Abstract. Enlargement of the European Union has led to much discussion on the need to reform institutions so that the various inequalities between the member states to be removed. Such Treaties of Nice and Lisbon do not grant to citizens of member the same influence in the decision-making in the Council of Ministers. One of the solutions proposed to remedy this problem is to establish a voting scheme that gives each country a share of votes proportional to the square root of the population and determining the optimum of a threshold, known as the Jagiellonian Compromise. Starting from the analysis of Penrose square root law in the decision-making Council of Ministers, the article presents a case study on the influence of approximation by rounding the share of votes on the coalition’s formation in the case of Romania.

Keywords: Council of Ministers; decision-making processes; Jagiellonian Compromise; coalition’s formation.