In this lecture, we focus on how to estimate the health or general status of large complex systems. This is motivated by the concern that systems that appear, at a macroscale, to be stable might actually be undergoing changes from within that affect their resilience. We provide one example from social welfare economics, which starts with an introduction to the Lorenz curve for wealth distributions and the related Gini coefficient/index used to measure the distance in a distribution from the equal-wealth distribution. We show how the Gini index has changed over time for different countries based on their political decisions, which allows us to talk about Pareto optimality as a framework for thinking about social-welfare policy decisions. We introduce things like the Pareto improvement and the Pareto frontier. We then pivot to community ecology and use the Pareto framework as a lens for thinking about how evolution (and natural selection, in particular) is a sequence of Pareto improvements that moves communities toward a Pareto frontier. Although they diversify in getting to the frontier, that diversification can be limited in later movements along the frontier (which will affect resilience). We begin to talk about how to use Shannon entropy as an index for biodiversity, helping to estimate the "health" of a given ecological community.
Whiteboard notes for this lecture can be found at: https://www.dropbox.com/s/9xflupesoz0rqx0/SOS220-LectureF1-2023-03-02-Assessing_Development_Growth_and_Diversitiy_in_Systems.pdf?dl=0
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