Human decision-making is controlled by various factors including material cost–benefit considerations, values and beliefs, social influences, cognitive factors and errors. Among social influences, those by external authorities (e.g. educational, cultural, religious, political, administrative, etc.) are particularly important owing to their potential reach and power. To better understand the effects of ‘soft’ power of authorities we develop a unifying theoretical framework integrating material, cognitive and social forces controlling the joint dynamics of individual actions and beliefs. We apply our approach to three different phenomena: evolution of food sharing in small-scale societies, participation in political protests and effects of priming social identity in behavioural experiments. For each of these applications, we show that our approach leads to different (or simpler) explanations of human behaviour than alternatives. We highlight the type of measurements which can be helpful in developing practical applications of our approach. We identify and explicitly characterise the degree of mismatch between individual actions and attitudes. We assert that the effects of external authorities, of changing beliefs and of differences between people must be studied empirically, included in mathematical models, and accounted for when developing different policies aiming to modify or sustain human behaviour.