Relevant bibliographies by topics / ARROW'S IMPOSSIBILITY THEOREM

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  2. Dissertations / Theses
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Academic literature on the topic 'ARROW'S IMPOSSIBILITY THEOREM'

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Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "ARROW'S IMPOSSIBILITY THEOREM"

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Gendin, Sidney. "WHY ARROW'S IMPOSSIBILITY THEOREM IS INVALID." Journal of Social Philosophy 25, no. 1 (March 1994): 144–59. http://dx.doi.org/10.1111/j.1467-9833.1994.tb00311.x.

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DENICOLÒ, VINCENZO. "AN ELEMENTARY PROOF OF ARROW'S IMPOSSIBILITY THEOREM*." Japanese Economic Review 47, no. 4 (December 1996): 432–35. http://dx.doi.org/10.1111/j.1468-5876.1996.tb00061.x.

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Pouzet, Maurice. "A projection property and Arrow's impossibility theorem." Discrete Mathematics 192, no. 1-3 (October 1998): 293–308. http://dx.doi.org/10.1016/s0012-365x(98)00077-6.

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Hansen, Paul. "Another Graphical Proof of Arrow's Impossibility Theorem." Journal of Economic Education 33, no. 3 (January 2002): 217–35. http://dx.doi.org/10.1080/00220480209595188.

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Dardanoni, Valentino. "A pedagogical proof of Arrow's Impossibility Theorem." Social Choice and Welfare 18, no. 1 (January 11, 2001): 107–12. http://dx.doi.org/10.1007/s003550000062.

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Denicolo, Vincenzo. "An Elementary Proof of Arrow's Impossibility Theorem: Correction." Japanese Economic Review 52, no. 1 (March 2001): 134–35. http://dx.doi.org/10.1111/1468-5876.00186.

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Fountain, John. "A simple graphical proof of arrow's impossibility theorem." New Zealand Economic Papers 34, no. 1 (June 2000): 89–110. http://dx.doi.org/10.1080/00779950009544317.

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Lützen, Jesper. "How mathematical impossibility changed welfare economics: A history of Arrow's impossibility theorem." Historia Mathematica 46 (February 2019): 56–87. http://dx.doi.org/10.1016/j.hm.2018.11.001.

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Terao, Hiroaki. "Chambers of arrangements of hyperplanes and Arrow's impossibility theorem." Advances in Mathematics 214, no. 1 (September 2007): 366–78. http://dx.doi.org/10.1016/j.aim.2007.02.006.

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Patty, John W., and Elizabeth Maggie Penn. "Measuring Fairness, Inequality, and Big Data: Social Choice Since Arrow." Annual Review of Political Science 22, no. 1 (May 11, 2019): 435–60. http://dx.doi.org/10.1146/annurev-polisci-022018-024704.

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Kenneth J. Arrow was one of the most important intellectuals of the twentieth century, and his “impossibility theorem” is arguably the starting point of modern, axiomatic social choice theory. In this review, we begin with a brief discussion of Arrow's theorem and subsequent work that extended the result. We then discuss its implications for voting and constitutional systems, including a number of seminal results—both positive and negative—that characterize what such systems can accomplish and why. We then depart from this narrow interpretation of the result to consider more varied institutional design questions such as apportionment and geographical districting. Following this, we address the theorem's implications for measurement of concepts of fundamental interest to political science such as justice and inequality. Finally, we address current work applying social choice concepts and the axiomatic method to data analysis more generally.
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Dissertations / Theses on the topic "ARROW'S IMPOSSIBILITY THEOREM"

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Vernersson, Anton. "The Chichilnisky-Heal Approach to Arrow's Impossibility Theorem." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-149516.

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This essay explores a surprising intersection between economics and algebraic topology. On the economical side social choice is studied. A field which includes topics such as voting theory. Within standard economics this is often approached by discrete methods, such as Arrow's impossibility theorem. This essay will instead follow a continuous proof by Chichilnisky and Heal, which is based on a considerable amount of algebraic topology. Therefore the essay will cover a great deal of algebraic topology. In particular, the subject of obstruction theory, which provides clear conditions for the extension of a function to a larger space, is studied.
Denna uppsats utforskar en oväntad blandning av nationalekonomi och algebraisk topologi. På den ekonomiska sidan så studeras "Social choice". Ett ämne som bland annat inkluderar valteori. Inom den rådande ekonomiska teorin så används ofta diskret matematik för att lösa problem i ämnet. Denna uppsats följer istället en kontinuerlig metod konstruerad av Chichilnisky och Heal. Vilken bygger på algebraisk topologi och speciellt på "obstruction theory" som syftar till att utdvidga funktioner till större mängder.
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Castelluber, Jaqueline Dayanne Capucci. "O Teorema da impossibilidade de Arrow e suas consequências sobre sistemas eleitorais." reponame:Repositório Institucional da UFABC, 2017.

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Orientador: Prof. Dr. Roberto Venegeroles Nascimento
Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2017.
Neste trabalho foram apresentados, contextualmente, os métodos de "eleições por ordem de mérito" e de "eleições particulares", ambos propostos em [1] pelo matemático francês Jean Charles Borda (1733 ¿ 1799) em 1770 como alternativa ao "método usual de contagem de votos". Borba percebeu que o "método usual de contagem de votos" apresenta falhas porque em eleições com mais de dois candidatos pode-se não reproduzir adequadamente a preferência da maioria dos eleitores. Posteriormente, foi apresentado o "método de Condorcet", proposto em [2] pelo matemático francês Marie Jean Antonie Nicolas Caritat de Condorcet (1743 ¿ 1794) em 1785 para responder às falhas identificadas nos métodos propostos por Borda e, consequentemente, no "método usual de contagem de votos". Condorcet percebeu que, embora menos que o "método usual de contagem de votos", os métodos propostos por Borda também apresentam falhas porque é possível que sejam utilizados votos ou candidatos de maneira estratégica para manipular o resultado da eleição. O referido método foi apresentado com base no método publicado pelo matemático e economista americano Hobart Peyton Young (1945 ¿) em 1988 na obra "Condorcet¿s Theory of Voting" [3] pelo American Political Science Review. Por conseguinte, foram apresentadas três demonstrações distintas do "Teorema da Impossibilidade de Arrow", proposto em [4] pelo matemático e economista americano Kenneth Joseph Arrow (1921 ¿ 2017) em 1950, no qual, mostrou que considerando determinadas condições, em eleições com mais de dois candidatos, não há um método democraticamente consistente de escolher um candidato vencedor, pois não existe uma forma perfeita de construir uma preferência social a partir das preferências individuais dos eleitores. As referidas demonstrações foram apresentadas com base nas demonstrações publicadas pelo matemático e economista americano John Geanakoplos (1955 ¿) em 2005 no artigo "Three brief proofs of Arrow¿s Impossibility Theorem" [5] pelo Journal Economic Theory. Por fim, foram apresentadas as conclusões e consequências do "Teorema da Impossibilidade de Arrow" sobre sistemas eleitorais.
In this work were presented, contextually, the methods of "elections in order of merit" and "private elections", both proposed in [1] by the french mathematician Jean Charles Borda (1733 ¿ 1799) in 1770 as an alternative to the "usual method of counting votes". Borda realized that the "usual method of counting votes" presents flaws because in elections with more than two candidates it doesn¿t reproduce the adequately preference of the majority of voters. Posteriorly, the "Condorcet method" was presented, proposed in [2] by the french mathematician Marie Jean Antonie Nicolas Caritat de Condorcet (1743 ¿ 1794) in 1785 to respond to the flaws identified in the methods proposed by Borda and, consequently, in the "usual method of counting votes". Condorcet realized that, although less than the "usual method of counting votes", the methods proposed by Borda also present flaws because it is possible that votes or candidates are used strategically to manipulate the election result. This method was presented based on the method published by the american mathematician and economist Hobart Peyton Young (1945 - ...) in 1988 in the work "Condorcet¿s Theory of Voting" [3] by the American Political Science Review. Therefore, three distinct demonstrations of the "Arrow Impossibility Theorem" were presented, proposed in [4] by the american mathematician and economist Kenneth Joseph Arrow (1921 ¿ 2017) in 1950, in which, it has been shown that given certain conditions, in elections with more than two candidates, there is no democratically consistent method of choosing a winning candidate, as there is no perfect way to build a social preference based on the individual preferences of voters. These statements were presented based on the statements publishe by the american mathematician and economist John Geanakoplos (1955 - ...) in 2005 in the article "Three brief proofs of Arrow¿s Impossibility Theorem" [5] by the Journal Economic Theory. Finally, the conclusions and consequences of "Arrow¿s Impossibility Theorem" on electoral systems were presented.
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"Arrow's impossibility theorem and electoral systems." Chinese University of Hong Kong, 1989. http://library.cuhk.edu.hk/record=b5886192.

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Books on the topic "ARROW'S IMPOSSIBILITY THEOREM"

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Sen, Amartya Kumar, and Joseph E. Stiglitz. Arrow Impossibility Theorem. Columbia University Press, 2014.

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Sen, Amartya Kumar. The Arrow Impossibility Theorem (Kenneth J. Arrow Lecture Series). Columbia University Press, 2014.

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D'Agostino, Susan. How to Free Your Inner Mathematician. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198843597.001.0001.

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How to Free Your Inner Mathematician: Notes on Mathematics and Life offers readers guidance in managing the fear, freedom, frustration, and joy that often accompany calls to think mathematically. With practical insight and years of award-winning mathematics teaching experience, DAgostino offers more than 300 hand-drawn sketches alongside accessible descriptions of fractals, symmetry, fuzzy logic, knot theory, Penrose patterns, infinity, the Twin Prime Conjecture, Arrows Impossibility Theorem, Fermats Last Theorem, and other intriguing mathematical topics. Readers are encouraged to embrace change, proceed at their own pace, mix up their routines, resist comparison, have faith, fail more often, look for beauty, exercise their imaginations, and define success for themselves. Mathematics students and enthusiasts will learn advice for fostering courage on their journey regardless of age or mathematical background. How to Free Your Inner Mathematician delivers not only engaging mathematical content but provides reassurance that mathematical success has more to do with curiosity and drive than innate aptitude.
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Book chapters on the topic "ARROW'S IMPOSSIBILITY THEOREM"

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Kelly, Jerry S. "Arrow’s Impossibility Theorem." In Social Choice Theory, 80–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-662-09925-4_8.

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Feldman, Allan M. "Arrow’s Impossibility Theorem." In Welfare Economics and Social Choice Theory, 178–95. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4615-8141-3_11.

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McLean, Iain, Alistair McMillan, and Burt L. Monroe. "On Arrow’s Impossibility Theorem." In The Theory of Committees and Elections by Duncan Black and Committee Decisions with Complementary Valuation by Duncan Black and R.A. Newing, 331–52. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-4860-3_23.

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Skala, Heinz J. "What Does Arrow’s Impossibility Theorem Tell Us?" In Theory and Decision, 273–86. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3895-3_14.

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Dubas, Khalid M., and James T. Strong. "Arrow’s General Impossibility Theorem and Five Collective Choice Rules: Pareto, Condorcet, Plurality, Approval Voting, and Borda." In Proceedings of the 1993 Academy of Marketing Science (AMS) Annual Conference, 334–38. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-13159-7_76.

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"Arrow's Theorem." In Interprofile Conditions and Impossibility, 17–23. Routledge, 2013. http://dx.doi.org/10.4324/9781315014760-10.

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"Informal Algorithms, Impossibility Theorems, and New “Learning” Business/Compensation Models for the Credit Rating Agency Industry." In Complex Systems and Sustainability in the Global Auditing, Consulting, and Credit Rating Agency Industries, 283–316. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7418-8.ch009.

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This chapter adopts agent-based and complexity approaches and introduces new “learning business models” and compensation contracts for CRAs that can solve the conflicts of interest, antitrust, greed, regret, deadweight-losses, complexity, and industrial organization problems inherent in the credit rating agency industry, and each model contravenes Myerson-Satterthwaite impossibility theorem, Arrow's impossibility theorem, Sen's impossibility theorem, Gibbard's theorem, the Gibbard-Satterthwaite impossibility theorem, and the Green-Laffont impossibility theorem. The business models include “quasi multi-sided auctions” wherein at any time t several auctions can simultaneously occur, and the payoff functions of any buyer-seller pair in any auction depends on the bidding done by at least another buyer-seller pair either at the same time, or at a different time. This “long-memory bias” of buyers and sellers in auctions is new in the literature.
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"On Impossibility Theorems, Informal Algorithms, and International Trade." In Complex Systems and Sustainability in the Global Auditing, Consulting, and Credit Rating Agency Industries, 169–210. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7418-8.ch006.

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The “Big-Four” accounting firms dominate the global accounting/auditing industry, and the big-seven consulting firms (Bain; McKinsey; Booz; Deloitte; PwC; KPMG and E&Y) dominate the global business/management consulting industry and stifle competition. During 1990-2017, the global auditing/accounting industry and the global management consulting industry experienced significant structural changes that have implications for Financial Stability, systemic risk and the proper functioning of capital markets. Some of the results included the collapses of stock prices and bond prices of firms suspected of earnings management; and substantial litigation against auditing firms, CRAs and board of directors. Accounting/audit firms and consulting firms have always been key elements in the fight against earnings management, securities fraud, corruption and asset quality management because of their unique position as external auditors and advisors. This chapter introduces some efficient Auditor allocation and Compensation Mechanisms. These new “Learning Business Models” and contracts can solve the conflicts of interest, Antitrust, greed, Regret, Deadweight-Losses, complexity and industrial organization problems inherent in the Auditing/consulting industry; and each such model contravenes Myerson-Satterthwaite Impossibility Theorem, Arrow's Impossibility Theorem, Sen's Impossibility Theorem, Gibbard's Theorem, the Gibbard-Satterthwaite Impossibility Theorem, and the Green-Laffont Impossibility Theorem. These issues have implications for international trade and international capital flows given the prevalence of accounting and management consulting in almost all aspects of modern business.
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Landemore, Hélène. "Epistemic Failures of Majority Rule: Real and Imagined." In Democratic Reason. Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691155654.003.0007.

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This chapter addresses a series of objections to the claimed epistemic properties of majority rule and, more generally, aggregation of judgments. It first considers a general objection to the epistemic approach to voting, which supposedly does not take seriously enough the possibility that politics is about aggregation of interests, rather than aggregation of judgments. The chapter also considers the objection from Arrow's Impossibility Theorem and the doctrinal paradox (or discursive dilemma). Next, the chapter addresses the problem of informational free riding supposedly afflicting citizens in mass democracies, as well as the problem of the voting paradox (as a by-product). Finally, the chapter turns to a refutation of the objection that citizens suffer from systematic biases that are amplified at the collective level.
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"Arrow’s impossibility theorem." In 100 Years of Math Milestones, 199–203. Providence, Rhode Island: American Mathematical Society, 2019. http://dx.doi.org/10.1090/mbk/121/38.

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Conference papers on the topic "ARROW'S IMPOSSIBILITY THEOREM"

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Mata Diaz, Amilcar, and Ramon Pino Perez. "Impossibility in Belief Merging (Extended Abstract)." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/799.

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With the aim of studying social properties of belief merging and having a better understanding of impossibility, we extend in three ways the framework of logic-based merging introduced by Konieczny and Pino Perez. First, at the level of representation of the information, we pass from belief bases to complex epistemic states. Second, the profiles are represented as functions of finite societies to the set of epistemic states (a sort of vectors) and not as multisets of epistemic states. Third, we extend the set of rational postulates in order to consider the epistemic versions of the classical postulates of social choice theory: standard domain, Pareto property, independence of irrelevant alternatives and absence of dictator. These epistemic versions of social postulates are given, essentially, in terms of the finite propositional logic. We state some representation theorems for these operators. These extensions and representation theorems allow us to establish an epistemic and very general version of Arrow's impossibility theorem. One of the interesting features of our result, is that it holds for different representations of epistemic states; for instance conditionals, ordinal conditional functions and, of course, total preorders.
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Saaty, Thomas L. "A Ratio Scale Metric and the Compatibility of Ratio Scales: On the Possibility of Arrow's Impossibility Theorem." In The International Symposium on the Analytic Hierarchy Process. Creative Decisions Foundation, 1994. http://dx.doi.org/10.13033/isahp.y1994.004.

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Li, Simon. "Independence of Irrelevant Alternatives in Engineering Design." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34586.

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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.
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Allen, Beth. "On the Aggregation of Preferences in Engineering Design." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/dac-21015.

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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.
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Pandey, Vijitashwa, and Deborah Thurston. "Non-Dominated Strategies for Decision Based Design for Component Reuse." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35685.

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Component level reuse enables retention of value from products recovered at the end of their first lifecycle. Reuse strategies determined at the beginning of the lifecycle are aimed at maximizing this recovered value. Decision based design can be employed, but there are several difficulties in large scale implementation. First, computational complexities arise. Even with a product with a relatively small number of components, it becomes difficult to find the optimal component level decisions. Second, if there is more than one stakeholder involved, each interested in different attributes, the problem becomes even more difficult, due both to complexity and Arrow’s Impossibility Theorem. However, while the preferences of the stakeholders may not be known precisely, and aggregating those preferences poses difficulties, what is usually known is the partial ordering of alternatives. This paper presents a method for exploiting the features of a solution algorithm to address these difficulties in implementing decision based design. Heuristic methods including non-dominated sorting genetic algorithms (NSGA) can exploit this partial ordering and reject dominated alternatives, simplifying the problem. Including attributes of interest to various stakeholders ensures that the solutions found are practicable. One of the reasons product reuse has not achieved critical acceptance is because the three entities involved, the customers, the manufacturer and the government do not have a common ground. This results in inaccurate aggregating of attributes which the proposed method avoids. We illustrate our approach with a case study of component reuse of personal computers.
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