Standard model: Initial random assignment of vari-

i=1

∑

p²_i (5.5)

whereR corresponds to the total number of existing variants in the system (richness). D ranges from 0 (one variant dominates the cultural system completely) to 1 (all variants are equally present).

5.3 Results

5.3.1 Standard model: Initial random assignment of variants with replacement (wR)

We first considered a model in which agents were initially assigned a cul-tural variant selected from a pool of variants with replacement. Simulation

outcomes show that the co-evolutionary processes of value systems, cogni-tive biases and institutions implemented in the model tend to stabilize the diversity of the produced variants over time.

Figures 5.4 and 5.5 show the evolution of the cultural diversity of the set of produced variants at each round for a selection of representative parameter combinations of institutional power (ε), compliance bias (κ), confirmation bias (γ) and content bias (β). Figures 5.6 and 5.7 show the evolution of the diversity of institutional values over time.

In general, ε facilitates the emergence of shared cultural conventions when κ>0. This effect is amplified or minimised depending on how di-verse institutions are at each time step. When ε =1, institutions have an immense capacity to convey their values effectively to the agents. In this scenario, when institutions are less diverse, convergence on shared cultural conventions is faster and diversity reduction stronger. This can be observed when we compare results of simulations using PR, where each agent was initialised with a randomised value system, against simulations using OTA, where agents where initialised with an homogeneous and hegemonic value system. As figures 5.4 and 5.5 show, diversity of produced variants is lower under OTA, and this is due to the reinforcing role of institutions, which push diversity up (PR) or down (OTA) according to how diverse their own value systems (the ones that they convey to the society) are. In general, content bias (β) amplifies the effect of any parameter combination that al-lows the emergence of asymmetries in the dispersion of values among the set of existing cultural variants.

Interestingly, under PRand ε=1, fully conformist populations (κ=1) yield lower levels of convergence than populations with intermediate levels of κ. This result seems counterintuitive, but it is explained by the intrin-sic properties of the institution: the emergent institution in this scenario is highly diverse and also has capacity to influence the agents’ choices, resulting in a relatively high diversity of produced variants for all levels of content bias β. In other words, a compliance bias pushes diversity up when institutions are diverse, and pushes diversity down when institutions convey value systems with low diversity and strong dominance of one or few cultural variants.

Intermediate values of ε drastically reduce the formation of cultural conventions when compared to high levels of ε, and this effect increases with κ. Interestingly, a decrease inε increases diversity in both scenarios, PR and OTA, regardless of the diversity of institutional values promoted by the institution. Indeed, we can expect diverse institutions, like those that

emerge in PR, to boost diversity. But, how is it possible that institutions in OTA, which convey extremely unambiguous and hegemonic value sys-tems, also increase diversity. The answer lies in the strength with which these values, whether diverse or not, are transmitted to the population by the institutions. When ε = 0.5 and κ = 1, institutions are just partially successful conveying their values. This leads to a weaker transmission of institutional values over time (i.e. on average, the institutional value as-signed to each existing cultural variant loses value at each time step). This combined with a population of agents willing to nevertheless keep adopt-ing institutional values, ends up weakenadopt-ing agents’ value systems too. The result is a society where values fade over time, leading to a limit in which the change in the frequency of an existing variant in the population is due to random sampling of variants. However, whenε=0.5 and agents do not fully conform,κ<1, alternative options for the emergence of cultural con-ventions arise. This is the case when κ=0.5 and γ<1: In this scenario, cultural conventions can emerge from the mutual reinforcement of local interactions and institutional values. This is because as agents cease to fully conform with the social norms promoted by the institution, they be-gin to assign value to variants according to what is produced in their local interactions, which produces a stable convergence equilibria according to β. In a relatively wide range of these intermediate situations the model can be thought of as the most realistic example of most human communities, where neither are institutions fully powerful to direct the agents’ choices, nor are agents fully conformist or fully non-conformist.

When ε=0, institutions have no capacity to convey their values to the agents, so agents end up converging due to local interactions or not con-verging at all. For example, agents can attain moderately to high levels of convergence on cultural conventions without any institutional intervention when ε is 0 and γ is very high. In this scenario, agents converge due to their capacity to coordinate in their local interactions. On the other hand, a reduction in γimplies that the agents’ value systems become more volatile and less dependent on their individual experiences, resulting in a decrease in convergence.

An unusual simulated case is when agents are fully conformist, κ=1, and institutions have no power at all. In this scenario, the system tends to high diversity of produced variants because variant selection ends up being similar to a random choice among variants with null value. A model that can be thought of as a society of believers drifting around and looking for something to believe in. On the other extreme, when κ = 0 and γ = 1,

we have a society where agents do not conform at all but are fully biased towards their prior beliefs. In this case, convergence on shared conventions is dependent on the degree of initial similarity between the agents’ value systems.

γ :0 γ :0.5 γ :1 Normalized entropy (Hn)

Content bias 0 0.2 0.5 0.8 1

H_n of produced variants: wR and PR

Figure 5.4: Cultural diversity (measured as Normalised Shannon EntropyH_n) of the set of produced variants over each level ofinstitutional power (ε),compliance bias(κ), confir-mation bias(γ) andcontent bias(β). Simulations with initial random assignment of vari-ants selected fromX with replacement (wR) and initial randomised value system (PR).

γ :0 γ :0.5 γ :1 Normalized entropy (Hn)

Content bias 0 0.2 0.5 0.8 1

H_n of produced variants: wR and OTA (OTA)

Figure 5.5: Cultural diversity (measured as Normalised Shannon EntropyH_n) of the set of produced variants over each level ofinstitutional power (ε),compliance bias (κ), confir-mation bias(γ) andcontent bias(β). Simulations with initial random assignment of vari-ants selected fromX with replacement (wR) and initial randomised value system (OTA).

γ :0 γ :0.5 γ :1 Normalized entropy (Hn)

Content bias 0 0.2 0.5 0.8 1

H_n of institutional values: wR and PR

Figure 5.6: Diversity (measured as Normalised Shannon EntropyH_n) of institutional val-ues over each level ofinstitutional power (ε), compliance bias(κ),confirmation bias (γ) and content bias (β). Simulations with initial random assignment of variants selected fromX with replacement (wR) and initial randomised value system (PR).

γ :0 γ :0.5 γ :1 Normalized entropy (Hn)

Content bias 0 0.2 0.5 0.8 1

Hn of institutional values: wR and OTA (OTA)

Figure 5.7: Diversity (measured as Normalised Shannon EntropyH_n) of institutional val-ues over each level ofinstitutional power (ε), compliance bias(κ), confirmation bias(γ) and content bias (β). Simulations with initial random assignment of variants selected fromX with replacement (wR) and initial randomised value system (OTA).

5.3.2 Assumptions concerning initial variant assignment: Assignment