Discovery of Hidden Variables for the Evolution of Ethical Religions
RESEARCH ARTICLE
Multiple Hypotheses and Divergent Explanations: The Evolution of Moralizing High Gods
1
Douglas R. White
*
1,2 , Tolga Oztan 1 , Giorgio Gosti 1 , Elliott Wagner 1 , and John Snarey 3
Institute for Mathematical Behavioral Sciences, UCI, 2 Santa Fe Institute, 3 Human Development and Ethics, Emory University
SFI working group on robustness of models for sociocultural evolution 10-25-2011
*To whom correspondence should be addressed. E-mail: drwhite@uci.edu SOM:Supplementary On Line Materials
Shortened version intended for PNAS
Notes : Periods after references such as (3..) are to facilitate searches in revising the bibliography.
The abstract will be integrated into the main text.
Abstract.
As Darwin noted (1..), religious beliefs are evolved cultural characteristics (see SOM#0.5: What did
Darwin say about Religion?). In the 1980s, evolutionary biologist Richard Alexander (3..) sparked new interest in the factors affecting the evolution of religious belief and in particular of ethically-centered religions. His work stimulated diverse theories about the adaptive benefits of belief in moralizing high gods focused on reproductive fitness, prosociality within and between groups, group-level adaptation, costly signaling and group commitment, supernatural punishment, and game-theoretic models of indirect reciprocity, altruism and the freerider and punishment problems.
Comparative studies of religion often use Swanson’s (2..) moral gods variable (5..,6..,8.., 10..,12..,39..) as coded for the Standard Cross-Cultural Sample (SCCS, 25..,37..) to study ethical religious beliefs within an evolutionary framework. Few of these studies, however, have followed up on Alexander’s ideas of how ethical dilemmas (
SOM#1: Are the “ethical principles” of moral gods universal?
) faced by different societies have influenced systems of beliefs. Rich cross-cultural datasets are available to identify the ranges of societal, adaptive, and environmental variables that would help clarify the specifics of more general (“under fitted”) theories of evolution in religious beliefs. Yet, studies that have tested hypotheses and developed models with
SCCS data have failed to simultaneously test multiple working hypotheses, a recurrent topic of the journal
Science (18..,19..). This methodological shortcoming has led to conflicting hypotheses and misidentification of important factors in the origin and diffusion of beliefs about moralizing gods. We use multi-method and multihypothesis approaches to compare models and results with complementary types of analytic techniques. Our approaches lead to two new models that illustrate how complex problems of sociocultural evolution might be resolved and results of various studies could be synthesized. These models identify the factors that are likely to lead to grossly unequal disparities of wealth and which, as Alexander argues, may have encouraged the invention or diffusion of belief in moralizing high gods. In this study, we find that, among other variables, including scarcity of water, the critical predictor identified for pastoralists is the social inequality produced by cyclical variations in animal stock and for agricultural societies it is the inequality produced by cyclical variations in the ownership of land.
Introduction
Despite being a topic long neglected by researchers since Darwin (1..), who argued that religious belief was an evolved characteristic, explanations of the origins and diffusion of moralizing religions (2..) have recently received much attention from evolutionary biologists (3.., 4.., 5..), anthropologists (6.., 7..), scholars of religion
(8..,9..), psychologists (10.., 11..), and a political economist (12..). This resurgence of interest in the evolution of
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religious beliefs began with Alexander (3..), who, while not familiar with the work of Swanson (2..), perceived many of the same issues in morality, ethics, and religion. Both suggested that the adoption of ethical principles into religion would often serve common issues of all members of a group, and/or the interests of the powerful, those inadvertently harmed by excessive inequalities of power, and instabilities in social relationships that are harmful to the group or society. Oddly, many of the problems that defined as theorists (See SOM#1: Alexander and Swanson) have been ignored in favor of investigating the role of indirect reciprocity in the evolution of prosociality. Many researchers have been inspired to hypothesize that the invention of moralizing “high gods” is an adaptation to promote cooperation within society. Other hypotheses are that religious beliefs serve as hardto-fake costly signals of group commitment (13..,14..); that religion’s moral dictates are group-level adaptations that promote group success (2..,15..,16. SOM#2 : Intergroup competition ); that fear of supernatural punishment serves to increase contributions to public goods (12..); or that belief in moralizing “high gods” facilitates costly cooperation between strangers in societies too large for reputations to be easily tracked (10..).
Few of the game-theoretic models thought to be relevant to these issues or to explaining the origin of moralizing high gods are supported by statistical evidence from cross-cultural studies. Even fewer evolutionary theorists incorporate full consideration of what Alexander and/or Swanson (1..,2..) saw as the relation between the ethical concepts of moral-god religions and concepts of justice or fairness.
In fact, among studies that have used cross-cultural data to test hypotheses about the relevant correlates of moral gods and the effects of multiple variables in regression models, little agreement exists about which hypotheses are confirmed by the data. The failure to consider alternative hypotheses has led many researchers to neglect the nuances of earlier theories or misconstrue the variables of earlier studies. A common mistake in such cases has been the failure to follow the lead of Alexander (3..), who cautioned researchers to consider effects of different periods in evolutionary time, as for example, the independent invention of moral gods in earlier periods versus increasing cultural diffusion in later periods. Table 1 shows seven sets of variables considered in five prior cross-cultural studies (2.., 5.., 6..,8.., 12..) and two new variables in models of our own that test and synthesize these results while using improved regression techniques and controls for the nonindependence of observation.
The table shows the factors that each study found to be associated with a society’s belief in moralizing gods.
Salient in the discrepancies among the prior studies listed in the Table is the tendency of conclusions to diverge according to whether the authors used simple correlations, multiple variables, or controls for spatial and linguistic (common origin) autocorrelation. One study (5..), without autocorrelation controls, for instance, surmised that high rates of external warfare and plentiful subsistence resources might affect multiple levels of political hierarchy that in turn might predict moralizing gods (R 2 =.29, p = 0.0001, inflated by autocorrelation).
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View this table in
…
Table 1: Sets of variables are considered in prior cross-cultural studies and two of our own models that synthesize prior results and add refinements to prior variables. The major conflicting hypotheses are those of Alexander, Snarey, and Brown and Eff versus Swanson and Roes and Raymond.
Types of
Topic Vars. Controls Positive predictors of moralizing gods
Spatial Language Community Structure Habitat Conflict Pastoralist
Topics


Studies
Roes &
Raymond
(5..)-2003
Diffusion
Not controlled
Common origin
Not controlled
Political hierarchy
(Superjh) &
Prosociality
Community size
(Commsize) or
Fixity
Food & water resources
Rich resources cor.with political hierarchy
External or
Internal War
External war cor .w/ political hierarchy
Pastoral society features
Animal husbandry not tested
Johnson
(12..)-2005
Our OLS
Model 1*
(17..)-2011
Brown & Eff
2SLS*
(6..)-2010
Our primary
2SLS-IS*
Model 2
(17..)-2011
Not controlled
Not controlled
Yes
Yes
Inter-societal & ecological interactions
Not controlled
Not controlled
No effect
No effect
Theories supported by our models
Theories disconfirmed by our models
Levels of political hierarchy
Superjh
**Prosocial
Political-Economic
Institutions
Levels of political hierarchy
( Superjh ) given other variables
Community size
Commsize
Fixed comm- unities & wages
(episodic inequality)
FxCmtyWages
Def
1 st principal component of
Superjh &
Commsize
Levels of political hierarchy
( Superjh ) given other variables
Moderate community size
(Non-monotonic
& curvilinear)
Fixed comm- unities & wages
(labor inequality )
FxCmtyWages
Def
Population, community size & structure increase in last three centuries, relevant for all models
Swanson ( 2..) partial support;
Models 1,2 and
Brown & Eff
Alexander elsewhere uncertain
(3..)
Models 1,2;
;
Roes &
Raymond (5..) Johnson (12..)
Not considered
Scarce water:
Lo_rain_Dry Def
No external war
Internal war (?) Not considered
No Effects
Pronounced episodic inequality in herd sizes
AnimXbwealth
Def
Food scarcity
Scarc
Scarce water
No external war
Lo_rain_Dry Def No Effects
Ecological spread of deserts ***
Snarey (8..)
Modified in
Models 1,2
Not applicable
None
Animal husb. problems of theft
& moral regulation
Episodes of pronounced inequality in herd sizes
AnimXbwealth
Def
Pastoral societies spread with deserts
Brown & Eff
(6..) as Modified in Models 1,2
Roes &
Raymond (5..)
Roes
&
Raymd.
Brown & Eff (6
..)
Brown & Eff
(6..)
Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8
Def - Variable defined in the text. *Each imputes missing data *** add quote to strengthen argument
**Johnson: Money, Credit; Levels of political hierarchy, Police, Taxes, Formal sanctions; No variables are found to be significant for SCCS measures of prosocial individual behaviors: Compliance of individuals with community norms, Loyalty to the local community (sccs$v778),
Loyalty to the wider society (sccs$v779), Compliance of Individuals with Community Norms (sccs$v775), Formal Sanctions and
Enforcement for Community Decisions (sccs$v775), and Sharing of food (sccs$v1718) .
Table 1: Sets of variables are considered in prior cross-cultural studies and two of our own models that synthesize prior results and add refinements to prior variables. The major conflicting hypotheses are those of Alexander, Snarey, and Brown and Eff versus Swanson and Roes and Raymond. The last two rows list studies that are at least partially supported or are disconfirmed with respect to certain variables. These include disconfirmations such as Roes & Raymond’s assertion that plentiful resources and external war have indirect effects on the likelihood of occurrence of moral gods and Brown & Eff’s conclusions that pastoralism and lack of external war are predictors of moral gods. The full set of variables (e.g.., Moralizing gods, Superjh) are defined in the
SOM text (Description of Variables . SCCS society numbers for the 43 societies with moral god beliefs are 21 24 25 26 29 34*
36 37 38 39 40 41 42 43 44 46 47 48 50 51 52 54 55 56 57 58 59 64 65 70 82*/ 120* /140 /151 154 155 156 158 160 162 / 172
186 (*indicates those coded for Snarey’s HiGod4 variables that Murdock codes as missing data). Numbers are keyed to Figure 1 and those underlined refer to local rather than world religions.
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Figure 1: Societies of the Standard Cross-Cultural Sample ordered from 1-186 (southern Africa to South
America) by most similar neighbors for use in calculating diffusion effects. The smaller figure, 1a, shows the distribution of high gods (1=none, 2=present but inactive, 3=present but not concerned with human morality, 4= concerned with morality).
Fig. 1: Hi gods 1=none (black) 2=punish (gray) 3=indifferent (organe) 4=moralizing (red); green numbers show
SCCS societies along the maximum diffusion path from 1 to 186
High gods on the maximum diffusion path of Murdock and White (1969)
A weakness of all but two of these studies (6..,17..) is that nonindependence among societies surveyed is not taken into account, resulting in inflated results for significance tests. A key study with controls for spatial diffusion within the same SCCS database (6..) found that the presence of moralizing high gods is not predicted by political hierarchy but predicted instead by low levels of external warfare, food scarcity, moderate community sizes, and dependence on animal husbandry. The latter (6..) is said to result because animal husbandry invites easy theft, for which belief in a moral god might provide protection.
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Table 2 shows an evaluation if conflicting hypotheses and guided by the conception of “multiple working hypotheses” (18. 19) to reconcile contrasting results and reflect on the value of considering multiple working hypotheses and multiple methods. Chamberlain (18,19) warned against the premature adoption of favored hypotheses, and this recommendation is particularly relevant when seeking to understand and interpret discrepant findings. The key is not necessarily to select one or another method or model over others but, in the case of explaining the origins and spread of religious beliefs, to recognize that while controlling for autocorrelation may give us models for early origins of moralizing “high gods” prior to the extensive diffusion of world religions, standard regression methods such as OLS (ordinary least-squares) may provide information about factors that affect the wide-reaching diffusion of religious beliefs and institutions. Therefore, the contrasting results of a correlational or OLS model (5) and a 2SLS (two-stage least squares) model controlling for autocorrelation (6..) can be viewed as providing complementary information about the initial invention of moral gods and the eventual diffusion of world religions. We will show that in two improved models, one in which spatial and language autocorrelation is controlled for and one in which it is not, three types of societies are identified that form beliefs in moralizing high gods: those in dry zones; those with permanent settlements, rights over land, and wage labor; and those pastoral societies in which wealth is characterized by slowreproducing animals used for trade and travel such as camels and horses. The latter two types of societies are subject to episodic cycles of resource abundance followed by periods of excessive inequality (20, 21).
Consequently, these results suggest that the invention or adoption of belief in moralizing “high gods” may be the result not only of resource-poor environments (8..) or one in which property was prone to theft (6..) but of a culture’s need to cope with periods of heighted inequality that are amplified in periods of scarce resources relative to overabundance of population. Excessive inequality is generated more readily, for example, when property values relative to wages are amplified by scarcity and overpopulation or when pastoralist wealth in animal stock is unequally accumulated through exchanges that also increase the strength of some kinship groups at the expense of others.
Table 5: Evaluation of two conflicting models
Solo
Model
R 2 =.35
R 2 =.48*
Effect Signif.
Mixed
Model
R 2 =NA Brown &
Eff
White-Snarey
“Hidden
Effect Signif. Variables
Variables”
Mixed
Model
R 2 =.43
>Left=.35
Effect Signif.
Solo
Model
R 2 .41
Effect Signif.
1.906
0.654
-.737
-.878
-.298
0.807
0.679
0.445
.00000 1.714
.123(.
012 ) 0.505
.051(.
038 ) 0.009
.078(.
011 ) -.626
.132(.
025 ) -.271
.036(.
113 ) -.050
.042(.
034 ) 0.296
.050(.
016 ) 0.151
**
.00000 Distance
.259 PCcap
.984 PCsize
.269
.152
.922
PCsize2
Eextwar
Anim
.380
.539
***
Distance
SuperjhW
AnimXb
Caststrat FxCmntyW
Foodscarc No_rain_D
Mission
Logdate
1.714 .00000 *** 1.589 .0000002 n.s.
0.279 .051 * 0.518 .044 **
0.589 .223 n.s. n.s.
0.071 .034 **
0.279 .107 ~*
0.504 .061 *
0.255 .094 *
1.739 .086 *
0.310 .058 *
0.642 .006 ***
0.301 .041 **
2.333 .001 ***
*In Brown and Eff (2010) R 2 is adjusted for two-stage least-squares. E.g., from .35 up to .48
** Nonsignificance due to a missing data bias: N=132 using v238, N=144 using HiGod4. The signif. Tests in parentheses are those from
Brown and Eff . Ecorich not in the original model
*** Nonsignificance due to additional Hidden Variables
Delete: Corrected: Foodscarc v1685 includes 26 cases of R code 7 (correct the codebook!) that are missing data.
Variables & Definitions
Distance – W matrix autocorr.
PCcap – PCA(v921,928) Agric Pot.
PCsize – PCA(v63, v237) Cmty size
Eextwar – v1650
Anim – v206
AnimXbwealth – Anim* v208=6
Caststrat – v272
Foodscarc – v1685
No_rain_Dry Rain+(v855>4)*1
PCsize2 = PCsize squared
SuperjhWriting - produce
FxCmtyWages -((v2010>=2)*1) Mission
*((sccs$v61==6)*1) Logdate - log(v838)-6
1. Description of the dataset and relevant variables
The SCCS database contains information about the beliefs, values, economies, and living conditions of 186 societies. The database (25..) was originally developed to include codes for 480 different topics but to date over
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100 new sets of cross-cultural codes have been added by different authors, totaling more than 2,000 variables.
The coded data range now from the mundane variable 1, Intercommunity Trade as Food Source, to variable
2001, Deep Islamization/Christianization. The HiGod4 variable includes circa twelve independent or successive
(e.g.., world religions of Judaism, Christianity, and Islam) developments of beliefs in moral gods, including those of nine local religions. The database is ideal for investigating the origins and diffusion of religious beliefs because the database includes data about the sorts of gods, if any, for each society. In the SCCS societies, a high god is considered absent for 37%, inactive for 27%, active but not supportive of human morality for 12%, and supportive of human morality for 23%. Of the societies in the sample, 106 (57%) have local rather than world religions, and of these, ten have moral god beliefs. Afro-Eurasian societies 21-82 include 19 (10%) with early
“deep” Islam and six with early Christianity, for a total of 13% (25/186) of the SCCS sample. Many (19) of the
24 societies coded as “superficially Christianized” (13% of SCCS) have been missionized. Of the seven
“superficially Islamized” societies (4% of SCCS), four have been missionized (2%). The Gros Ventre exemplify one type of reporting of religious belief in moralizing gods in Indian America (a translation of their term for
"Supreme Being" is "He Who Rules All by the Power of Thought."). Kroeber’s well-known ethnography (1908)
“abounds in descriptions of ceremonial dances, but lacks data on sacred beliefs” while Cooper’s (1956), according to the editor, “reflects the change during the last fifty years on the Plains; the old tribal secret ceremonies and beliefs are fading away, the visionaries are almost gone, and the few remaining medicine men and oldtimers are willing to communicate what they know- sometimes in the expectation that the anthropologist will save the old traditions for the future” (See SOM#17: Missions).
Figure 1 and 1a, however,
The coded data most relevant to the study of high gods include variables for moralizing gods, levels of jurisdictional or political hierarchy, date of ethnographic description, missionization, community size and fixity, food scarcity, scarcity of water resources, general ecological resources, caste and class stratification, wage labor, external and internal warfare, agricultural potential, type and percent dependence on animal husbandry, type of marriage transactions, and various forms of prosociality such as specific types of norms, loyalties, sanctions, and punishments. Further variables among others defined in the SOM text (1: Description of variables relevant to SCCS Moral gods) include sources for variables with common names and explanations of names for composite variables used in the text, such as Lo_rain_Dryzone (water scarcity), FxCmtyWages, and AnimXbwealth.
2. Comparison of Models and Explanations of Results in Table 1
In spite of all the predictors associated with potential sources of inequality (and various kinds of scarcity), proximity (and thus spatial diffusion) as an autocorrelation control is by far the strongest predictor of a belief in moral gods (p < 0.0000001). Consequently, the significance tests in OLS regressions for moral gods are exaggerated estimates (falsely positive Type I error) for rejecting a true null hypotheses (H0). Significance tests are valid in 2SLS models that succeed in controlling for autocorrelation if the independent variables test as exogenous, i.e.., uncorrelated with the regression errors. Proximate distance and possible advantages of religious solidarity in warfare (4), however, do not account for origins of beliefs in high gods. External war as a predictor of moral gods is suspect given that different models listed in Table 1 report a positive correlation in one case and a negative effect in another, when autocorrelation (row 4) is controlled for. One author (27..) considers "Religion ... has many properties that make it an excellent adaptation for war. Perhaps this is an accident. Alternatively, perhaps it was so effective because it was designed for exactly this purpose."
Scarcity of resources, however, presents a more direct effect on the need for cooperation in survival, and may also motivate warfare. Results of testing Snarey’s (8) hypothesis that moralizing gods are generated as a cooperative response in societies with an ecology that leads to scarce water are consistently significant in our
Models 1 and 2 (OLS and, significantly, 2SLS, controlling for autocorrelation) in competition with other variables.
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Swanson (2..) hypothesized that a) the origin of high gods was linked to the emergence of higher levels of jurisdictional hierarchy in the political system (see Table 1 rows 1-2, col. 4), and b) the “supernatural support of human morality was more common in societies that also had parallel explicit social rules legitimating the morality of ‘interpersonal differences according to wealth’.” Table 1 lists three regressions on multiple variables: the 2SLS model (6..) in the SOM text (SOM#3: Brown and Eff), our 2SLS-IS (17..) model ( SOM#4:
White et al ..), the “-IS” referring to inferential statistics that do not support some of the primary variables of the prior model (6..), and our OLS model ( SOM#5: Table 2 ), used for comparison of regression methods. Support for a secondary regression effect on belief in moral gods is found in the two 2SLS models (6..,17..): in the first model only as a composite of the Superjh and Commsize variables in Table 1; and in the second with multiple variables not in the first model and Swanson’s main variable –Superjh- the least robust of all.
Swanson’s (2..) secondary hypotheses for precursors of moralizing high gods (see SOM#1: Alexander and
Swanson ) are supported both for “explicit social rules legitimating the morality of interpersonal differences according to wealth” but for conditions that violate the expectation of some form of social justice in the distribution of wealth, consonant with Alexander (1). Our models show results with two compound variables in both OLS and 2SLS-IS that were constructed to identify moral dilemmas of recurrent periods of property-based inequality generated by certain forms of exchange in agricultural and pastoral societies, respectively: variables
FxCmtyWages and AnimXbwealth. The latter model specifies a mechanism that would explain why pastoralism as a predictor of moral gods (6..) is disconfirmed in our 2SLS-IS model: herders both of cattle and horses and/or camels have a heightened possibility of the theft of animals (6..) but moralizing high gods are largely present only in the latter case and largely absent in the former.
Johnson (12..) finds a correlation between Commsize and Moralizing gods (Table 1 col. 5) that was not replicated in the OLS or 2SLS models that include other variables. His analysis of correlates of Moralizing gods with variables (col. 4) that support prosociality in the political and economic domains (Money, Credit, Superjh,
Taxation, and Police, and less so for Size of local communities and Sanctions for enforcing community decisions (see SOM#13: Description of variables relevant to SCCS Moral gods ). His predicted prosociality variables in behavioral domains like individual loyalties to the local community or wider society do not correlate with moral gods more highly than expected considering number of examined.
3. A multiple methods approach
Chamberlain’s (18..) multiple methods approach suggests that we might learn different things from different kinds of methods and models summarized above. Correlations, OLS, 2SLS, and the extension of 2SLS through inferential statistical methods (2SLS-IS software) form a continuum reflected in the ordering of rows in Table 1 that moves from the weakest forms of inference to methods that give robust estimations of regression effects.
We explain the differences among models in several steps. Earlier we posited a tendency for results to diverge according to whether the authors used simple correlations, multiple variables, or controlled for spatial and linguistic (common origin) autocorrelation. For the stronger types of methods, 2SLS and 2SLS-IS, rownormalized square proximity (“W”) weighting matrices multiplied by each of the independent variables (WX) are used in 2SLS methods (28..) to create an Instrumental Variable Y
WX
predicted in a first-stage linear model
(lm) regression of dependent variable Y (Moral gods) from weighted neighborhoods for each weighted WX variable ( SOM#6: Eff and Dow 2009: Controls for Autocorrelation ). Y
WX
is then used as an Instrumental
Variable in a second-stage regression that defines a new dependent variable Y

=Y – Y
WX
. A second-stage OLS model Y

=lm(X) is tested for exogeneity of the independent variables using a null hypothesis test for lack of correlation of ε, the second-stage error term, with any of the X variables. If ε is conditionally independent of each X then significance tests can be used to find best-fits of independent variables to (Y

=Y – IV
WX
).
Overfitting remains a problem with variables selected by significance tests without adequate tests of reliability.
To guard against overfitting, we extended the previous 2SLS software (28..) to include inferential-statistics
(17..), i.e.., 2SLS-IS. The 2SLS-IS procedure (17..) takes a random sample of 79% of the observations (e.g.., the
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186 SCCS societies) to train the regression coefficients in ten independent iterations of the model and calculates the model R 2 and significance tests for each independent variable for each of the ten holdout samples of 21% of the cases (those not sampled in successive training samples) to test model replication. Several of the variables in the 2SLS model (6..) fail to replicate, with food scarcity the least robust. When it is removed as an independent variable, the OLS (6..) variables for agricultural potential and caste stratification also fail, leaving a reduced but reliable model with only Distance (autocorrelation) and four other variables: external war, dependence on animal husbandry, and two combinations of levels of political hierarchy (Superjh) and community size
(Commsize). We then added to this reduced model the precipitation measure of resource scarcity (Lo_rain) that was predictive in Snarey’s (8..) regression model as a replacement to the less reliable food scarcity variable. Our
2SLS-IS software confirmed that Lo_rain was a reliable moral god predictor. It measures rainfall from the reports of ethnographers in 102 of the SCCS societies, and uses climate atlas data for the remainder of 84 cases.
Averaging this measure with other climate atlas precipitation measures from SCCS studies did not improve reliability or significance in the regression model. Averaging with societal locations from climate atlas data to fit an ordering of dry ecozones, however, produced a composite variable (Lo_rain_Dryzone) that improved reliability and significance in the new composite model. We also improved reliability and significance of the new model by replacing the dependent variable (“Moral gods”) coded by Murdock (26..) with the more fully coded “HiGod4” variable (8..).
After finding weaknesses and replacements for variables in the Brown and Eff model (6..), we tested variables that had greater explanatory specificity. Following the lead of Alexander (3..) in hypothesizing that beliefs in a moral high god might be promulgated due to ethical dilemmas in exchange economies (including our own) that might be resolved by concepts of prosociality (8..,10..) or punishment (4..,11..,12..). One example mentioned earlier is wealth inequality that becomes so disproportionate in certain periods (20..,21..,23..) that it generates social protest and conflict. Among some pastoralists, for example, breeding stocks of camels and horses constitute wealth that grows through reproduction but are also a form of capital expendable in transport and trade that can bring more wealth through exchange. This differs from viewing the value of animal stock in terms of sources of leather and meat for consumption, with breeding bulls for cows kept for milk and steers killed for consumption products of meat and hides. Herd sizes among cattle herders tend to be somewhat equally distributed. Camels breed at a slower rate than cattle (29..) and are retained as a productive stock of capital, heightening the possibility of amplified inequalities in herd size (30..). In support of this hypothesis, we found that the bivariate distribution of the variable for percentage subsistence dependence on animals, a non-resilient variable in previous models (6..), showed that those individual cases that correlated with HiGod4 were societies with valuable transport animals (camels, horses, mules and donkeys) that rarely raised cattle.
The parallels in agricultural societies are that land held in usufruct (with claims justified by usage and kinship ties) diminishes inequality whereas landed property held as wealth-producing capital has a greater likelihood of generating wealth inequalities. The prediction that inequalities in this context might be precursors of moralizing high gods (HiGod4) would be consistent with Alexander’s hypothesis (3..) and with Swanson’s (2..) first and second hypotheses—not only of (a) “interpersonal differences according to wealth” but (b) conditions that violate the expectation of some form of social justice in the distribution of wealth—as precursors to beliefs in moral gods.
The plentitude of societies in the SCCS that lack a belief in a moralizing high god might be partly explained because the conditions of boom-bust cycles that lead to highly unequal wealth distributions (20..,21..,22..) are not found everywhere. For pastoralists, in contrast, pastoralist property-and-exchange economies with mechanisms of unequal accumulation of wealth in breeding stock often had cyclical periods in which some groups were able to accumulate not only vast numbers of horses, camels, and other transport animals, but also wives, sons, herdsmen, affinal alliances, and armies (20..,21..). Such was the case with the Mongols of the
Golden Horde, whose empire was next in size only to the British Empire. The Golden Horde promoted commerce through animal transport and protection of trade routes and developed techniques of invasion and conquest that generated massive political inequalities (31..). See SOM text ( SOM#7 : Lindholm).
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4. The conceptual connection between Animal Husbandry/Bridewealth and Fixed Communities/Wage Labor
(Turchin, boom bust cycles, etc..)
Snarey’s hypothesis is that when societies face water scarcity in a dry ecological niche (mostly pastoralists but also intensive agriculturalists (see SOM text SOM#8 : Subsistence type and Dryness) a need for extended networks of cooperation is created, consistent with ethics of generosity offered by beliefs in a moral god who actively supports prosocial values. Our hypothesis, backed by Alexander’s and Swanson’s second hypotheses, adds the concept that once interpersonal differences in wealth are legitimized, in contexts of fluctuating wealth inequalities, moral gods become more likely as a means of maintaining cooperation. We used this hypothesis to motivate a search for specific mechanisms of exchange that are more likely to generate inequality in contexts of fluctuating wealth inequalities, especially for societies with intensive agriculture or pastoralism where moralizing gods were known to occur more frequently .
Thus, after doing extensive analysis of how bivariate distributions of variables relate to moral gods in prior studies (SOM text SOM#9 : Bivariate distributions), we searched for more specific predictor variables— especially those that might involve wealth inequalities that occur periodically rather than stratification by class or caste. We looked for explanatory power with regard to (a) concrete social processes, (b) hypotheses and results of prior authorities who had domain knowledge in evolutionary biology (3.., 20.., 21..), evolutionary sociology or archaeology (2..,23..,24..,35..), and the ethnography of religion (7..), and (c) consistency with empirical knowledge of historical processes in pastoral (30..,31..) and agrarian (20..,21..,22..) societies. Two of our theoretically motivated variables, which we thought might evoke elective affinities for moralizing high gods, proved to be predictive. As noted [avoid these earlier mentions], these were (a) AnimXbwealth (animal husbandry of pack animals, camels and horses, accompanied by exchange of wives for bridewealth) and (b)
FxCmtyWages, fixed (agriculturally based) communities with wage laborers. We called these “hidden” variables because they are not single variables in the SCCS codebook but compound variables, interaction terms in a regression equation, because we were motivated by a combination of circumstances that we thought would produce episodic moral or ethical problems of exchange. Whereas a previous study (6..) showed that moral gods could be predicted from pastoralism alone, explained by vulnerability to theft of animals that might be reduced by moral religious beliefs, our empirical analysis showed a much narrower range of pastoralists with moral gods and our compound AnimXbwealth variable correctly identified that narrower range with greater specificity.
5. The results, strength, and weakness of multiple models (our inferential 2SLS-IS model, and our weaker
OLS model)
What AnimXbwealth and FxCmtyWages have in common as predictors of moral gods in our 2SLS-IS and OLS models are contexts for moral dilemmas that result from certain forms of exchange that lead to contestation over inequality and the need for prosocial resolution. Pastoral clans or lineages that are wealthy in stocks of horses and camels and able to acquire brides in exchange for animals (SOM text SOM#10 : Bridewealth animals in pastoral societies), can easily come to dominate others in growth through female fertility and growth of stock and wealth. Similarly, in agrarian communities where families can accumulate productive property in land, and wage labor is paid to those without productive property, boom-bust extremes of inequality often occur. In either case, in those periods when resources are scarce, demographic surplus (fertility), relative to resources, produces scarcity. The stress of scarcity is reduced for groups with property ownership (e.g.., clans or socioeconomic classes) in hard times by the fact that heightened advantages accrue to owners in those periods when returns to labor are diminished by overpopulation of laborers. But women and subdominant wife-giving groups in the pastoral case, and wage laborers in the agricultural case, will be disadvantaged by scarcity of resources and oversupply of workers and may contest against groups with greater power. As with openness to other innovations (23..), the periods of resolution following those of stress may be the most likely times for adoption or spread of belief in an ethical high god that helps to restore or promote principles of fairness and equalization in access to resources.
9

The weaknesses of our 2SLS-IS model (17.., see SOM text SOM#11 : Tables I3, R4) are the following: it is still one of several possible models, its R 2 is somewhat lower (0.41 vs. 0.43) than that of the over-fitted model of
Brown and Eff (6..), and while the FxCmtyWages variable is a robust predictor when spatial proximity is controlled, it is less robust when using the Murdock-White alignment (Figure 1) as a control for autocorrelation.
Possibly the alignment method weakens this variable in particular because of its 41% missing data. The SOM text ( SOM#15 : The effect of wages on HiGod4 offers another hypothesis, consistent with the inferential robustness tests provided by our 2SLS-IS software, which support all our 2SLS-IS regression results, including
FxCmtyWages, still our weakest variable. Table 2 shows eleven runs of train-test samples with good replication for all variables in both the random 79% train and 21% samples. Distance and Water scarcity are uniformly significant; only in 9% of the runs are AnimXbwealth and Missions strongly nonsignificant (p > .30); and only in 27% for the Logdate control, which is not essential to the model. Using another measure of wage labor
(sccs$v1009) to add codes for an additional 13% of the 186 cases, shows strong confirmation of robustness for the FxCmtyWages variable. That is, FxCmtyWages with 41% rather than 52% missing data is a robust variable with 91% and 72% of the eleven runs for 79% and 21% replications significant at p < 0.10 (exceptions in red).
Variables
Distance
Logdate
Lo_rain_Dryzone
Missions
AnimXbwealth
Superjh
Missing data
0%
0%
0%
0%
0%
0%
100% Model
Pvalue
79% train
% p< 0.10
<0.00001
0.006
0.006
0.028
0.039
0.061
100%
64%
100%
82%
82%
91%
36%
21% test
% p< 0.11
# 8 pvalues
# 9 pvalues
# 3 pvalues
# 7 pvalues
# 4 pvalues
# 2 pvalues
#10 pvalues
# 1 pvalues
# 5 pvalues
# 6 pvalues
#11 pvalues
100% 1 x
10
-4
1 x
10
-4
1 x
10
-4 1x10 -4
1 x
10
-4
1 x
10
-4
1 x
10
-4
1 x
10
-4
1 x
10
-4
1 x
10
-4
1 x
10
-4
64% 0.01 0.00 0.01 0.03 0.00 0.58 0.01 0.89 0.03 0.67 0.02
91% 0.11 0.03 0.01 0.03 0.02 0.02 0.04 0.04 0.02 0.01 0.01
55% 0.05 0.01 0.10 0.11 0.07 0.15 0.07 0.22 0.18 0.21 0.44
55% 0.03 0.02 0.03 0.31 0.10 0.13 0.05 0.20 0.19 0.10 0.22
73% 0.16 0.09 0.06 0.17 0.03 0.18 0.05 0.09 0.06 0.02 0.06
22% 0.24 0.03 0.16 0.08 0.17 0.15 0.16 0.39 0.32 0.29 0.14 FxCmtyWages 52% 0.057
FxCmtyWages* 41% 0.036 91% 72% 0.35 0.21 0.13 0.11 0.11 0.10 0.08 0.08 0.06 0.03 0.02
Average R 2 = 0.33 for 11 runs, in descending order of the 11 R 2 0.49 0.49 0.47 0.34 0.33 0.30 0.30 0.28 0.26 0.24 0.17
Table 2: 2SLS-IS Inferential statistics showing 11 runs of 79% train and 21% test samples.
*After the run with 52%, a second wage labor variable (sccs$v1009) was used that added 13% more cases to FxCmtyWages
(R 2 =.80 with the old variable). The 11 runs of 79% and 21% train and test samples improved to 91% and 72%. Average significance for FxCmtyWages, with 52% or 41% missing data, does not improve lowering the train ratio from 79% to 66.7% or lower, which is also true for other variables.
Key to Variables : These and further variables are defined in the SOM text ( SOM#13 : Description of variables relevant to
SCCS Moral gods ). The dataset name is sccs.Rdata and variable construction and labels used in the model are given below:
Logdate =log(sccs$v838)-6): Date of ethnographic description.
Missions (8..): Missionization at the date of ethnographic description.
Lo _ rain _ Dryzone =sccs$Rain+(sccs$v855>4)*1: Precipitation (8..) & dry ecozones. Water scarcity.
AnimXbwealth =((sccs$v208==1)*1)*(sccs$v858==6)*1: Pastoralism & Bridewealth.
Superjh =sccs$v237: Levels of jurisdictional or political hierarchy.
FxCmtyWages ( SOM#14 )=((sccs$v2010>=2)*1)*((sccs$v61==6)*1): Community fixity & Wages labor.
In the final model that includes 59% of the SCCS cases for FxCmtyWages, Superjh has the lowest replication rate (45% for the 79% sample and 28% for the 21% sample, at p < 0.11). FxCmtyWages covers a larger range of cases than Superjh, both correlate with agricultural societies, and high Superjh tends to entail high
FxCmtyWages, the more robust variable.
6. Control Variables: Interpreting time (observation and missionization), spatial diffusion, and independent invention
Chamberlain’s (18..,19..) recommendation of multiple working hypotheses is important not only for testing variables and models against one another but for comparing the results of different methods. In regression models it proves useful to compare results of 2SLS models that control for autocorrelation to OLS regression results that do not, even if the OLS significance tests results are inflated. For example, lack of diffusion is indicated when OLS significance is nearly equal to or less than that of 2SLS, providing evidence of independent invention or non-spatial effects of the independent variable. In Table 3 this applies for Missions (full sample)
10

and FxCmtyWages, with and without Missions. Conversely, in the full sample, the higher OLS significance suggests that FxCmtyWages diffused along with Missions later in a time when Milk has high 2SLS significance, probably in synchrony with the broad spread of Missions and pax colonia as animal husbandry shifts to domestic consumption rather than wealth acquisition through trade and conquest (Verified in SOM#15: The effect of wages on HiGod4— almost all societies with wages that predict moral gods are cases with intensive plow agriculture are missionized). For the full sample the near equality of significance for missions in the OLS and
2SLS models shows the lack of spatial clustering that would be expected for the spread of missions. The negative coefficient for date of observation (Logdate) in premissionized societies, where diffusion patches
(measured in OLS/2SLS ratios of Logdate coefficients) occur earlier, may indicate that independent adoption of broadly spread beliefs in moral gods occur early rather than later in time in the premissionized period. This conclusion hints at the possibility that these beliefs diffused from early European (Christian) and Middle
Eastern (Islamic) societies.
The SOM text ( SOM#16: Controls for time of observation, missing data, and other biases ) provides an assessment of (a) how proximal are seven of the ten “local religion” societies with world-religion societies having moral god beliefs. The remaining three local-religion cases of moralizing gods may have been influenced by premissionary Christianity in Russia (Yukaghir) and Amerindia (Gros Ventre). If so, then this study is largely about the diffusion of Christianity and Islam, with controls for autocorrelation for the many historical processes that are operative in their adoption ( SOM#17 : Missions ). With autocorrelation controls for diffusion, however,
2SLS regression can model diffusion not as a pure spatial effect but as the effects of variables that influence elective decisions as to adoption, or what Snarey calls “elective affinity.” This echoes Alexander’s statement of
“The efforts of moralizers to use gods to serve their own interests caused them to create the concept of a single, just God of all people” that does not serve only the interests of the powerful.
Some authors (32..) have thought that belief in high gods “seems to have been suggested by the pastoralists' experience of the relationship between themselves and their flocks. The modern religions based on this view of the relationship between human beings and god—Judaism and its offshoots, Christianity and Islam—originated among pastoral peoples" and "Pastoral peoples tend to develop a belief that is found in very few religions; they commonly believe in a God or gods who take active interest in human affairs and look after the people who worship them." In Table 3, AnimXbwealth shows much higher OLS significance than that of 2SLS in both the premissionized societies and the full sample, i.e.., suggesting early diffusive pastoralism that is dampened in the presence of Missions, along with the effect of the Water scarcity variable.
View this table in …
Table 3: Comparisons of 2SLS and OLS regression coefficients for independent variables predicting moral gods and controls and checks for OLS significance equal or less than those of 2SLS.
Logdate Superjh Variables
Samples
2SLS-IS
No Missions
Full Sample
Missions
Missions as control
Table 4A
0.32*
Table 6
OLS
No Missions
Full Sample
Missions
Ratios
No Missions
Table 4B
0.41
Table 3
3.83*^
0.91*
3.96*
-11.4
0.51
3.2
-3RIInv <<
Lo_rain_
Dryzone
0.27*
0.23*
0.28*
FxCmty-
Wages
0.20*
0.14*
0.25*
AnimXbwealth
0.39
0.62*
0.44
Milk
0.27
0.40*
0.23
0.06
0.24
0.26
1.51*
1.12*
0.60
-0.08
0.87
Pvalue ratios:
IInv+ .01~.03 IInv+ .03<.62 Diff+ .36>.004
No effect?
Calc!
0.12*
(*)
0.04
0.15
0.13
No effect
11

Full Sample
Missions
ISpr V .03~.01
0.5 ½ Diff
2Diff 10 -3 >10 -5 2Diff .10>.004 2Diff .04>.0001
No effect?
0.8 IInv 10 -3 <.05
IInv+ .002<.02 No effect Consumption
IInv .03~.02
No effect
Theory
Supported
Snarey (8..) Alexander (3..) Alexander (3
..)
None Swanson
(2 ..)
*Significant <<Date reversal V ISpr=Non-spatial ^Exceeds OLS, which excludes diffusion effects
Table 3: Comparisons of 2SLS and OLS regression coefficients for independent variables predicting moral gods and controls and checks for OLS significance equal or less than those of 2SLS. Although the Circum-
Mediterranean and East Asia have 53% moral god societies, there is no effect of this region or others on the
2SLS or SLS models in Table 2 or 3.
Key to symbols
IInv+ Accelerating invention
IInv0 Neutral invention
IInv- Deccelerating invention
ISpr V Indep spread,
not spatially clustered
-3RIInv negative accel ratio
2Diff strong diffusion
1Diff medium diffusion
½ Diff retarded diffusion
As for invention vs. adoption after missionization, as was the case in the pre-missionized societies, the inference from comparison of 2SLS and OLS results are that moral god beliefs spread widely without spatial clustering.
That is, more cases of moral god beliefs would appear to be “independently invented” if not for a missionization effect that is independent of spatial clusters.
Conclusions
Two variables that were hidden from previous researchers play a key role in supporting Alexander (3..) and
Swanson’s (2..) second hypotheses, that moral gods are a potential ethical regulator of inequalities, and in reinforcing Snarey’s (8..) prosocial hypothesis about cooperation in the face of scarce water resources. This triumvirate of variables wins out over Swanson’s first hypothesis of beliefs in religious hierarchy as projections of levels of political hierarchy, as first posited by Durkheim. The two new variables identify with greater specificity the intersections of variables likely to generate recurrent periods of property-based inequality generated by certain forms of exchange in agricultural and pastoral societies that create a need for prosocial ethics embodied in moral-god religions, as suggested by Alexander. Mechanisms likely to create serious episodic inequalities, and thereby motivate the invention or spread of moral god beliefs also appear in agricultural societies but take a different form. The following conflicting hypotheses were resolved in our
2SLS-IS and OLS models: neither external war (5..) nor external peace (6..) are predictors of moral gods; neither levels of jurisdictional hierarchy (2..,5..,6..) nor community size (6..) are good predictors; scarcity of water (8..) is a better predictor than food scarcity (6..); and AnimXbwealth (17..) is a far better predictor than animal husbandry (6..). The cross-cultural data support the view that scarcity of the key resource of water makes the cooperative advantages of unifying moral gods as well as beliefs in godly punishments for defectors a clear incentive for elective inventions or the adoption of moral gods. It also affects both agriculturalists and pastoralists ( SOM#8: Subsistence type and Dryness ).
Episodic crises of inequality, however, also appear to create incentives for cooperativity enhanced and potentially enforced by moral god beliefs. More generally, pastoralists with animals that are useful in trade
(camels, horses, etc..) and thus wealth-producing animals often had cyclical periods in which some groups were able to accumulate not only vast numbers of horses, camels, and other transport animals, but also wives, sons, herdsmen, affinal alliances, and armies. Origins and adoptions are common in pastoral societies largely for elective reasons or social and geographic affinities if not outright conquest or missionization.
Two key steps that enabled us to resolve conflicting hypotheses were to (a) introduce inferential statistics to identify robustly predictive variables and (b) Chamberlain and Platt’s (18..,19..) admonitions as to usefulness of not choosing between 2SLS and OLS regression methods but comparing their results to reach conclusions.
Robust 2SLS coefficients identify independent invention given that that OLS coefficients do not exceed them in significance and that spatial and other sources of nonindependence in the sample data are controlled for.
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The fact that moral gods are most strongly predicted by spatial diffusion reflects historical processes such as adoption or conquest, which are consistent with the spread of the moral-god Abrahamic world religions of
Christianity and Islam. Some adoptions are those of imperial powers that hope to gain new forms of religious unity (e.g.., Constantine Roman adoption of Christianity). Other adoptions follow from conceptually similar processes as those in pastoral societies, thought to be affected by ethical issues of inequality, e.g.., values of early Christianity or prohibitions against usury in early Islam. Although calendar time for diffusion and the introduction of missionaries also have significant effects, Snarey found that the Missionization variable has the expected positive effect on adopting moral god beliefs ( see SOM#17: Missions ), if they are not already present, but does not alter the effects of other significant variables and their Premissionization effects.
Given that regression models of any sort can be subject to overfitting, our 2SLS-IS model may be unique in that it brings out the parts of regression models that are robust to random perturbations of sample data and the parts that are unreliable. Innovations that carry over from the software prototype (28..) on which our modeling methods were built were also critical in imputing missing data across all variables and providing with 2SLS regression with the corrections for autocorrelation that are essential for efficient estimation of significance tests.
Control variables were also evaluated in identifying potential biases of missing data, the sampling biases of different measures, and establishing areas of robustness or unreliability in model estimates.
As for invention vs. adoption, after missionization, moral god beliefs spread widely without spatial clustering as in the pre-missionized societies. That is, in the missionary period, more cases of Moral gods beliefs would have appeared to be “independently invented” if we did not have a missionization effect that occurs broadly instead of in spatial patches. In the pre-missionary period, diffusion patches (measured in OLS/2SLS ratio of Logdate coefficients) occur earlier, probably due to early diffusion of world religions such as Christianity and Islam.
Problems for future investigation include whether other dependent variables for measures of high god religious beliefs are predicted by the variables in our models, for example, in one case in which, after a “new dependent variable was substituted for High Gods, much stronger results were obtained” (33..), whether an analysis of the networks of variables in our models would be suitable for causal graph modeling that incorporates rigorous analysis and correction for potential sources of bias (34..,35..,36..), whether imputation of missing data not only of independent variables (28..,6..) but of all the dependent variables in a causal graph of direct and indirect effects on moral gods would facilitate a better use of controls for missing data, and whether a sample of religions not represented by the societies in the SCCS (15..) would show ethical dilemmas similar to those of our “hidden variables,” FxCmtyWages and AnimXbwealth. Building on writing as a new variable found to be significant in the burgeoning cross-cultural literature on moral gods (33..,40..), suggested as a measure of how literacy in complex polities helps elites preserve their privileges, we found that a compound variable we call
Superjh*Writing outperformed Superjh alone, Swanson’s main variable (2..), and improved the robustness of other variables in our 2SLS-IS and OLS models.
Acknowledgments
We are indebted to Santa Fe Institute for hosting two-week working groups on this topic in September 2010 an
2011 and to Jürgen Jost and the MPI for Mathematics in the Sciences for two-week hosting working groups in
June 2011. We thank Scott White for refactoring the prior 2SLS software (28..) and adding inferential statistics,
Anthon Eff for a great deal of help with R in building on previous code (26..,6..), Ren Feng for participation in two of our working groups (SFI and MPI) and assistance to White and TA Tolga Oztan to students using these methods in class, and thank Laura Fortunato, Duran Bell, Peter Turchin, Halbert White, Judea Pearl, Simon
DeDeo and Lilyan Brudner-White for helpful commentaries.
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Main Text Outline (followed by Supplementary Online Materials)
Abstract (p.1)
Introduction and Table 1 two pages (2-4)
1. Description of the data set and relevant variables page 5
2. Comparison of Models and Results in Table 1 two pages (5-6)
3. A multiple methods approach pages 7-8
4. The conceptual connection between Animal Husbandry/Bridewealth and Fixed Communities/Wage Labor (Turchin, boom/ bust cycles, etc..) page 8-9
5. The results, strength, and weakness of multiple models (our stronger 2SLS-IS Model 2, and weaker OLS Model 1) page 9-10
6. Control Variables: Time of ethnographic observation, before and after Missionization, and measurement of missing-data imputation bias page 11
Conclusions page 12
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