Aim of this research is a quantitative study in the subject of International Institutions by using theory of Neo-Liberal Institutionalism. International institutions –including international organizations and regimes- are of main actors in international relations which a number of states are members of them. Changing in amount of members which can happens for various reasons, has direct effect on their performance and efficiency. Performance of each international institution evaluated based on the goals and duties which founders had in mind when they were constructed them and are mostly serving the demands of countries which cannot individually being provided. Therefore the question is: what effect has the enlargement or shrinkage of international institutions on their performance? Two reasons will be analyzed in this research to capture the mathematical model of evaluating performance; reducer of efficiency which caused by the difficulty of getting to consensus and also coordination for effective operation and the possibility of cheating, and the other one increaser of efficiency which comes from economic, natural and human resources and etc.
Quantitative studies in social science and mathematical regard to phenomenas have a long term background in the history of science. But behaviorism in politics and international relations in particular gets to its peak in the middle of 20th century. Those discussions which quantified power will be used in modeling of this research. My case study is summit of great powers (G5-G7/8-G20) which final model and equation will be evaluated by that; highest performance rate gained by G20 and lowest for G8.
But extracted model is comprehensive and can be applied for all international institutions after doing premier studies and optimizing the indicators for instance in ASEAN. Results of this study are datas which analyzer can calculate every change in number of members and its effect on performance and capability for action in an inter