Quantifying the degree of democracy in the decision-making process of a group is an important problem in political science, organizational studies and social decision making. Existing democracy indices are primarily intended for evaluating countries or institutions and are not designed to measure the level of democratic participation within an individual group. In this work, a simple mathematical model is proposed to quantify the degree of democracy based on the participation indices of group members. An empirical expression is introduced for the distribution of participation levels, from which analytical expressions are derived for the democracy index and the percentage of fully participating members. The proposed model requires only one empirical parameter and is computationally simple to implement. The calculated results show that both the democracy index and the percentage of fully participating members increase monotonically with the model parameter, consistent with the intuitive expectation that greater participation corresponds to a higher degree of democracy. Although the present formulation is preliminary and the adopted participation distribution has certain limitations, the proposed framework provides a simple quantitative basis for analyzing and comparing the democratic nature of decision-making processes in different groups and organizations.