Author summary The movement of groups can be heavily influenced by ‘leader’ individuals who differ from the others in some way. A major source of differences between individuals is the repeatability and consistency of their behaviour, commonly considered as their ’personality’, which can influence both their position within a group as well as their tendency to lead. However, links between personality and behaviour may also depend upon the immediate social environment of the individual; individuals who behave consistently in one way when alone may not express the same behaviour socially, when they may be conforming with the behaviour of others. Experimental evidence shows that personality differences can be eroded in social situations, but there is currently a lack of theory to identify the conditions where we would expect personality to be suppressed. Here, we develop a simple model of a small group of individuals who differ in their tendency to perform risky be