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Philos Trans R Soc Lond B Biol Sci. 2016 April 19; 371(1692): 20150154.
PMCID: PMC4822434

Evaluating reproductive decisions as discrete choices under social influence

Abstract

Discrete choice, coupled with social influence, plays a significant role in evolutionary studies of human fertility, as investigators explore how and why reproductive decisions are made. We have previously proposed that the relative magnitude of social influence can be compared against the transparency of pay-off, also known as the transparency of a decision, through a heuristic diagram that maps decision-making along two axes. The horizontal axis represents the degree to which an agent makes a decision individually versus one that is socially influenced, and the vertical axis represents the degree to which there is transparency in the pay-offs and risks associated with the decision the agent makes. Having previously parametrized the functions that underlie the diagram, we detail here how our estimation methods can be applied to real-world datasets concerning sexual health and contraception.

Keywords: Bangladesh, contraception, discrete choice, fertility, sexual health, social influence

1. Introduction

Evolutionary theory is becoming more prominent in studies of changing fertility [1], especially those that examine changes in fertility norms over historical time-scales [2]. Central to most theories of the demographic transition—a decline in human fertility and mortality in a society [3]—is individual choice, often structured with the assumptions of rational choice theory [4], including the trade-off between quality and quantity of children [5]. This is broadly consistent with human behavioural ecology, in which fertility (and other) decisions are viewed as being motivated by proximate goals, which are ultimately driven by an intrinsic utility function that accounts for energy balance, environmental resources and mortality risk of the socio-ecological environment [6]. This perspective likewise is consistent with a positive correlation between fertility and wealth, and a negative correlation between fertility and child-rearing costs [7].

Shenk et al. [8] describe three models that apply within this framework, one of which, the cultural-transmission model, is our primary focus here. It assumes that people make health decisions based on their knowledge of risks, costs and benefits, but also that it matters how they learn about these factors. For much of human prehistory, social learning within smaller communities was strategically directed towards familiar experts or best-informed members. In these long-term contexts, the benefits of social learning and friendship are substantial enough to have been a factor in human evolution [911]. In a typical collective-action problem, such as changing fertility norms, the transparency about what others are doing is essential [12]. Conversely, secrecy reduces transparency in the sense that it adds ‘noise’ (e.g. [13]), the effect that we later quantify as μ.

Broadly consistent with these underlying principles, community medicine often emphasizes two drivers of behavioural change—information and supply—although in some models (e.g. [14]) those variables are seen as insufficient to change behaviour without the addition of social influence [15]. For example, in Poland, poor uneducated women living in a wealthy educated group tend to adopt the low-fertility level of the group rather than the higher fertility that otherwise would be associated with their low income and low education as individuals [16].

In characterizing a case study in terms of information, supply and social influence, we might use population-scale data to estimate the relative magnitude of socially influenced learning versus individual learning. We might focus on the function of heterogeneity in how people make decisions, particularly the balance of individual learning, which produces information, and social learning, which diffuses and exploits that information [10,17,18]. All too often, however, observational data alone fail to distinguish not only between social learning and individual learning, but also between social learning and homophily—the tendency for people with similar traits to co-associate [19,20]. Sorting this out may require explicit temporal ordering of socially influenced events in observational data [21,22].

There is another important dimension in addition to the continuum between individual learning and social learning: the transparency of pay-off (and risk) of a particular decision. Transparency, sometimes referred to as the intensity of choice, can have an explicit social dimension in terms of how information spreads—from one to many or from many to many—and the rate at which it spreads. With respect to the successful and decades-long family-planning programme in Matlab, Bangladesh, Phillips et al. [23] attributed the success of the 1978 programme to the training of community health workers, in contrast to the less successful 1975 programme. Simmons et al. [24, p. 32], for example, observed a community health worker in a Matlab household easing the fears of a woman concerning a tubectomy by pointing towards a nearby house and saying, ‘All of them had the operation. I took them for the operation. Did any of them get pregnant? Did you hear it?’ This reveals both expertise and direct social influence concerning an important decision for the woman. Because the inherent decision was an intense one—a frightening surgical operation resulting in permanent sterility—the transparency of social influence arguably needed to be high as well.

2. A model of decision-making

These principal components motivated us to consider social influence versus transparency of choice as two continuous, intersecting dimensions of decision-making (figure 1), one that captures how transparent a decision is in terms of benefits and risks (vertical axis) and the other how socially influenced the decision is (horizontal axis). We have proposed that this modelling framework can be used to extract, from popularity statistics, estimates of social learning and the transparency of decisions at a population scale [25,26]. If we think of the diagram as a map, at its extreme corners are rational choice at the northwest, well-informed social learning at the northeast, indiscriminate copying at the southeast and isolated guesswork at the southwest.

Figure 1.
A diagram depicting domains of human decision-making, based on a continuum from individual learning to social learning on the horizontal axis (J) and the transparency of pay-offs informing a decision (intensity of choice) on the vertical axis (b). After ...

This decision map, while aimed at sociological or anthropological phenomena, has a sound biological basis in the study of social animals. A study of GPS-tracked wild olive baboons in Kenya [27], for example, reduced decision-making (primarily about where to go) to two dimensions similar to our map: directional agreement and number of initiators. We might say directional agreement, which is lowest when individuals move in opposing directions and highest when all individuals move together, is analogous to transparency. Number of imitators would then be analogous to social influence in our model, in which the social pay-off is proportional to the product of the social-learning parameter and the difference in popularity between the two choices (electronic supplementary material, appendix). As shown in figure 2, we see a correspondence between Strandburg-Peshkin et al.'s [27] directional agreement and our transparency and between their number of initiators and our strength of social influence. Both approaches find the highest predictability of following in the northeast corner, where leadership is transparent [28]. Less intuitively, when low on the vertical axis, increasing social influence (moving eastward) may actually decrease the predictability of followers (figure 2). In colloquial terms, if social transparency is low, adding more leaders may lead to the proverbial ‘too many cooks spoiling the broth’.

Figure 2.
A comparison between a plot for understanding the group movement among social animals and the outcome of the decision heuristic in figure 1. (a) Field data among wild baboons [27] showing directional agreement among initiators of movement on the ...

(a) The map quadrants

Let us see how the map works with respect to fertility. In the northwest, the pay-offs of having a certain number of children are transparent to a mother, and social influence is minimal. To put it another way, the northwest quadrant is where the net benefits of having n children (as n varies) are clearly understood, and both local and global sources of social influence have little influence on fertility choices. Costs of giving birth to another child include the physical demands for giving birth, such as adequate body fat, nutrition and energy [29]. This type of cost should be quite transparent to the mother. Also in the northwest are decisions influenced by the net benefits governed by many of the economic realities of giving birth [29]. If children are net assets in terms of labour (agricultural work, for example), then fertility will be high, but as children require increased parental investment (in education, for example), then fertility will be lower. This is why, broadly speaking, fertility declines as wealth increases. Inside this broad trend across populations, however, are subpopulations within which the correlation is positive between wealth and fertility but on a smaller scale. This too is modelled after individual pay-offs to fertility, in the simple economic reality that wealth enables a mother to have more children [30].

The northeast quadrant contains fertility outcomes that are maintained by transparent social influence and governed by norms of kinship, religion, gender roles and community expectations. Transparent social influence might come from an acknowledged village expert in a particular category [31], whereas less-intense influence might diffuse among passive members of village social networks, who might not necessarily adopt the behaviour themselves [32]. Among over 20 high-fertility communities in rural Poland, for example, Colleran et al. [16] found that the low-fertility norms of educated women were learned socially by lesser educated women within the same social networks who were using the more-educated women as models.

The two quadrants in the southern half of the map are less well explored in terms of fertility. In wealthy urban media-saturated societies, however, these quadrants seem increasingly relevant. A potential mother in the modern West, for example, might read news stories that debate the benefits of breastfeeding versus bottle feeding. She may see vigorous debates in the popular media contesting the ‘joys’ of having children versus the ‘pains’ of raising a child—she might, for example, see bumper stickers on expensive cars that say ‘DINK’ (dual-income, no kids). This bombardment by the media about the costs and benefits of having children might cause enough confusion that transparency is reduced about the net benefits of having n children as n varies.

Homophily might have an influence on the level of transparency in decision-making. Homophily is clearly a reality as parents often socialize with other parents, either through shared membership in schools and clubs or simply so that their children can play together. Similarly, non-parents often seek each other out and steer clear of people who have annoying children. All these social effects have ambiguous transparency: is fertility simply a matter of the fertility of those around you? If so, how accurately does it track ambient fertility? Can fertility be subject to fashion, at least within broader economic constraints (e.g. having one child instead of two)? These are issues that reside in the southeast quadrant.

In the southwest quadrant, fertility is not transparent in terms of individual pay-offs or social norms. This is probably uncommon because fertility is so strongly directed by physiological, economic and social influences. The expectations of this quadrant, however, can serve as a benchmark to test whether the individual pay-offs of fertility may be becoming less transparent, or, equivalently, ‘noisier’. As a thought experiment, what if a mother decides to have just one child in order to invest more in the child's education, but by the time the child is of college age most people are receiving free, online degrees? Could she have had three children instead, to better the chances that free education would make at least one of her children wealthy? The fact that this is not a totally far-fetched scenario in itself shows that calculating the economic costs and benefits of children may be becoming less transparent.

(b) Generalized data patterns

Bentley et al. [25,33] describe generalized data patterns that help to locate a phenomenon on the map in figure 1, given time-series data on the relative popularities of different options. The aim is to extract as much information as possible from patterns, such as the distribution of popularity for a single time phase, or ranked popularity lists and/or time series in the popularity of each option over a number of successive time phases. Consider, for example, the effect of a targeted intervention in the past decade by the UK National Health Service (NHS). In 2003, the NHS instigated a campaign to promote more sexual-health screenings in an effort to reduce the incidence of sexually transmitted infections (STIs). The programme was successful, increasing the number of screenings from about 17 000 in the first year to over 340 000 in year 5 [34]. The NHS strategy was to increase information through a dedicated website, advertising and outreach, and to direct participants to particular options, including community contraceptive services, general practice and educational settings. In addition, it promoted various private means of performing tests individually, such as using personal testing kits one could purchase at the pharmacy or through the mail. The NHS had 24 different types of offerings by 2008 [34].

One question we might ask is how the decision environment of sexual-health screenings (at the regional or national scale) moved around on the map as the health department increased the amount of information, number of options and overall participation. Social influence may or may not have increased with more participation, and decisions may have become (i) more transparent as the NHS communicated cost/benefit information about screenings, or (ii) less transparent with the increase in options (and associated experts). Ideally, we would like to have popularity data on each option over the course of the programme, at finely resolved time intervals [25,33], such as monthly or quarterly data on the number of STI tests done, for each of the half-dozen options, over a decade and subdivided by gender, county, ethnicity and the like. In reality, the data available in this case include the popularity of the different choices, by gender, for two time periods: one at the start of the programme in 2003 and another for the end of the first phase of the programme in 2007–2008 [34]. Another dataset offered by the NHS presents quarterly statistics on the popularity of each option but for only 2 years (2012 and 2013) and without data on the frequencies of less popular options, which are subsumed under the category ‘other’.

Consider the two distributions of choice popularity shown in figure 3, one from 2003–2004 and the other from 2007–2008. The number of options listed in the data tables [34] was 10 in 2003–2004 and increased to 14 in 2007–2008. Even with these numbers, we can find that the distribution was probably lognormal, which is a type of long-tailed probability-distribution function that we expect in the eastern part of the map, where social influence contributes to the multiplicative growth, or proportional advantage, in the popularity of choices. Here is a simple model that generates a lognormal distribution at each date t as well as a limiting distribution that is lognormal with finite mean and variance. Assume the popularity, nt, of a choice at time t is given by the stochastic process An external file that holds a picture, illustration, etc.
Object name is rstb20150154-i1.jpg where the process {et} is independently and identically distributed normally with mean zero and variance unity. It follows by taking logs that ln(nt) conditional on nt−1 is normally distributed, with mean g0 and variance σ2. The stationary distribution of log(n(t)) is normal, with a finite mean and variance.

Figure 3.
Distributions of choice popularity for 2003–2004 (a) and 2007–2008 (b). Data shown for females in red and males in blue. The number of options listed in the data tables [34] was 10 in 2003–2004 and increased to 14 in 2007–2008. ...

So far, this would place the phenomenon in the eastern part of the map. Figure 3 shows that the peak of the lognormal distribution did not change much between 2003–2004 and 2007–2008, except that the distribution became narrower for the decisions of both women and men. This implies that the variance in the rate of multiplicative growth, σ, became smaller. If that variance were correlated with transparency of social learning—a doctor's recommendation carries more weight than an advertisement by a pharmacy—we could hypothesize that transparency actually increased between 2003 and 2008, despite the increase in number of options. Note also that the peak occurs at a higher popularity value among men's choices.

With this hypothesis in mind, we can turn to a second set of information, consisting of time-series data on the popularity of options in 2012 and 2013 [35]. These data have quarterly resolution, but unfortunately, frequencies of the least-popular options are subsumed under ‘other’. Nevertheless, we gain an additional, complementary insight by looking at these timelines (figure 4). As we proposed previously [25], generally the farther south on the map one goes, the noisier and less predictable the time series are for the different options, with flat, parallel time series generally indicating high transparency, except when a discovery is made and adopted. From the 2012–2013 UK screening data, we can see that the timelines from different regions are generally very smooth and parallel, but with some regions (e.g. Avon, Gloucester and Wiltshire) more so than others (e.g. North East). In the North East, choices were much more volatile than in the other regions—a pattern that needs to be explained through further work. Figure 4b illustrates the effect of the supply of a new health service (a discovery) in Cumbria and Lancashire in late 2013. There, contraception and sexual-health services almost overnight became the most popular options.

Figure 4.
Representative timelines for the popularity of different STI screening options in the UK for each quarter of the years 2012 and 2013 [35]. The publicly available data are specifically the numbers of chlamydia tests for 15–24 year olds, grouped ...

3. Parametrizing the map

In anticipation of future applications that use much larger datasets, we parametrized the vertical axis of the map as b (or bt if it changes through time), which represents the transparency of decision pay-offs, from absolutely transparent along the upper edge (bt = ∞) to completely opaque at the lower edge (bt = 0). The learning dimension—the horizontal axis—is parametrized by Jt, which represents the continuum from decisions made individually at the far left edge (Jt = 0) to pure social decision-making, or copying, at the far right edge (Jt = ∞).

Our approach is derived from the discrete choice random-utility model,

equation image
3.1

where the random variables An external file that holds a picture, illustration, etc.
Object name is rstb20150154-i2.jpg are independently and identically distributed with an extreme-value distribution [36]. Here, the parameter μ in equation (3.1) scales the amount of noise in choice making. If μ = 0, the decision-maker just chooses with probability unity the choice k*, where An external file that holds a picture, illustration, etc.
Object name is rstb20150154-i3.jpg is the largest. Our intensity-of-choice parameter, b, is proportional to 1/μ. If b = 0, i.e. μ = ∞, each choice k is made with probability 1/N. We define an increase in transparency as an increase in the parameter b. Any context in which b increases, i.e. reduces μ, is an increase in transparency for us. There are many different reasons why μ decreases (or increases) when a group of decision-makers are making a choice over N alternatives. If transparency becomes very small, then μ becomes very large, and the contribution of the intrinsic utilities, Uk, of the different options becomes negligible. For example, increasing easily available information about the benefits and costs of different contraceptive methods should increase b, i.e. decrease μ. At the same time, if transparency is small, a large degree of social influence, J, and/or conformity of practice (high pk for the consensus choice k) could offset the effects of the noise component, An external file that holds a picture, illustration, etc.
Object name is rstb20150154-i4.jpg This gives the model scope to account for cases where human social learning occurs over many generations with no explicit understanding of problems (e.g. [37]).

In resolving both axes together, the map calls for traditional and novel forms of time-series analysis of the form and temporal dynamics of popularity distributions. In the electronic supplementary material, appendix, we describe the details of the multinomial logit framework for the general case of N choices, in which k = 1, 2, … , N indexes the N different choices and Uk is the inherent utility of choice k. We have defined the map space analytically as functions of observable covariates and estimated parameters [26,36]. In expressing probability, Pk, of choice k (versus choice probability, P1), we parametrize b and J in terms of observable variables:

equation image
3.2

Here, i, g, t, denote a person or subgroup of group g at date t. The quantity [var phi]1(xikgtxi1gt) represents the difference in the personal component of pay-off of the individual choice k over choice 1, excluding the social component of pay-off, which is the second term in (3.2).

The key to applying this framework to a real-world case study is the proposal that the covariate vectors x, y, z represent observable quantities that can be constructed from data [36]. If we index the covariates by agent i, group g and time t, then the covariates for each agent can include those that predict the propensity of the behaviour, denoted by xitg, those associated with the presence of social influence, yitg, and those that relate how variable the choices were through time, zitg. Parameter vectors θ, [var phi]1 and [var phi]2 operate on covariates denoted by vectors x, y and z, respectively. Parameter vector [var phi]1 represents an individual's sensitivity to differences in choice, acting on the pay-off difference between options, and parameter vector [var phi]2 represents the transparency of social influence, which acts on the popularity of the option. Estimating the parameter vector [var phi]1 determines the individual sensitivity to differences in choice (xkx1).

In studies of fertility choice, as discussed in §2a, the social-choice transparency, [var phi]2, could reflect the tendency to have the same number of children as other mothers whose success and/or education has become more socially visible. In this formulation of equation (3.2), social learning is part of the pay-off, which corresponds to the fitness of the chosen behaviour. On a fitness landscape, a group might be on a local peak but not necessarily the globally optimal peak among multiple equilibria. In our parametrized map above, there can be a unique set of optima for each pair of b and J, each number of options N and each set of intrinsic utility values U. For a binary decision, such as whether or not to have a child, we would define N = 2, but for other decisions, such as which form of contraception to use (potentially including none), we would have N > 2 (e.g. pill, IUD, condom, surgery and so on). Because the social part of the fitness function depends on the relative popularity of each choice taken, the fitness landscape becomes more rugged moving to the right (figure 1) as the sensitivity to social influence, J, increases. We describe this in more detail in the electronic supplementary material, appendix. It actually becomes difficult to define the fitness landscape for multiple different options, even for N > 3 options [28].

4. Methods of estimating coordinates on b and J

In order to estimate coordinates on the dimensions b and J, we can use nonlinear least squares and the parametrization above (§3) through a log-odds regression [26]. As described in the electronic supplementary material, appendix, we can estimate bitg = b(θ, zitg) as well as the other parameters of the choice dynamics once we have adequate time-series data on a vector of covariates, xitg, and have parametrized the transparency-of-choice function, bitg = b(θ, zitg). Estimating the parameter vector [var phi]2 empirically determines the social influence function, J(.). Brock et al. [26] generated artificial data to see how these estimates can be used to describe a path through the map for each agent i in each group g for which we have data at date t. For example, data for a binary choice (N = 2) might have [var phi]2 = 1, [var phi]1 = 1 and θ = 5, with group size G = 100 and M = 100 agents per group. In figure 5, the red dots are simulated data, and the blue squares are our estimates. We can see that the largest discrepancies are in the vertical dimension, which is why we aim to improve the estimation of transparency of choice.

Figure 5.
Diagram comparing nonlinear least-squares estimates (blue squares) against simulations (red dots) of the model defined by the electronic supplementary material, appendix equations A4 and A5. After [24]. The simulations (red dots) used two choices, and ...

Having demonstrated its potential for simulated data, our objective is to apply the diagram to population-scale data on fertility choices and/or contraception use, sampled frequently (e.g. monthly) over a period of many years. A good dataset to which we could apply our framework is the 33-year record (1977–2010) of contraceptive choices in Matlab, an exceptional long-term dataset on about 250 000 people, comprising information collected since 1977 in a region where many health and family-planning interventions have been made [8,24,38]. The available data are records of decisions, together with associated (anonymous) details of the individuals making those decisions, including total fertility, surviving children, age at marriage, household income, education and media exposure. Additionally, Shenk et al. [8] surveyed 944 women from two areas, in three adult age categories, with recorded variables similar to those above.

The Matlab data were recorded fortnightly, so T in this case would be of the order of 850. There were 80 different catchments of community health workers, so G = 80. We can approximate the number of people per village, M, at about 1200 initially in 1977, when the Matlab area included 180 000 people in 149 villages [39]. Among the five main options for contraception, we might initially rank the inherent pay-off, x, hypothetically as tubectomy < injection < IUD < pill < condom. In other words, tubectomy has a higher cost/benefit ratio than asking a partner to use a condom. In terms of social visibility, y, the ranking could be considerably different and probably more variable through time, depending on region-wide conversations that take place and even potentially on individual preferences of the individual community health workers.

What we need to determine from the data for the example of having k children (for different k > 0) compared to none are (i) the covariates x that influence the individual component of the difference in pay-off from having k children to having no children, (ii) the covariates y that influence the social component of pay-off from having k children to having none, and (iii) the covariates z that influence the function, b(.), which governs the precision of choice between k children and none. These covariates might be derived from statistics such as total fertility, religion, surviving children, age at marriage, household income or education, as in the data used by Shenk et al. [8].

Datasets such as the Matlab data may be rich enough to estimate our model framework. The vector of parameters representing a person's sensitivity to inherent pay-off, [var phi]1 in the term [var phi]1(xikgtxi1gt), could potentially be estimated using covariates such as a wife's education, a husband's primary occupation, family land ownership and whether a family is engaged in agriculture [8]. In this case, [var phi]1 would be a four-dimensional vector with one parameter to be estimated for each covariate. In order to attempt to separate social influences from the endogenous social effects that have a social multiplier [40], we could add a term An external file that holds a picture, illustration, etc.
Object name is rstb20150154-i5.jpg where An external file that holds a picture, illustration, etc.
Object name is rstb20150154-i6.jpg denotes the averages of relevant covariates over the relevant reference group, g.

If the bari—a patrilineal group often consisting of two to six houses arranged around a courtyard [41], though frequently larger in more densely settled villages—is too small for use in calculating an average measure, the next largest reference group, for example, the village, would be the best choice. We expect the strength of social interactions to be strongest at the bari level and somewhat weaker at the village level. Based on the work of Shenk et al. [8], child deaths in each bari or village, infant mortality rate and the number of women in each health worker's intervention area appear to be reasonable candidates for contextual variables.

The vector of parameters [var phi]2 might be estimated for well-chosen specifications of the function J([var phi]2, yigt) for a vector of covariates such as average number of children born to women in the same reference group as person or subgroup i of that reference group. As already mentioned, however, it is difficult to prove social influence from the data, as opposed to contextual effects [40] and/or selection biases sorting unobservable covariates that influence fertility. It usually is the convention in empirical work using discrete-choice models [42] to normalize the intensity-of-choice function b(.) to a constant, i.e. unity. Brock et al. [26] discuss how one might estimate b(.) up to scale by using data over time, but they also show through simulation that it is more difficult to estimate b(.) with as much precision as other parameters such as [var phi]1, [var phi]2.

One possible approach to estimating the intensity-of-choice function is to normalize b(.) to unity for a first time segment of the data (t = 1) and to estimate the parameters [var phi]1, θ, [var phi]2 for that time segment. Then, estimate those same three parameters of b for each subsequent segment. If the estimates scale approximately proportional to those parameters at t = 1, then we have a means of estimating change in b(.) over time as a simple function of those parameters. If there are approximate scale factors An external file that holds a picture, illustration, etc.
Object name is rstb20150154-i7.jpg they could serve as estimates of the function b(.). Even with ideal data available, attempting to extract approximate proportional scale factors may often be the best way to estimate b(.) [26].

5. Conclusion

What contribution does our model bring to the table? Other models (e.g. [43]) allow for errors in pay-off estimation—our transparency dimension—but usually with no social influence. A few models, although they consider social influence (e.g. [44]), do not explicitly consider the econometric problem of identifying and estimating the strength of endogenous social interactions [36,45,46]. In addition, they do not employ elements of discrete-choice econometrics [47], nor, with two exceptions [26,42], do they estimate the intensity-of-choice (transparency) function, b(.), using observational data.

Our contribution here is combining the tools for these estimations and suggesting how to apply the tools to fertility-related choices. The toolbox is valuable because endogenous social interactions possess a ‘social multiplier’, which can be exploited to promote desired target behaviour by policy (e.g. a lowering of fertility or increased adoption of pit toilets, birth-control methods and the like). Estimating these models without correction for group-selection effects, correlated effects, correlated unobservables and general contextual effects easily leads to spurious findings of endogenous social interactions [36,40,46]. This problem occurs in the presence of many other social influences that do not possess a social multiplier [40,45].

Our framework was designed specifically to estimate social influence and transparency of choice from aggregated, anonymous decision data, even when we lack survey data about the motivations of individual decision-makers. The next step will be to apply our parametrized model to real data, such as the contraception and fertility data from Matlab, potentially to map a trajectory in terms of the parameters bt and Jt and determine how they change through time. Recall that each time-dependent variable is a vector, or list, not just a value. The variable x is a list of covariates that determine differences in pay-off to different choices; the variable y is a list of covariates that one thinks will play a role in pay-offs to social visibility; and the variable z is a list of covariates that one thinks will play a role in the precision of choice making over time.

In contrast to ancient contexts, major challenges today, such as global health, inequality and environmental change, are not transparent to many people either socially or factually. Often people make decisions based on emotions or hearsay. If our null hypothesis is to assume that individuals make decisions with clarity of pay-offs interpreted through an evolved psychological utility function, then departures from that null should include decisions made without clarity of pay-off or through social influence, which may underlie substantial intercommunity variation in social norms and perceived costs and benefits [48]. Classic studies of social conformity [49], as well as more recent experiments [50,51], confirm that social interaction can substantially undermine the independence of the judgements of participants. Conversely, although individual ‘rational’ learners may be in the minority, certain studies indicate that if their decisions are consistent or intense, they will guide a majority of social learners to a common goal [5254].

As decisions are increasingly mediated by online technologies [55], our framework may help with questions about change in the magnitude of social influence and the transparency (intensity) of its effect. In an age deluged by information, options and influences, transparency of social learning becomes a vital issue. More research is needed to characterize the strength of potential causal pathways over time and to document the potential importance of social influences on fertility behaviour. Endogenous social interactions are of special interest because the potential social multiplier effect can be exploited by policy to induce a ripple effect on fertility behaviour across communities. We believe the map shown in figure 1 is a useful organizing framework once it is operationalized within a precise statistical framework.

Supplementary Material

Supplementary material:

Acknowledgements

We are grateful to Mary K. Shenk and two anonymous reviewers for helpful comments on earlier versions of the manuscript.

Authors' contributions

R.A.B., W.A.B. and C.C.S.C performed the analysis. R.A.B., W.A.B., C.C.S.C. and M.J.O wrote the article.

Competing interests

We have no competing interests.

Funding

We received no funding for this study.

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