Independence of Irrelevant Alternatives in Engineering Design

2014 ◽  
Author(s):  
Simon Li
Keyword(s):  
Engineering Design ◽  
Quality Function Deployment ◽  
Choice Function ◽  
Irrelevant Information ◽  
Borda Count ◽  
Impossibility Theorem ◽  
Independence Of Irrelevant Alternatives ◽  
Decision Methods ◽  
Consistency Property ◽  
Kenneth Arrow

When discussing Arrow’s Impossibility Theorem (AIT) in engineering design, we find that one condition, Independence of Irrelevant Alternatives (IIA), has been misunderstood generally. In this paper, two types of IIA are distinguished. One is based on Kenneth Arrow (IIA-A) that concerns the rationality condition of a collective choice rule (CCR). Another one is based on Amartya Sen (IIA-S) that is a condition for a choice function (CF). Through the analysis of IIA-A, this paper revisits three decision methods (i.e., Pugh matrix, Borda count and Quality Function Deployment) that have been criticized for their failures in some situations. It is argued that the violation of IIA-A does not immediately imply irrationality in engineering design, and more detailed analysis should be applied to examine the meaning of “irrelevant information”. Alternatively, IIA-S is concerned with the transitivity of CF, and it is associated with contraction consistency (Property α) and expansion consistency (Property β). It is shown that IIA-A and IIA-S are technically distinct and should not be confused in the rationality arguments. Other versions of IIA-A are also introduced to emphasize the significance of mathematical clarity in the discussion of AIT-related issues.

The Implications of Arrow’s Impossibility Theorem on Approaches to Optimal Engineering Design

1996 ◽  
Vol 118 (2) ◽  
pp. 161-164 ◽  
Author(s):  
G. A. Hazelrigg
Keyword(s):  
Quality Management ◽  
Total Quality Management ◽  
Utility Function ◽  
Design Optimization ◽  
Engineering Design ◽  
Quality Function Deployment ◽  
Impossibility Theorem ◽  
Total Quality ◽  
Quality Function ◽  
Optimize Design

Many modern approaches to engineering design seek to optimize design in order to maximize the value of the system to its customers. These approaches rely on the formulation of a system utility function as a measure of system worth. It is shown here that, under certain circumstances, however, such a measure cannot exist. It is then indicated that these circumstances comprise the rule rather than the exception. Finally it is shown that pursuing the objective of design optimization as defined by the customers via contemporary approaches can lead the designer to highly inappropriate and undesirable designs. As a consequence of this, it becomes apparent that the methods of Total Quality Management (TQM) and Quality Function Deployment (QFD) can lead to highly erroneous results.

scholarly journals Aggregating multiple ordinal rankings in engineering design: the best model according to the Kendall’s coefficient of concordance

2020 ◽  
Author(s):  
Fiorenzo Franceschini ◽  
Domenico Maisano
Keyword(s):  
Engineering Design ◽  
Borda Count ◽  
Impossibility Theorem ◽  
Arrow’S Impossibility Theorem ◽  
Aggregation Model ◽  
Count Model ◽  
Ordinal Ranking ◽  
Arrow's Impossibility Theorem ◽  
Coefficient Of Concordance ◽  
Collective Ranking

Abstract Aggregating the preferences of a group of experts is a recurring problem in several fields, including engineering design; in a nutshell, each expert formulates an ordinal ranking of a set of alternatives and the resulting rankings should be aggregated into a collective one. Many aggregation models have been proposed in the literature, showing strengths and weaknesses, in line with the implications of Arrow's impossibility theorem. Furthermore, the coherence of the collective ranking with respect to the expert rankings may change depending on: (i) the expert rankings themselves and (ii) the aggregation model adopted. This paper assesses this coherence for a variety of aggregation models, through a recent test based on the Kendall's coefficient of concordance (W), and studies the characteristics of those models that are most likely to achieve higher coherence. Interestingly, the so-called Borda count model often provides best coherence, with some exceptions in the case of collective rankings with ties. The description is supported by practical examples.

A Comment on Arrow’s Impossibility Theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alec Sandroni ◽  
Alvaro Sandroni
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Social Preference ◽  
Social Choice Function ◽  
Individual Preference ◽  
Impossibility Theorem ◽  
Preference Order ◽  
Individual Choice ◽  
Choice Functions ◽  
Preference Orders

AbstractArrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow’s desiderata).

Decision Methods for Design: Insights from Psychology

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Konstantinos V. Katsikopoulos
Keyword(s):  
Engineering Design ◽  
Internal Consistency ◽  
Utility Theory ◽  
Research Question ◽  
Design Concept ◽  
Functional Requirement ◽  
Decision Method ◽  
Decision Methods ◽  
Multi Attribute Utility Theory ◽  
New Research

This work aims at stimulating constructive conversation about decision methods in engineering design by using insights from psychology. I point out that any decision method has two components: coherence, which refers to internal consistency (do design choices satisfy a logical axiom?) and correspondence, which refers to external effectiveness (does a design concept satisfy a functional requirement?). Some researchers argue for “rational” methods such as multi-attribute utility theory, whereas others argue for “heuristics” such as the Pugh process, and the coherence/correspondence distinction can clarify this debate in two ways. First, by analyzing statements in the design literature, I argue that the debate is essentially about different strategies for achieving correspondence: Multi-attribute utility theory aims at achieving coherence with the expectation that coherence will imply correspondence, whereas the Pugh process aims at directly achieving correspondence. Second, I propose a new research question for design: “Under what conditions does achieving coherence imply achieving correspondence?”

A Framework for Decision-Based Engineering Design

1998 ◽  
Vol 120 (4) ◽  
pp. 653-658 ◽  
Author(s):  
G. A. Hazelrigg
Keyword(s):  
Engineering Design ◽  
Operations Research ◽  
Quality Function Deployment ◽  
Value Theory ◽  
Decision Making Process ◽  
Design Decisions ◽  
Decision Sciences ◽  
Research Decision ◽  
Decision Based Design ◽  
Total Life

Engineering design is increasingly recognized as a decision-making process. This recognition brings with it the richness of many well-developed theories and methods from economics, operations research, decision sciences, and other disciplines. Done correctly, it forces the process of engineering design into a total systems context, and demands that design decisions account for a product’s total life cycle. It also provides a theory of design that is based on a rigorous set of axioms that underlie value theory. But the rigor of decision-based design also places stringent conditions on the process of engineering design that eliminate popular approaches such as Quality Function Deployment. This paper presents the underlying notions of decision-based design, points to some of the axioms that underlie the theory of decision-based design, and discusses the consequences of the theory on engineering education.

scholarly journals Cycles and Intractability in a Large Class of Aggregation Rules

2018 ◽  
Vol 61 ◽  
pp. 407-431 ◽  
Author(s):  
William S. Zwicker
Keyword(s):  
Computational Complexity ◽  
Related Problem ◽  
Borda Count ◽  
Impossibility Theorem ◽  
Approval Voting ◽  
Winner Determination ◽  
Voting Rule ◽  
Special Cases ◽  
The Mean ◽  
Cyclic Part

We introduce the (j,k)-Kemeny rule -- a generalization of Kemeny's voting rule that aggregates j-chotomous weak orders into a k-chotomous weak order. Special cases of (j,k)-Kemeny include approval voting, the mean rule and Borda mean rule, as well as the Borda count and plurality voting. Why, then, is the winner problem computationally tractable for each of these other rules, but intractable for Kemeny? We show that intractability of winner determination for the (j,k)-Kemeny rule first appears at the j=3, k=3 level. The proof rests on a reduction of max cut to a related problem on weighted tournaments, and reveals that computational complexity arises from the cyclic part in the fundamental decomposition of a weighted tournament into cyclic and cocyclic components. Thus the existence of majority cycles -- the engine driving both Arrow's impossibility theorem and the Gibbard-Satterthwaite theorem -- also serves as a source of computational complexity in social choice.

scholarly journals Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1083
Author(s):  
Xin Sun ◽  
Feifei He ◽  
Mirek Sopek ◽  
Meiyun Guo
Keyword(s):  
Quantum Information ◽  
Impossibility Theorem ◽  
Arrow’S Impossibility Theorem ◽  
Detailed Proof ◽  
Quantum Analogue ◽  
Independence Of Irrelevant Alternatives ◽  
Arrow's Impossibility Theorem ◽  
Definition Of

We study Arrow’s Impossibility Theorem in the quantum setting. Our work is based on the work of Bao and Halpern, in which it is proved that the quantum analogue of Arrow’s Impossibility Theorem is not valid. However, we feel unsatisfied about the proof presented in Bao and Halpern’s work. Moreover, the definition of Quantum Independence of Irrelevant Alternatives (QIIA) in Bao and Halpern’s work seems not appropriate to us. We give a better definition of QIIA, which properly captures the idea of the independence of irrelevant alternatives, and a detailed proof of the violation of Arrow’s Impossibility Theorem in the quantum setting with the modified definition.

On the Aggregation of Preferences in Engineering Design

2001 ◽  
Author(s):  
Beth Allen
Keyword(s):  
Engineering Design ◽  
Collaborative Design ◽  
Design Space ◽  
Decision Makers ◽  
Impossibility Theorem ◽  
Von Neumann ◽  
Aggregation Of Preferences ◽  
Ordinal Preferences ◽  
Additive Separability ◽  
Alternative Designs

Abstract This paper considers the possibility for aggregation of preferences in engineering design. Arrow’s Impossibility Theorem applies to the aggregation of individuals’ (ordinal) preferences defined over a finite number of alternative designs. However, when the design space is infinite and when all individuals have monotone preferences or have von Neumann-Morgenstern (cardinal) utilities defined over lotteries, possibility results are available. Alternative axiomatic frameworks lead to additional aggregation procedures for cardinal utilities. For these results about collaborative design, aggregation occurs with respect to decision makers and not attributes, although some of the possibility results preserve additive separability in attributes.

Define success for yourself, given Arrow’s Impossibility Theorem

2020 ◽  
pp. 27-33
Author(s):  
Susan D'Agostino
Keyword(s):  
Borda Count ◽  
Impossibility Theorem ◽  
Mathematics Students ◽  
Arrow’S Impossibility Theorem ◽  
Run Off ◽  
Arrow's Impossibility Theorem ◽  
Voting System ◽  
Definition Of Success ◽  
The Many ◽  
Definition Of

“Define success for yourself, given Arrow’s Impossibility Theorem” explains different voting methods, including plurality voting, run-off voting, sequential run-off, Borda count, and dictatorship, and explains how Kenneth Arrow’s Impossibility Theorem proves that, in an election with three or more candidates, the only fair voting system is a dictatorship. That is, every voting method other than a dictatorship has a known problem with fairness. Mathematics students and enthusiasts are encouraged to consider the many “candidates” for defining “success” in mathematical and life pursuits before letting their vote be the only vote in electing a personal definition of success. This way, Arrow’s Impossibility Theorem assures a fair outcome. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

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