In 2018, one of the biggest cooperatives of autonomous workers (CAW) in Europe, strong of more than 30.000 members, started the development of a unified lexicon as an informal conceptual model of the organization. Researchers participated in this ambitious project, following an action-designresearch method. Democratic and egalitarian values are essential at CAW, but the literature on how to account for these values when developing a conceptual model is scarce. This paper argues that defining a common vocabulary, which can be a first step to building a conceptual model for an organization, is not a politically neutral activity and should be executed transparently and fairly, especially in democratic organizations such as CAW. Based on the classic literature on language and power, this contribution presents five postulates to help modelers to account for power and influence when developing conceptual models in organizations, either when trying to acquire the monopoly of legitimate naming in a field, or when sharing the power he or she possesses, having acquired such a monopoly.