Workbook for Volume 1 - Part IV - Section #16: Foundational Papers from the 20th Century to WWII (3 of 3) – Wald & Koopmans
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Summary:
Volume 1 - Part IV - Section #16: Foundational Papers from the 20th Century to WWII (3 of 3) – Wald & Koopmans - As WWII begins, statistical decision-making becomes a matter of life-and-death, as shown by Abraham Wald’s debunking of “Survivorship Bias” in the analysis of bullet holes in returning bombers, and documented by Marc Mangel & Francisco J. Samaniego’s 1984 paper “Abraham Wald’s Work on Aircraft Survivability”. Additionally, Wald extends probabilistic analysis based on “Expected Value” & “Expected Utility” to non-probabilistic scenario analysis based on rank-ordered outcomes. Finally, Tjalling Charles Koopmans’ focus on balance-sheets marks an important transition from “Expected Value Optimization” to “Client-Centric Planning” where the capabilities of the empirical “Decision-Maker” can be objectively quantified with institutional or household balance-sheets for comparison with the subjective elicitation of psychological preferences. This brings “Ecological Rationality” to investment decision processes that would otherwise use the limiting assumptions of the “Rational Investor” in order to fit the client in the “Task Environment” of the theoretical “Disinterested Observer”. Finally, the Minimax/Maximin decision rule starts in 1945 with Abraham Wald’s paper “Statistical decision functions which minimize the maximum risk” Originally, it was a two-player, zero-sum game decision-rule to minimize a possible loss from the worst-case scenario (Minimax), or to maximize the gain from the lowest gain scenario (Maximin). Wald’s work delivers a resilient order of conclusions due to non-probabilistic scenario analysis based on outcomes that can be compared and ranked [Ordinal] as opposed to probabilistic “Expected Values” & “Expected Utilities” that return a specific number [Cardinal]. About 50 years later, Ole Peters shows that people operate as first-order, rank-ordering, growth optimizers based on the circumstances of the specific “Growth Dynamic” of their wealth process. The 2019 paper by Meder, et al. “Ergodicity-breaking Reveals Time Optimal Economic Behavior in Humans” provides the first empirical documentation of such context-switching decision-making based on “Growth Dynamics”. Meder’s empirical validation work shows that “Decision-Makers” tolerate risk differently in different “Task Environments”, and change the nature of their choices according to the specific “Growth Dynamic” of the situation that they face. This provides an interpretation of utility functions as ergodic transformation functions uniquely matched to each “Growth Dynamic”. For instance, linear utility matches an “Additive Growth Dynamic”, and logarithmic utility matches a “Multiplicative Growth Dynamic”. This means that coming out of WWII, Financial Economics has three established lines of development: (i) the dominant “Expected Value Optimization”, the never-quite censored-out “Growth Optimal Solution”, and the outside-looking-in “Client Centric Planning”.
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”CTRI by Francois Gadenne” writes a business book in three volumes, published serially on Substack for public peer-review. The book connects the dots of life-enhancing practices for the next generation, free of controlling algorithms, based on the lifetime experience of a retirement age entrepreneur, & continuously updated with insights from reading Wealth, Health, & Statistics research papers on behalf of large companies as the co-founder of CTRI.