Fig. 7: An illustration of gross synergy and synergy contributions from individual countries.

a a general illustration of G7’s changes in SDG indicators. For a specific SDG indicator, the change of each country can be either positive (matching the expected direction of this SDG indicator) or negative (moving towards the opposite direction of the SDG indicator). The space is split into two parts to represent both positive and negative changes from member countries. The change of each country can be represented by an arrowed line with the arrow pointing towards one of the two spaces to represent either a positive or negative change. The magnitude of the change can be represented by the length of the line. b: an illustrative example for the SDG indicator for GDP growth. The expected direction of GDP growth is to “increase GDP”, therefore all member countries are hoping to make changes towards to the space of GDP increase. In this example, four countries (including Canada, France, UK, and US) manifest positive changes (i.e., increases in GDP) while the remaining three countries (including Japan, Italy, and Germany) show negative changes (i.e., decreases in GDP). The gross synergy for the G7 countries is positive, indicating that the majority of member countries (i.e., Canada, France, UK, and the US) are moving towards the expected direction (i.e., GDP growth), and thus these countries are contributing positively to the gross synergy. However, the magnitude of synergy is small because some member countries (i.e., Japan, Italy, and Germany) are moving in the opposite direction and they are contributing negatively to the gross synergy. Therefore, the policy implication here is that the countries with negative contributions should adjust their policies to increase collaboration with other member countries in order to achieve the goal for GDP growth. Note that the numeric values displayed in the example are not true data and only for illustrative purposes. The detailed contributions from individual countries can be calculated with Eq. (11), which also requires the calculation of foreign changes by Eq. (4).