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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 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). 

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. 

Abstract 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.