Search for: All records

Of importance when selecting a voting method is whether, on a regular basis, its outcomes accurately capture the intent of voters. A surprise is that very few procedures do this. Another desired feature is for a decision approach to assist groups in reaching a consensus (Sect. 5). As described, these goals are satisfied only with the Borda count. Addressing these objectives requires understanding what can go wrong, what causes voting difficulties, and how bad they can be. To avoid technicalities, all of this is illustrated with examples accompanied by references for readers wishing a complete analysis. As shown (Sects. 1–3), most problems reflect a loss of vital information. Understanding this feature assists in showing that the typical description of Arrow’s Theorem, “with three or more alternatives, no voting method is fair,” is not accurate (Sect. 2).

 

The modeling and simulation community has devoted considerable attention to the question of model validity. Their work has focused on the concept of “accuracy,” loosely defined as the difference between a model-computed result and a real-world result. This paper makes use of an example case that results in a paradox to illustrate weaknesses in an accuracy-focused approach, and proposes in its stead a value-focused approach based on classical decision theory. Instead of advocating the use of a model based on its accuracy, this work advocates using a model if it adds value to the overall application thus relating validation directly to system performance. The approach fills significant gaps in the current theory, notably providing a clearly defined validity metric and a fundamental rationale for the use of this metric.

 

All complex designs emerge as the result of the decisions made by the design engineers. It can be shown that the designs are best when the preferences guiding the engineering decisions align with the overall system or corporate preference. But we know that all people make decisions based on their own personal preferences, which are unlikely to align well with the corporate preference. This research addresses the question, what mechanisms can be used to better align engineers’ decisions to the system or corporate preference, but particularly such that major catastrophes might be prevented? Inspiration for this work comes from a number of very substantial losses that likely would have been prevented by the systems engineers had they the incentive to come forth with knowledge they certainly had. Examples include Boeing’s experience with the 737MAX, which appears to be costing Boeing more than $100 billion, and Volkswagen’s experience with the falsified emission testing of their diesel-engine vehicles, which resulted in over 31 billion euros in fines, penalties and other direct costs. We believe that incentive mechanisms could have been in place that would have prevented these very significant losses. Thus, we believe that there exist potential mechanisms that would benefit both the corporation and the engineers. We further believe that these mechanisms would not only improve corporate profitability but they have the potential to save many lives as well.

 

It is well known that decision methods based on pairwise rankings can suffer from a wide range of difficulties. These problems are addressed here by treating the methods as systems, where each pair is looked upon as a subsystem with an assigned task. In this manner, the source of several difficulties (including Arrow’s Theorem) is equated with the standard concern that the “whole need not be the sum of its parts.” These problems arise because the objectives assigned to subsystems need not be compatible with that of the system. Knowing what causes the difficulties leads to resolutions.

 

Features of graphs that hinder finding closed paths with particular properties, as represented by the Traveling Salesperson Problem—TSP, are identified for three classes of graphs. Removing these terms leads to a companion graph with identical closed path properties that is easier to analyze. A surprise is that these troubling graph factors are precisely what is needed to analyze certain voting methods, while the companion graph’s terms are what cause voting theory complexities as manifested by Arrow’s Theorem. This means that the seemingly separate goals of analyzing closed paths in graphs and analyzing voting methods are complementary: components of data terms that assist in one of these areas are the source of troubles in the other. Consequences for standard decision methods are in Sects. 2.5, 3.7 and the companion paper (Saari in Theory Decis 91(3):377–402, 2021). The emphasis here is on paths in graphs; incomplete graphs are similarly handled. 

Abstract Tolerancing began with the notion of limits imposed on the dimensions of realized parts both to maintain functional geometric dimensionality and to enable cost-effective part fabrication and inspection. Increasingly, however, component fabrication depends on more than part geometry as many parts are fabricated as a result of a “recipe” rather than dimensional instructions for material addition or removal. Referred to as process tolerancing, this is the case, for example, with IC chips. In the case of tolerance optimization, a typical objective is cost minimization while achieving required functionality or “quality.” This article takes a different look at tolerances, suggesting that rather than ensuring merely that parts achieve a desired functionality at minimum cost, a typical underlying goal of the product design is to make money, more is better, and tolerances comprise additional design variables amenable to optimization in a decision theoretic framework. We further recognize that tolerances introduce additional product attributes that relate to product characteristics such as consistency, quality, reliability, and durability. These important attributes complicate the computation of the expected utility of candidate designs, requiring additional computational steps for their determination. The resulting theory of tolerancing illuminates the assumptions and limitations inherent to Taguchi’s loss function. We illustrate the theory using the example of tolerancing for an apple pie, which conveniently demands consideration of tolerances on both quantities and processes, and the interaction among these tolerances. 

The activity that most distinguishes engineering from mathematics and the physical sciences is the design of technologically challenging devices, products and systems. But, while ABET recognizes design as a decision-making process, our current educational system treats engineers as problem-solvers and delivers a largely deterministic treatment of the sciences. Problem solving and decision making involve significantly different considerations, not the least of which is that all decision-making is done under uncertainty and risk. Secondly, effective choices among design alternatives demand an understanding of the mathematics of decision making, which rarely appears in engineering curricula. Specifically, we teach the sciences but not how to use them. Decision makers typically earn 50-200 percent more than problem-solvers. The objective of this paper is to make the case that this gap in engineering education lowers the value of an engineering education for both the students and the faculty, and to provide suggestions on how to fix it. 

Problems with majority voting over pairs as represented by Arrow’s Theorem and those of finding the lengths of closed paths as captured by the Traveling Salesperson Problem (TSP) appear to have nothing in common. In fact, they are connected. As shown, pairwise voting and a version of the TSP share the same domain where each system can be simplified by restricting it to complementary regions to eliminate extraneous terms. Central for doing so is the Borda Count, where it is shown that its outcome most accurately reflects the voter preferences. 

Without imposing restrictions on a weighted graph’s arc lengths, symmetry structures cannot be expected. But, they exist. To find them, the graphs are decomposed into a component that dictates all closed path properties (e.g., shortest and longest paths), and a superfluous component that can be removed. The simpler remaining graph exposes inherent symmetry structures that form the basis for all closed path properties. For certain asymmetric problems, the symmetry is that of three-cycles; for the general undirected setting it is a type of four-cycles; for general directed problems with asymmetric costs, it is a product of three and four cycles. Everything extends immediately to incomplete graphs. 

Abstract The derivation of a theory of systems engineering has long been complicated by the fact that there is little consensus within the systems engineering community regarding precisely what systems engineering is, what systems engineers do, and what might constitute reasonable systems engineering practices. To date, attempts at theories fail to accommodate even a sizable fraction of the current systems engineering community, and they fail to present a test of validity of systems theories, analytical methods, procedures, or practices. This article presents a more theoretical and more abstract approach to the derivation of a theory of systems engineering that has the potential to accommodate a broad segment of the systems engineering community and present a validity test. It is based on a simple preference statement: “I want the best system I can get.” From this statement, it is argued that a very rich theory can be obtained. However, most engineering disciplines are framed around a core set of widely accepted physical laws; to the authors’ knowledge, this is the first attempt to frame an engineering discipline around a preference.