This paper presents a model of influence where agents' beliefs are based on an objective reality, such as the properties of an environment. The perception of the objective reality is not direct: all agents know is that the more correct a belief, the more successful the actions that are deduced from this belief. (A pair of agents can influence each other when )Agents can influence eachother by pair when they perform a joint action. They are not only defined by individual beliefs, but also idyosynchratic confidence in their belief - this means that they are not all willing to (engage in action with) act with agents with a different belief and to be influenced by them. We show here that the distribution of confidence in the group has a huge impact on the speed and quality of collective learning and in particular that a small number of overconfident agents can prevent the whole group frow learning properly.