Combining Conformist and Payoff Bias in Cultural Evolution : An Integrated Model for Human Decision-Making

Weak individual preferences stabilize culture

Outcomes in the cultural arena are due to many factors but are there general rules that can suggest what makes some cultural traits successful and others not? Research in cultural evolution theory distinguishes factors related to social influence (such as copying from the majority, or from certain individuals) from factors related to individual, nonsocially influenced, propensities such as evolved cognitive predispositions, or physical, biological, and environmental constraints. Here, we show, using analytical and individual-based models, that individual preferences, even when weak, determine the equilibrium point of cultural dynamics when acting together with nondirectional social influence in three out of four cases we study. The results have implications regarding the importance of keeping into account individual-level, nonsocial, factors, when studying cultural evolution, as well as regarding the interpretation of cross-cultural regularities, that must be expected, but can be product of weak directional forces, intensified by social influence.

Prestige bias in cultural evolutionary dynamics

If the traits of more successful individuals are more likely to be adopted, the resulting cultural transmission is described as success biased. In contrast, if the traits of 'prestigious' individuals-those who have already been copied many times-are more likely to be adopted, this is described as prestige-biased cultural transmission. In this case, prestige can be a convenient proxy for success. However, it is unclear how success and prestige biases interact to determine the outcome of cultural evolutionary dynamics. Here, we aim to clarify this using mathematical analysis and stochastic simulations. We find analytic approximations to the stochastic role-model choice process that facilitate the mathematical analysis and reduce the computational complexity of simulations. Approximations are given to the fixation probability and the fixation time of an invading cultural trait in different environments. Our results show that success bias effectively plays the role of natural selection, whereas prestige bias effectively plays the role of genetic drift. Prestige bias, which may be strong in highly social communities, also accelerates the evolutionary dynamics, as expected in a rich-get-richer process. These results signify a step forward in understanding how different cultural transmission biases interact.

The Cultural Evolution of Games of Chance : A Historical Investigation of Chinese Gambling

Chance-based gambling has been a recurrent cultural activity throughout history and across many diverse human societies. In this paper, I combine quantitative and qualitative data and present a cultural evolutionary framework to explain why the odds in games of chance in premodern China appeared "designed" to ensure a moderate yet favorable house advantage. This is especially intriguing since extensive research in the history of probability has shown that, prior to the development of probability theory, people had very limited understanding of the nature of random events and were generally disinclined to think mathematically about the frequency of their occurrence. I argue that games of chance in the context of gambling may have culturally evolved into their documented forms via a process of selective imitation and retention, and neither the customers nor the gambling houses understood the probability calculus involved in these games.

On random conformity bias in cultural transmission of polychotomous traits

Mathematical models of conformity and anti-conformity have commonly included a set of simplifying assumptions. For example, (1) there are m=2 cultural variants in the population, (2) naive individuals observe the cultural variants of n=3 adult "role models," and (3) individuals' levels of conformity or anti-conformity do not change over time. Three recent theoretical papers have shown that departures from each of these assumptions can produce new population dynamics. Here, we explore cases in which multiple, or all, of these assumptions are violated simultaneously: namely, in a population with m variants of a trait where conformity (or anti-conformity) occurs with respect to n role models, we study a model in which the conformity rates at each generation are random variables that are independent of the variant frequencies at that generation. For this model a class of symmetric constant equilibria exist, and it is possible that all of these equilibria are simultaneously stochastically locally stable. In such cases, the effect of initial conditions on subsequent evolutionary trajectories becomes very complicated.