We Put the “UN” in FUN: The Mathematical Guide to Saving the World
Authors: Elizabeth Cutting  , Madison Jones  , Erick White  
Published: May 2024

Imagine a world without hunger, without poverty, with equality and education. Could this ever truly be a worldwide possibility? While some of these goals may appear distant, the United Nations (UN), with their Sustainable Development Goals (SDGs), aims to create change across seventeen different categories by 2030. These goals focus on various contemporary challenges that can improve the quality of life for people across the globe. However, with such a broad range of topics and the short time frame, it becomes necessary to prioritize some goals over others in order to have the greatest chance of success and impact.
In searching for a method to prioritize a subsection of the seventeen different goals, our team used a weighted graph model with nodes and edges as a method to represent some set of elements and relationships between them. For our model, we constructed a network of connections with each node representing one of the SDGs. The edges between the nodes are weighted, representing the positive or negative impact correlation between two goals. Each node is connected to every other node in the graph. To determine the proper weighting between each node, we analyzed data from a 2017 study which utilized Spearman’s correlation ranking to determine interactions between different goals [Pradhan et al., 2017]. Another popular metric for measuring correlation between SDGs is the 7-point scale, where correlations are ranked from -3 to +3, where -3 represents the most negative correlation and +3 represents the most positive (Pradhan et al., 2017). However, there are no current global values measured with this scale, so we combined both approaches to scale the Spearman's correlation rankings and the 7-point scale to create our scale, which ranges from -1 to +1.
As a metric to model the synergy between the SDGs, we used an achievement score, a value between 0 and 1, where 1 indicates complete achievement and 0 indicates no progress. The achievement scores can be propagated through the network as a function of the weights and distance from the parent vertex. Using our model, we experimented with various connection weights and initial achievement values to determine the most interconnected and most influential goals. From this analysis, we determined that SDG 1: No Poverty holds the highest positive priority, while SDG 12: Responsible Consumption and Production holds the greatest negative priority. This indicates that SDG 1 holds the most positive correlations with the other goals and SDG 12 holds the most negative correlations. This model was also used as a foundation for what we might expect to be accomplished in 10 years if actions based on our priorities were enacted. We believe that while focusing on SDG 1 would allow the UN to better meet the holistic needs of people worldwide, the initial value for SDG 1 is not high enough to expect completion by 2030.
We also included constant multipliers within each node to represent the probable impact that certain worldwide events could have on the achievement level of each goal. Constant multipliers represent a percentage change in the achievement levels of each of the SDGs and are calculated for each potential event separately. The COVID-19 pandemic, which erased four years’ worth of progress towards ending poverty, is one example (United Nations, 2015). Statistics like this impacted the relative values of our multipliers for war, technological advancements, pandemics, climate change, and refugee movements. From implementing the multipliers, we determined that SDG 1: No Poverty, SDG 2: Zero Hunger, SDG 4: Quality Education, SDG 10: Reduced Inequalities, and SDG 16: Peace, Justice, and Strong Infrastructure would be most impacted by a variety of possible future events.