Human decision-making is affected by a diversity of factors including material cost–benefit considerations, normative and cultural influences, learning and conformity with peers and external authorities (e.g. cultural, religious, political, organisational). Also important are dynamically changing personal perceptions of the situation and beliefs about actions and expectations of others as well as psychological phenomena such as cognitive dissonance and social projection. To better understand these processes, I develop a unifying modelling framework describing the joint dynamics of actions and attitudes of individuals and their beliefs about the actions and attitudes of their groupmates. I consider which norms get internalised and which factors control beliefs about others. I predict that the long-term average characteristics of groups are largely determined by a balance between material payoffs and the values promoted by the external authority. Variation around these averages largely reflects variation in individual costs and benefits mediated by individual psychological characteristics. The efforts of an external authority to change the group behaviour in a certain direction can, counter-intuitively, have an opposite effect on individual behaviour. I consider how various factors can affect differences between groups and societies in the tightness/looseness of their social norms. I show that the most important factors are social heterogeneity, societal threat, effects of authority, cultural variation in the degree of collectivism/individualism, the population size and the subsistence style. My results can be useful for achieving a better understanding of human social behaviour and historical and current social processes, and in developing more efficient policies aiming to modify social behaviour.