but largely untouched by mere neighbors, much less the mass of strangers who make up
99.9 percent of their city, state, or region.
Standard statistical models reduce social influence to a homogeneous regional attribute,
indexed by regional averages. But averages and dummy variables ignore social structure; they
collapse relationships and local networks down to a shared set of “social” parameters. In essence,
each individual becomes an atomized particle in a uniform soup of other such particles. Regional
effects enter the regressions as exogenous variables with no local content and no reciprocal
effects—the social equivalent of a static equilibrium price in a fully equilibrated competitive
market.10
Failure to appreciate social structure is, of course, the sin that sociologists routinely attribute to
economists. In an influential article on social “embeddedness,” Mark Granovetter (1985:483–86)
observes that
neoclassical economics operates . . . with an atomized, undersocialized conception of human action [that disallows] . . . any impact of social structure and social relations [483]. Even when economists do take social relationships seriously . . . they invariably abstract away from the history of relations and their position with respect to other
relations . . . . The interpersonal ties described in their arguments are extremely stylized, average, “typical”—devoid
of specific content, history, or structural location [486].
The same problems plague statistical studies of migration and regionalism. Social influence
and interpersonal ties are reduced to “stylized, average” parameters “devoid of content, history of
structural location.” More appropriate models—whether in economics or sociology of religion—
must recognize that “culture is not a once-for-all influence but an ongoing process, continuously
constructed and reconstructed during interaction” (Granovetter 1985:486).11
THE MULTI-AGENT ALTERNATIVE
Within the social sciences, statistical methods typically operate as a form of simulation.
Researchers start with a collection of numbers and a preselected family of equations that link a
“dependent” number Y to various “independent” numbers X. They then use regression or other
mechanical methods to calculate specific parameter values for their simulation. If a great many
assumptions about the data and the relationship between Y and X happen to be correct, the
simulating equations generate meaningful outcomes that can be summarized in terms of “predicted
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ACCIDENTAL ATHEISTS
values,” “confidence intervals,” and other statistics. As we have seen, however, these simulations
fail in the present context and many other contexts important to the study of religion and other
social phenomena.
Multi-agent models provide an alternative approach to simulation—one that is well adapted
to studies of social environments populated by numerous actors, each of whom operates within a
small “neighborhood.”12
The Schelling Model
Thomas Schelling (1971) introduced multi-agent modeling as a way to interpret residential
segregation. Thirty-five years later, Schelling’s model remains the best-known and most informative example of the MA approach to social theory.13 Schelling’s simulation represents different
types of people by markers of different color or shape, and it represents potential home locations as
the square cells of a large grid. Each person “lives” on a separate cell, surrounded by “neighbors”
located in adjacent cells. By assumption, each person prefers to live at locations where at least
C-percent of his neighbors share his color. (C is often assumed to be around 20 to 35 percent,
but the simulation works with any threshold.) At the start of the simulation, people are randomly
distributed over the grid. Figure 1A illustrates a typical setup: 90 percent of the squares occupied,
half by circles and half by crosses, and there is no pattern to the spacing or symbols. To run the
simulation, we select a “person” at random, determine whether “he” is content with the composition of his immediate neighborhood, and if not, randomly move him to any open location that
has a sufficiently large number of same-color neighbors.14 We then repeat this procedure until an
equilibrium emerges.
Schelling’s simulation inevitably leads to total segregation if each person insists on living
where a majority of neighbors share his color—i.e., if the minimally acceptable “C” threshold
is greater than 50 percent. But for lower thresholds, it is possible to create integrated equilibria
in which all neighborhoods have roughly equal numbers of each color and no person wishes to
move. In practice, however, even mild preferences for neighbors like oneself yield very high levels
of segregation. This is not a “trick.” In the simulation, and very probably in real life, residential
segregation truly is an emergent characteristic. Though caused by micro-level actions, it is not
necessarily desired by the micro-level actors. Figure 1 displays a typical run, which starts with
the 50-50 randomly placed population of Panel 1A but rapidly evolves into the heavily clustered
FIGURE 1
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configuration in Panel 1B.15 We encourage readers to visit the MARSmodels.com website, where
they can view the complete evolution of this particular simulation, experiment with the general
Schelling model, and run the other simulations described below.
The MARS Model
The simplest variant of MARS turns the Schelling model on its head. In Schelling’s world,
individuals choose locations based on their (exogenously determined) personal characteristics.
In the world of MARS, individuals choose their personal characteristics based on their exogenously determined locations. Upon being randomly moved to a new location, an individual has
the option of changing his religious characteristics to better fit his new neighborhood. Random
movement appears to be an appropriate assumption because religion appears to have little impact (relative to wages, weather, and housing costs) in determining where and when Americans
move.16
Figures 2A through 2D illustrate the simulation in action. In each panel of Figure 2, the grid
is divided into two regions. Dark circular agents initially dominate in the upper region, and light
cross-shaped agents dominate in the lower, the majority/minority ratio being 70/30 in each case.
To start the simulation, we randomly select an individual from anywhere on the grid, move him to
an open location also selected at random, and then let this individual “choose” whether to change
or maintain his religious attributes (i.e., his shape and color) based on his own characteristics
and the religious attributes of his new neighbors. (A formal description of the choice process
appears in the article’s appendix.) We then repeat this procedure for the next randomly selected
person, and so forth. As in the original Schelling simulation, the aggregate results will depend on
individual preferences, but the dependence is far from simple.
To get a feel for the process, let us begin with extreme cases. Consider first a world in which
childhood training is so effective that people never change religions no matter what their new
neighbors are like. In this case, mobility quickly leads to a homogeneous mix within and across
regions—the “melting pot” result anticipated by most scholars of the 1950s and early 1960s.
Figure 2B depicts the result of 1,000 moves after the initial position of panel 2A—time enough
for the average agent to have moved twice. The cross-circle ratio within each region rapidly
converges toward the cross-circle ratio for the population as a whole.17
Consider next the opposite extreme: a simulation in which movers always switch to the
religion held by the majority of their new neighborhoods. Panel 2C displays the result of this
alternative regime, starting from the same initial position (depicted in 2A) and continuing again
for 1,000 moves. Thanks to localized social pressures, the two regions become less similar and
color clustering increases within most subregions. In this regime of pure social pressure, each
regional “market” is eventually monopolized by a single religion.
Social conformity can thus cause regional differences to persist indefinitely in the face of
migration that would otherwise induce homogeneity. In this sense, the simulation validates the
explanation for persistent religious regionalism offered by Stump (1984). But the simulations also
highlight problems with prior explanations. Whereas pure inertia cannot account for persistent
regional differences, pure conformity works too well. It causes each region to tip toward one
religion. Figure 2C illustrates this phenomenon, and the degree of tipping would be even more
striking had we begun with less lopsided ratios of red to blue agents. Something more is needed
to explain the observed macro-level combination of persistent differences across regions and
persistent diversity within. Likewise, something more is needed to bring the simulation’s microlevel behavior into line with that of real-world movers—people who do not always alter their
religious behavior to fit their new neighborhood.
Intuitively, we can obtain more realistic results with a mixed regime—one that combines
both social conformity and preference for one’s original religion. Figure 2D displays results that
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ACCIDENTAL ATHEISTS
FIGURE 2
again start with configuration 2A but evolve according to a new set of rules. We have reset the
simulation parameters so that each agent displays a mild preference for his original religious
affiliation but discards his original affiliation if a substantial majority of his neighbors belong
to some other religion. Hence, agents will convert when the social pressure grows large, but
they maintain their original identity, or revert to it, when the pressure is weak. (The on-line
appendix provides a formal description of the choice process.) In this last scenario, the regional
patterns remain remarkably stable even after 2,000 moves, during which time the average agent
has moved about four times.18 This result is not a fluke. By replicating the scenario 100 times,
always starting from a different randomly determined initial configuration, we can determine the
typical outcome after 2,000 moves—or, more precisely, the distribution of outcomes. The results
remained very close to the initial 70/30 split: the circles averaged 74 percent of the population
in the upper region and 27 percent in the lower region (with standard deviations of 8.0 and
7.8 respectively).19
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Result
Within the MARS framework, moderate levels of social conformity and personal identity
solve the paradox of persistent religious regionalism. Whereas the pull of initial identity homogenizes the population mix across regions and strong social conformity promotes uniformity within
regions, the two effects can jointly sustain diverse but distinctive regions in the face of ongoing
geographical mobility.
We have thus traced the “magic” of persistent regionalism back to the joint force of internal
identity and social conformity. If movers adapt to their new social environment, then a region can
remain “blue” despite a large influx of “reds.” As newcomers change their colors, the West can
acquire “accidental” atheists while the South gains “accidental” enthusiasts. But the two forces
do not automatically yield the observed result. The equilibrium requires a balance of internal and
external effects.
MARS has thus served up an existence theorem together with a sensitivity analysis. This
combination is typical of the multi-agent approach. By adjusting the parameters and running each
variant numerous times, we can readily explore the macro-level consequences of different microlevel assumptions. Although some models (such as Schelling’s) are robust, the outcomes in many
others prove sensitive to small micro-level changes. Sometimes this sensitivity mirrors reality, as
in many weather systems and some ecologies of predators and prey. But in other simulations it
signals problems with the model. As Einstein famously observed, “a theory should be made as
simple as possible, but not any simpler.”
The simplest versions of MARS are indeed too simple. Regions tip toward complete segregation or complete homogeneity unless we carefully balance the effects of conformity, upbringing,
and inertia. But stability increases when these effects differ from person to person. As we show in
our on-line appendix, the stability of our 70/30 simulations effectively doubles when each agent
receives unique conformity, upbringing, and inertia parameters, drawn from random distributions
rather than fixed values.20
LIFE ON MARS
In the spirit of Einstein’s dictum, MARS incorporates only the most important features of
region, religion, and migration. These include: diversity, disequilibrium, mobility, randomness,
individuality, conformity, localism, quasi-symmetry, and denominationalism.21 In contrast to video
games and training simulators, MARS does not “look” like the real thing. Rather, it is designed to
give scholars and students a basic framework suitable for testing common claims about religious
change and social dynamics.22
In simple variants of the MARS model, movement is entirely random and religious change
occurs only in conjunction with movement. An agent exercises no control over when and where
he moves, and after moving he reevaluates his religious attributes based on his original attributes
(determined at birth or by nurture), his current attributes (just before the move), and his new
social environment (which depends on the agents in his new neighborhood). The process is
mathematically equivalent to maximizing an objective function, but the resulting “choice” need
not be rational in the standard economic sense.23
The full MARS model has many more features. The population can include three or more
religious types, distinguished by color or shape. Agents can also have different rates of religious involvement, ranging from 0 to 100 percent and indicated by varying size or shade. Agents
can periodically reevaluate their religious choices without moving,24 and movement can be influenced by preferences for certain types of neighbors as in the Schelling model.25 The user
can at any time drop individual agents onto specific cells, rather than rely upon the computer
to randomly populate the grid, and the user can also selectively transform individual agents into
charismatic “superstars” who exercise exceptionally strong influence over the other agents in their
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neighborhoods. One can specify a full matrix of parameters governing the weights that agents
accord to their initial religion, current religion, and neighbors’ religions—and these effects can
differ across religions. The parameters can also be randomized so that no two agents have identical
preferences.
The shape of the “world” can also be varied. For any given run, the user can divide the grid
into one or more distinct regions and can control the population density within each region.26 The
user also controls the number of religions, represented by different colors and/or shapes, and their
relative population shares within each region.
As the program runs, the view screen displays the changing state of the world. An adjacent
graph tracks the changing population shares of each religion and the degree to which agents of
the same religion are clustered together. Other summary statistics can be displayed on a separate
control panel or saved for subsequent analysis. At any point, the simulation can be slowed, stopped,
saved, restarted, or reverted to an earlier stage. The parameters can likewise be reset at any point
to test alternative scenarios.
EXPLORING MARS
MARS can be used to study many different aspects of religion, including commitment, conversion, conformity, social networks, religious capital, and denominational growth. We conclude
with a few examples.
How Small Groups Survive
Multi-agent models highlight the difficulty that small religions face in modern, pluralistic
societies. When members of a small sect randomly move to new locations, they inevitably find
themselves surrounded by members of larger, more “mainstream” groups. In the absence of special
countervailing factors, we would therefore expect most sects to diminish and die over the course
a few decades. This, in fact, has happened to the vast majority of small groups documented in
Melton’s (2002) Encyclopedia of American Religions. But some groups, like the old-order Amish,
hang on for centuries.
What differentiates the few long-lasting sects from their many short-lived counterparts? The
literature on cults and sects bristles with potential explanations, and statistical studies confirm the
existence of many special attributes—including distinctive beliefs, costly demands, high levels of
commitment, and a rejection of mainstream culture. But as with religious regionalism, standard
analyses fail to demonstrate which attributes are necessary or sufficient for sectarian survival.
MARS makes it relatively easy to test different hypotheses and compare outcomes across different
sectarian regimes. The results suggest that no single sectarian attribute suffices to explain survival
in the context of pluralism, mobility, and conformity—although many attributes (such as high
participation and effective socialization) do slow the rate of decline. Long-term survival appears
to require a special mix of attributes.
Figures 3A through 3C illustrate this claim. We establish a small sect in Figure 3A with
two congregations, each of which is surrounded by the mainstream religious culture. We also
give the sect a relatively strong hold over its current members. These strong attachments slow
but do not prevent the march toward extinction. As can be seen in Figure 3B, the sect is all but
dead within 2,000 moves. But things change if we introduce a second sectarian trait: a strongerthan-normal tendency to seek out other members of one’s group. We thus give sect members a
Schelling-like preference for members of their own group. When forced to move, they randomly
sample several different locations and choose the location with the largest number of sectarian
neighbors. The result appears in Figure 3C. The sect remains viable for many generations thanks
to the combination of strong commitment and selective association.27
We thus obtain another “emergent” result that depends upon the interaction of two distinct
attributes. Neither one suffices to keep the group alive, but together they yield strong enclaves
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FIGURE 3
that can stand up to the pressure of mainstream society, even when the mainstream actively seeks
to convert outsiders.
How New Groups Grow
Most religious groups never become major denominations. As Stark and Bainbridge (1981)
showed in a systematic study of American-born sects, only 6 percent of all groups have grown
rapidly since their founding, and only 15 percent appear to have experienced any period of rapid
growth. This may not be particularly surprising, for we have demonstrated that it takes a very
special combination of attributes simply to survive. Moreover, the critical attributes (which we
described as “strong commitment” and “selective association”) tend to work by insulating the
sect from the larger society. But insulation also limits opportunities for outreach. Thus Stark and
Bainbridge (1981:139) argue that
many sects fail to grow . . . because their initial level of tension is so high as to cause their early social encapsulation.
Once encapsulated, a sect may persist for centuries, depending on group fertility and the ability to minimize
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defection, but it will rarely be able to recruit an outsider. For such recruitment to occur there must be contact
between member and nonmembers of sufficient quality and duration to permit the formation of close interpersonal
bonds.
The MARS framework makes it relatively easy to test this argument and to identify additional
factors that tip the scales from mere survival toward rapid growth. Extraordinary members can be
one such factor, as readers can verify by creating several “superstar” agents within a small religious
population. An extraordinary message can also do the trick, assuming that the message makes
the group exceptionally attractive to outsiders. But one does not expect to encounter many such
messages in the crowded and competitive religious markets characteristic of developed nations,
and (as MARS readily demonstrates) the impact of “superstars” wanes as they become surrounded
by converts and insulated from outsiders.
Active outreach is the critical determinant of rapid growth within the MARS model, but
only when combined with selective mobility. Superstars turn out to be much more effective if
they move more frequently than other agents. This strategy is as old as evangelism itself: plant a
congregation, nurture it, and then move on and plant another. But as seen in Figure 3D, ordinary
members can be as effective as superstars if they move in groups.28 They become seed crystals for
new congregations by converting outsiders who lack strong attachments to other religions and by
retaining insiders who might otherwise defect to other religions. Once again, however, success
requires a special combination of attributes.
How the Past Shapes the Present
We have focused on “small” theories about persistent regionalism and group growth, but
MARS can also capture broader phenomena and longer time spans. Consider, for example, the
following two-stage “history” of religion in America. In stage 1, large and relatively unpopulated
areas develop due to immigration of many people from just a few places. (Thus the MARS
grid starts out nearly empty and steadily adds new agents from beyond its borders.) As these
immigrants arrive, they naturally settle with others of their type because their language, customs,
and culture differ so greatly from those of other immigrant groups. During this stage, Schellinglike immigration and mobility yields a high level of clustering. Thus the nation comes to resemble
Figure 1B, with distinct regions dominated by different types of people.
When immigration slows, however, a different dynamic asserts itself. In stage 2, the children
and grandchildren of immigrants adopt the dominant language and most other elements of the
dominant national culture, and the more they assimilate the less they gain from limiting their
movement as in the Schelling model. They move wherever opportunity leads and thereby weaken
the enclaves created by their immigrant ancestors. After moving, they tend to accommodate
themselves to the religious character of their new locations. But that character was established in
stage 1! Hence, initial religious patterns persist, albeit in modified forms, even after the dominant
social dynamic reverses.
This simulated history bears a striking resemblance to actual history as interpreted by John
Egerton (1974), who characterizes 20th-century trends as “the Americanization of Dixie [and]
the Southernization of America.” Mark Shibley (1996:1) likewise speaks of “the southernization
of American religion and the Californication of conservative Protestantism.” Both authors trace
the trends back to migration and accommodation, the critical combination in our model.
CONCLUSIONS
Over a century ago, Emile Durkheim sought to understand religion through its most “primitive” forms, and Max Weber sought similar insights through the analysis of “ideal types.” Although
neither approach enjoys much current popularity, the quest for simple starting points remains a
12
JOURNAL FOR THE SCIENTIFIC STUDY OF RELIGION
compelling strategy. Theories of rational choice and religious markets provide one such set of
starting points, leading to new hypotheses and new empirical strategies. But economic models
often ignore social networks and local variation. MA models provide a different starting point for
theory and research.
Multi-agent models provide new ways of exploring the implications of almost any theory
that embeds individual choice within social networks. Moreover, the process of recasting a theory
into MA form automatically demonstrates whether the theory is sufficiently clear and complete to
yield observable implications. If so, we can “run” the theory and literally see whether its results
match its claims. We can also see how the consequences change when we alter the parameter
values that capture the theory’s underlying behavioral assumptions. Of course, a theory may work
inside a simulation yet fail in the real world, but a good theory must at least succeed within the
world implied by its own assumptions.
The MA approach helps identify gaps in sociological arguments and methods, particularly
those that link collective outcomes to individual propensities. As we have seen, many standard
micro-to-macro claims must be rethought, and perhaps totally reconstructed. Regionalism is a
case in point. Although MARS ultimately sustains longstanding claims about the impact of social
networks and conformity, it does so in ways that highlight problems with past research. The
old arguments lacked precision, making it difficult to test or even know their implications. The
statistical methods used to assess the arguments were weak, and many methods contradicted
the very assumptions from which the arguments were derived. The standard stories about religious
regionalism (and much more) need major repairs, especially where micro meets macro. One such
repair concerns the minimal requirements for persistent regionalism in the face of mobility and
pluralism. As we have seen, stable regional patterns require a balanced combination of adaptation
to one’s current social environment and attachment to one’s personal identity.
Multi-agent models overcome many limitations associated with traditional research while
not requiring us to ignore existing data, statistics, or theory. Indeed, the most compelling MA
models link standard theoretical insights to standard empirical findings. This capacity to leverage
existing work may be the most valuable feature of the multi-agent approach.
ACKNOWLEDGMENTS
We thank Andrew Iannaccone and Matthew Zilli for their help with early versions of the MARS program and Eli
Berman, Evelyn Lehrer, James Spickard, and David Voas for helpful comments. This work was supported in part by grants
from the Center for Study of Public Choice and the Mercatus Center at George Mason University and was first presented
at the October 2004 meetings of the SSSR.
NOTES
1. About 17 percent of Americans move each year, and the typical American makes about 12 moves during his or her
entire life (Hansen 2001). About 45 percent of Americans move at least once during any given five-year period.
Although most moves are local, about 60 million people (20 percent of the total population) moved from a different
county, state, or country between 1990 and 1995 (Schachter 2000). Rates of long-distance migration have declined
throughout the past 150 years, so that these numbers understate the actual mobility behind the observed regional
distributions (Fisher and Hout 2000):
2. The regional distribution of denominations is also quite pronounced and persistent, with Baptists and Methodists
dominant in the South, Catholics most common in the Northeast and Southwest, and Lutherans concentrated in
the Midwest (Halvorson and Newman 1994). Although our simulation framework incorporates denominations and
religiosity (though of different “types” and variable “rates”), this article focuses on changes in type. Type changes
provide a better introduction to MA models because they are easier to visualize and easier to associate with regional
mobility.
3. The work of William Bainbridge is a notable exception. In the mid-1990s, Bainbridge (1995, 1997:171–74) used
computer-based methods to study belief formation and sect growth. These studies derive from programs that Bainbridge originally published as teaching tools (1987). He has now completed a greatly expanded version of this
work, including several multi-agent models, in God from the Machine: Artificial Intelligence Models of Religious
ACCIDENTAL ATHEISTS
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
13
Cognition (2006). Although we did not encounter any of these simulations until completing our own, we wish to
acknowledge Bainbridge’s path-breaking contributions to the simulation-based study of religion. For a diverse collection of sociological research using multi-agent methods, see the January 2005 issue of the American Journal of
Sociology (Gilbert and Abbott 2005). For recent working papers and on-line articles that model religious beliefs or
behavior using simulations and multi-agent methods, see Chattoe (2005), Metzler (2002), Spickard (2005), and Upal
(2005).
Interest in religious regionalism has been fueled by the distinctive character and impact of 20th-century Southern
evangelicalism. See, for example, Egerton (1974), Hill (1988), and Shibley (1996).
Immigration explains only a small portion of the overall pattern. Inflows of Hispanics keep the Catholic population
growing in several border states, but elsewhere the impact of immigration is relatively small. Over time, immigration
has radically altered the religious-ethnic mix of many neighborhoods, but it has had less impact on cities (at least
since the 1920s), and impact at the state and regional level has been smaller still. Moreover, more than 90 percent of
all moves occur within the United States, and for the most part these internal flows really do mimic random religious
mixing, the principal exceptions being members of groups that maintain a strong ethnic/communal identity (Toney
1973; Toney, Stinner, and Kan 1983).
McCloskey (1998) and Leamer (1978) explain why “statistical significance” almost never deserves the attention it
receives in social research. See Kennedy (1998) for a more general review of standard statistical pitfalls, including
heteroskadasticity, autocorrelation, multicollinearity, and misspecification.
One might argue that the relative magnitude of these effects was not previously known, but one must also concede
that the estimated magnitudes vary considerably from one study to the next and that no research has ever converted
these numbers into behavioral parameters that might show—at least in theory—how changing patterns of mobility
affect regional religiosity.
One might try other tricks, but the old problems tend to persist and new ones get added. For example, it does not
help to restrict the respondent sample to recent immigrants while estimating the social effects based only on the
nonmigrants in region or neighborhood. Nor can we patch things up with intertemporal data that permit us to regress
the current religiosity of individuals onto past religiosity of their regions or neighborhoods.
Statistically minded readers will note that there exist estimation methods to circumvent these types of estimation
problems—see, for example, Manski (1993). All we need is sufficient information about the structure of the data,
such as the precise form of the equations that determine individual-R as a function individual- and group-level effects.
But these “solutions” merely highlight the fundamental problem. In the case at hand and many others like it, social
researchers employ standard statistical techniques precisely because they generate seemingly informative results in
the absence of information about the underlying social dynamics. The entire point of the statistical exercise was, after
all, to obtain such information on the cheap.
For an overview of this literature in the context of conversion, see Stark and Finke (2000).
This by no means exhausts the list, of serious omissions in the standard estimation models. For example, it ignores
the fact that newcomers’ social networks look nothing like those of longtime residents. Newcomers initially exert
relatively little social influence on those around them, whereas random others may heavily influence them because
moving has disrupted the newcomers’ old ties. Over time, however, relationships and social influence become more
symmetric. A good model should address these and other “asymmetries” that exist across actors and over time.
For more on the micro-macro problem in social-scientific research, see James Coleman (1990:1–23) and Dennis
Wrong (1961).
MA methods are neither the only alternatives to statistical estimation nor always the best. For examples of many
different approaches, see the Journal of Mathematical Sociology.
For the seminal work on the application of multi-agent computer simulations of social models, see Epstein and Axtell
(1996).
Calling an agent “he” is mere convention. Gender is just one of the many real-world attributes that have no counterpart
in Schelling’s model or MARS.
Although the C-threshold is only 30 percent, the social system “tips” because the initial configuration includes a few
individuals surrounded almost entirely by people not like them. When these people move, their departure tips their
old neighborhoods even farther (making the old neighborhoods even less attractive to people like them) and their
arrival tends to tip their new neighborhoods in the opposite direction. Thus, the initial similarity index (for Figure
1A) is 0.48—meaning that on average 48 percent of each agent’s neighbors are of the same type as the agent—but
by the time equilibrium is reached (in Figure 1B) the index has risen to 0.78.
The primary determinants of mobility are family-related, work-related, and housing-related—see Schachter’s (2000)
summary of results from Current Population Survey interviews. Together with college, health, and climate, these
reasons account for 98 percent of all stated reasons for moving. School quality and population characteristics (such as
age, race, ethnicity, and socioeconomic status) do influence the neighborhoods that people select, but movers can be
reasonably confident that almost any major metropolitan areas will contain several neighborhoods that satisfy their
demographic preferences.
Most Americans seem relatively uninterested in (and largely ignorant of) the religious demographics of cities
and regions. They seem content to live within driving distance of an acceptable congregation. Ultra-Orthodox Jews
14
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
JOURNAL FOR THE SCIENTIFIC STUDY OF RELIGION
and Old Order Mennonites are obvious exceptions to this rule. More generally, the tendency to seek out co-religionists
should mirror the cost of living among people of other religions—whether from conflict, discrimination, or alienation.
Toney (1973) has shown that from the 1940s through the 1960s Catholics were more likely than Protestants to move
into the (heavily Catholic) state of Rhode Island and also more likely to remain there. And Toney, Stinner, and Kan
(1983) document a similar pattern for Mormons in and around the state of Utah. As we show near the end of our
article, nonrandom mobility is critical for the survival of small, sectarian groups.
Note, however, that as in Figure 2B random mixing usually yields many small clusters in which one group dominates.
Because this consequence of true randomness violates our biased intuition, observers tend to impute special conditions
where none exist. For more on this bias and others like it, see Kahneman, Slovic, and Tversky (1982).
In repeated runs, stable regional patterns typically persist for 10,000 moves or more—the equivalent of many decades.
In Figure 2A the initial red-blue ratio was 30/70 in the upper region and 70/30 in the lower region. Two thousand
moves later, in Figure 2D, the corresponding ratios are 22/78 and 77/23. (In contrast, the ratios are 49/51 and 51/49
in Figure 2B, which displays the result of 1,000 moves in the absence of neighborhood effects. And the ratios are
6/94 and 91/9 in Figure 2C, which captures the effect of strong conformity.) One noteworthy change from Figures
2A to 2D is the increased level of local clustering (reflected by the similarity index rising from 57.6 to 78.1. This
result appears to capture an important feature of real-world pluralism, namely, the tendency for people to form
relatively homogeneous subgroups—sustained through schools, neighborhoods, workplaces, voluntary associations,
and especially congregations. Diversity is much harder to maintain in the absence of these and other “mediating
structures.”
We likewise confirmed the representativeness of Figures 2B and 2C by running each of those scenarios 100 times.
Individual variation enhances stability within a Schelling-like “world” because each agent now has a unique set
of tipping points that determine when to switch types. The spatial conditions that trigger change for any given
agent are unlikely to trigger corresponding changes among the other similarly situated agents. The overall system
becomes less likely to tip at any given moment and more likely to evolve in a slow and steady manner. For details,
see www.MARSMODELS.com. We thank Eli Berman for noting that our results might become more stable as the
population of agents becomes more diverse.
Briefly defined: Mobility here indicates migration that occurs continuously, as households move one by one, rather
than intermittently or in groups. (We do not model the system as in a Markov process that has various shares of the
population making “state transitions” in each period, nor do we calculate Nash equilibria that—in our opinion—
more appropriately model mass movement.) Randomness refers to the fact that people move without regard for
the religious characteristics of locations. Individuality means that personal attributes and personal history influence
religious behavior. Conformity means that people respond to social influence, and localism limits that influence to
their networks of close contacts. Quasi-symmetry means that when people move, social influence initially runs only
in one direction, from the existing neighbors to the newcomer. Denominationalism means that behavior varies across
different types of religion. Diversity means that religious variation exists at every level—individual, neighborhood,
and region. Disequilibrium means that the system keeps changing at every level, rather than converging to a static
equilibrium.
Despite its lack of realism, MARS models give rise to considerable complexity. This underscores how much more
difficult it is to properly evaluate standard models of religious behavior. Even the simplest theories of church attendance
(such as those that underpin a typical regression) include many factors that we deliberately left out of MARS—such
as age, race, gender, income, education, and family ties.
In MARS and most other agent-based simulations, the agents “choose” actions X that maximize the value of an
objective function U(X;a). The values depend upon parameters a, which capture the impact of the agent’s origin,
immediate past, current location, and current neighbors. The choice process falls short of the rationality assumed
by standard economic models, insofar as the agent responds only to local conditions, follows unchanging rules of
conduct, ignores the future consequences of current choices, ignores most of the information obtained before the
current move, and makes no effort to anticipate the choices of other agents.
A “move” can thus involve remaining in place. In such cases, the agent simply reevaluates his type and rate choices
based on his own current state and those of his current neighbors. A move-rate slider determines what percentage of
“moves” involves actual changes in location. If move rate is zero, the agents never change location and the simulation
becomes an example of a class of models known as “cellular automata.” William Bainbridge (2006) develops a
variety of sophisticated CA models in his forthcoming book, God from the Machine: Artificial Intelligence Models
of Religious Cognition.
The user can force each agent to compare one, two, four, or eight randomly selected locations before moving, and the
choice process can be different for different types of agents. The user also selects whether the agent then moves to the
location with the greatest number of neighbors (without regard to their religion) or the greatest number of neighbors
who share his own current religion.
MARS regions are fully bounded and agents “feel” no social influence beyond the edges of each region. It is,
however, relatively easy to introduce alternative “topologies” that wrap each region around its vertical borders,
horizontal borders, or both. These alternatives remove “edge effects” but almost never change the overall tendencies
described in the article.
15
ACCIDENTAL ATHEISTS
27. Here again, the full results appear on the MARS models website. And as with the scenarios corresponding to Figure
2B through 2D, the qualitative results in Figure 3B and 3C hold up in repeated runs. The same is true for the Figure
3D scenario described below.
28. Figure 3D displays the system after 5,000 moves in order to highlight the growth of the sect. Growth is less visible,
but no less real, in early periods. As in the real world, multiplicative growth takes a long time to produce a large
denomination even when the growth rate is very high.
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HW Questions on the “Accidental Atheist” MARS model
1.
Briefly summarize the empirical puzzle (but not the proposed solution) that motivated the
AA paper.
Answer each of the following questions with reference to the
basic MARS model (whether or not it fits real world religiosity!)
and briefly justify any “yes-no” answers.
2.
In what sense does the basic MARS model “stand the Schelling model on its head.”
3a.
What factors determine a person’s religiosity in the basic MARS model?
3b.
Explain the sense in which the following equation governs behavior in MARS?
𝑀𝑎𝑥
(𝑅𝑖𝑡 , 𝑅𝑖𝑡−1 , 𝑅𝑖0 ; {𝑅𝑗𝑡 })
𝑅𝑖𝑡
… where 𝑅𝑖𝑡 represents the religiosity of agent i in period t (and likewise period t-1 and period
0), and where {𝑅𝑗𝑡 } represents the religiosity of the agents who border on agent i.
4a.
When do agents choose to change or maintain their religiosity?
4b.
What determines where agents move? How does their religion influence where they move?
5a. What happens over time if each agent displays a high degree of religious inertia (i.e.,
agents strongly resist the pull of their neighbors’ choice or religious identity and level of
religious involvement). Assume that different regions begin the simulation with different
dominant religions.
5b.
Is American history consistent with the high-inertia version of the basic MARS model?
6a. What happens over time if each agent displays a high degree of religious conformity (i.e.,
agents are strongly influenced by the pull of their neighbors’ choice or religious identity and
level of religious involvement). Assume that different regions begin the simulation with
different dominant religions.
6b. Is American history consistent with the high-conformity version of the basic MARS
model?
7a.
What version of basic MARS fits the data best? Intuitively speaking, why does it work?
7b. In what sense does the MARS model lead to “accidental atheists” and “accidental”
Christians, Jews, Muslims, Catholics, Buddhists, Mormons, etc?
8.
Why do new or small religions have almost no chance of survival in the basic MARS
model?
9a. What single relatively small change in the behavior of their members greatly increases a
small group’s probability of surviving in MARS?
9b. What two or three relatively small changes in the behavior of their members greatly
increases a small groups’ chance of surviving and growing?
10a. Describe a relatively simple strategy that a small group can use to survive even if its
members are widely dispersed and unable to control where they live.
10b. Explain how the MARS framework might be adjusted or extended to include your
proposed strategy. I.e., formulate your strategy in terms of adjustments or additions to the
specific rules that govern behavior of agents in the MARS model.
Think carefully before answering questions 10a and 10b! Describe a strategy that can be
described in terms of the MARS framework and can be implemented by the members of the group
whether or not the members of other groups adopt the same strategy. Don’t expect to find the
answer in the AA paper, but review the “Exploring MARS” section for other examples of
relatively simple extensions to the model.
10b. Describe some real-world examples of your proposed strategy. Do modern technologies
make this strategy easier to implement?
10d. Explain why your proposed strategy might (or might not) be especially helpful for small
groups that include some “superstars” as defined in the paper. Do modern technologies make
these “superstars” more or less effective than in times past?
11. Aside from the extensions already analyzed in the paper and your comments above,
describe one or two other extensions to the MARS model that, in your opinion, would be most
likely to make it more useful for understanding religiosity in the real-world. Be sure to describe
your proposed extensions in terms of adjustments or additions to the concrete rules and features
that govern the MARS model.
12. Reflect on the following question, and then answer it briefly unless you’d prefer to keep
your thoughts to yourself: To what extent are your own religious beliefs, activities, identity, and
commitment an accident of the particular “social neighborhoods” in which you have lived, as
opposed to deliberate religious decisions that you yourself have made along the way?
*** Build your brain! ***
Go to the end of the paper and study footnotes
#1, 2, 5, and 10, and especially notes #21 and 23!
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