The preceding post, Part 7, introduced some concepts applicable to complex system analysis. These included representations of reality and a property called ergodicity. This article delves more deeply into the challenges that arise from these sources in modeling complex systems.
NOTE: This preliminary draft has been revised and expanded. The finished article can be seen here.
The preceding post, Part 7, introduced some concepts applicable to complex system analysis. These included representations of reality and a property called ergodicity. This article delves more deeply into the challenges that arise from these sources in modeling complex systems.
The complexity of analyzing a process as simple as flipping a coin three times raises concerns about how to describe reality in modeling. In dealing with coin flips, we have a known probability for the result of each flip. Also, many modeling scenarios may have more than three elementary steps. Additionally, the probabilities associated with elementary steps may not be known. How does this complicate the modeling process? This review will address that question with specific emphasis on social science models, especially economics.
In Part 5, we found that there are 6,435 possible outcomes for the complete characterization of a process of repeating three coin flips. This arises because a 3-flip sequence must be repeated eight times to allow for the possibility of all eight equally probable sequence results occurring. In this article, we calculate the probability of obtaining any individual outcome and also the probability of obtaining an outcome of each of the 22 outcome types.
