Choice of the model

We think that our approach to model the evolution of social learning is more appropriate to meet the goal of modeling non-cumulative culture than previous approaches. In previous approaches, it was often assumed that an environmental state is characterized by one choice being correct and the other(s) wrong. The image that is often invoked was that of a mushroom that could be poisonous or not [90, 100, 101]. The state would, however, reverse from time to time. But imagine that we had a social learner who copies the choice of others. If she sees others eating the mushroom, she will also give it a try. If we are in the environmental state where the mushroom is poisonous, clearly, she will become sick. Nevertheless, according to previous models, she will continue to eat the mushroom and pass this behavior on to following generations. Only when an individual learner appears who comes up with the idea of not eating the poisonous mushroom will social learners

who copy this individual stop eating the mushroom. This whole description seems totally unrealistic. The problem is that if outcomes allow the learner to clearly distinguish between good and bad, as in the mushroom example, learning is trivial and there is nothing worth modeling.

One has to think of other situations where the outcomes are not of the all-or-nothing type. Perhaps the mushroom example could be modified so that the mushroom either has a slightly positive or slightly negative energy balance. Then the bad outcome is not so obviously bad. But this does not resolve the implausibility. The difference has to be detectable – if it were not, individual learners could not learn it. The social learner, after having copied a choice, should thus also be able to detect the difference and adopt the best behavior afterwards. There is no specific reason why the social learner should ignore her private information (except if one assumes that social learners totally lost their ability to learn individually). So we still cannot find a plausible application of this model assumption to the real world.

What would happen if the outcomes of the choice options were noisy?

That is, although one option is at least temporarily better than the other, for each individual, the outcomes vary so much that the probability dis-tributions of the two options overlap. Then, if a social learner chooses A and receives a worse outcome than her choice of B yielded, she can still reasonably choose A if her social information indicates that A is better (as e.g. in models of informational cascades [10, 16]). She thus ignores her personal information because it could be faulty. This, for us, is the most plausible scenario that would allow social learning strategies to evolve. As indicated earlier, examples that would fit this description include foraging, clothing styles, manners, consumption decisions, or the choice of interaction partners.

A more detailed example may help illustrate what situations our model captures. Imagine a teenager who wants to inquire whether wearing yellow shirts increases his attractiveness. If he wears a yellow shirt and encounters the target group, he receives feedback that allows him to infer his perceived attractiveness. This feedback, however, is noisy; another target group may respond differently, and there may not be sufficiently many opportunities to reduce the variance to a reasonable level, especially since fashions change.

Therefore, this teenager may instead opt to wear shirts of the color that his peers most frequently wear or that a person he admires often wears. Such situations can be captured well by our model. One might object that since there are so many different shirt colors, a binary choice task is too simplistic.

However, humans often search sequentially (e.g. [29]), so that our teenager might first test yellow against blue, then the (supposedly) better of the two against red, etc.

Another example that is probably closer to the life of a scientist might be whether publishing in journal X will lead to more citations. Imagine a

scientist who has published an article in X with the result that few people read and cited this article. She concludes that it does not pay to submit to X. But maybe, this failure was due to other factors such as the particular topic not being fashionable at that time. If other people did have success with publishing in journal X, as suggested for instance by a high impact factor, the scientist may be best off ignoring her own experience and should continue submitting to X. (But perhaps even scientists can relate more to the former example.)

We also think that it is important that models of gene-culture coevolution allow for multiple decisions per lifetime. Having to make more than just one choice gives rise to intergenerational dynamics of decisions. It could thus happen that at the beginning, A is better than B, followed by periods of about equal payoffs from both choices, and ending with B being better than A. The choice of the individuals could or could not reflect this pattern, depending on how the individuals learn. Such dynamics cannot be studied if there is only one decision per generation.

Having more than one decision per lifetime also allows us to model the learning process itself in a more realistic fashion. Previously, it was assumed that individual learning consists of paying an exogenous costs to receive the information which of the choices is better, sometimes allowing for the possi-bility of a fixed error rate. Phenomena, such as that even individual learners do not immediately notice sudden changes, cannot be captured by simplistic models. However, if there are several trials and errors per lifetime, a more realistic learning mechanism can be implemented, e.g. learning strategies such as reinforcement learning [97]. As a byproduct, there is no more need for exogenous costs of individual learning; the cost of individual learning is the opportunity cost of not using social learning.

Dropping exogenous learning costs has the additional advantage of al-lowing us to drop two otherwise crucial parameters – the cost of learning individually and the cost of learning socially. First of all, the values of those costs are hard to measure. Moreover, our results do not rely anymore on the assumption that individual learning is more costly than social learning.

Social learning requires a sophisticated cognitive apparatus and it requires time to follow others around to observe them. Individual learning, however, relies on a system that is already there and probably optimized by evolu-tion. One can at least doubt the assumption that social learning is under all circumstances the cheaper way of learning. Our choice to exclude exogenous learning costs should, however, not be interpreted to mean that we believe there to be no costs of learning. We just believe it is best to leave this question open until more is known.

Interestingly, figure 1.15 reveals that as long as conformists are not too frequent, increases in their frequency actually improve their performance – there is positive frequency-dependent selection. This contrasts with the usual findings (figure 1.3) that social learners perform worse the more social

learners there are. Consequently, we think that in our model’s framework, it is inappropriate to think of individual learners as “information producers”

and social learners as “information scroungers” or free-riders [69, 70, 101].

This terminology implies that social learners do not contribute to the infor-mation pool used by the population, which is contradicted by the transiently positive frequency-dependence.

Our model shows that for certain frequencies, social learners make more accurate decisions than individual learners. Their advantage stems from the performance boost and not from saving the cost of learning individually, which are non-existent in our model. Therefore, at least hypothetically, there can be an equilibrium involving social learning which leads to more accurate decision making. The adaptedness of culture would not simply stem from saving the costs of learning individually but also from increasing overall performance.