Pareto's Impossibility Theory, And Pairwise Comparison Matrices?

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Introduction Vilfredo Pareto graduated from the University of Turin and practiced as a civil engineer before switching to economics, and becoming a famous economist known for his application of mathematics to economic analysis. Pareto’s theories and research have been discussed several times in Praxis with several different applications, including the Pareto Chart, the Pareto Principle, and Pareto Efficiency (relating to Arrow’s Impossibility Theorem and Pairwise Comparison Matrices). The connections between these topics and their limitations, however, are not developed in class.

Pareto Charts and Pareto Analysis The first mention of Pareto occurred in Lecture 11, when discussing the point at which the return on investment for “effort” expended
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The concept of Pareto Optimality describes the selection in which there is no alternative where an individual (or objective) is better off (or satisfied better), and there is no individual (or objective) who is worse off (or not satisfied as well) [15]. Pareto’s Efficiency is considered a criteria in fair voting, as described in Arrow’s Impossibility Theorem [3]. The theorem explains that it is impossible to have a social welfare function that allows for fair voting, that does not break at least one of the “fairness” criteria [13]. The first criteria mentioned on Professor Foster’s slide on the theorem states, “if every voter prefers alternative X over alternative Y, then the group prefers X over Y;” this is known as the Pareto Efficiency [3]. In the following Praxis slides, however, Michael J. Scott and Erik K. Antonsson explain why Arrow’s Impossibility Theorem does not have a direct impact on engineering design decisions [3]. One of the reasons for this is that the social choice problem involves all orderings being assigned equal worth, whereas in engineering problems there is no need to do that for objectives [14]. Furthermore, the “heart of the multi-criteria engineering problem is the inter-attribute comparison of attributes,” which is not permitted in social choice problems [14]. These differences indicate that …show more content…
Pareto’s theorems require assigning specific values to objectives in order to rank their importance, despite not always having grounds to do so. Just as the first two applications of Pareto’s economics were deemed not helpful in an engineering context, the pairwise comparison matrix should receive the same assessment. These tools cannot effectively assess a set of alternatives in an engineering context, and thus should not be used to draw final conclusions. However, given that the problem in the Pareto Analysis is mirrored in the Pairwise Comparison, one may want to use the Pareto Analysis with a similar amount of caution. A Pareto Chart succinctly shows the effect meeting an objective has on the determined quality of the solution. Thus, this tool could be considered when fulfilling the Design Critique’s requirement to include another criterion-referenced tool. The flaws in applying Pareto’s economic principles to Praxis should always be considered whenever extending economic or social principles to engineering. Economic theories are always based on several assumptions, such as “all other things being equal”, and assuming people act rationally. These assumptions are not always warranted and will raise problems when applied to an engineering context which requires large amounts of evidence. Therefore, one must carefully consider all

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