So how to make group decisions? Arrow's impossibility theorem 70 years after

PurposeIn 1951, Kenneth Arrow proved that it is not possible to have a group decision-making procedure that satisfies reasonable requirements like fairness. From the theoretical viewpoint, this is a great result – well-deserving the Nobel Prize that was awarded to Professor Arrow. However, from the practical viewpoint, the question remains – so how should we make group decisions? A usual way to solve this problem is to provide some reasonable heuristic ideas, but the problem is that different seemingly reasonable idea often lead to different group decision – this is known, e.g. for different voting schemes.Design/methodology/approachIn this paper we analyze this problem from the viewpoint of decision theory, the basic theory underlying all our activities – including economic ones.FindingsWe show how from the first-principles decision theory, we can extract explicit recommendations for group decision making.Originality/valueMost of the resulting recommendations have been proposed earlier. The main novelty of this paper is that it provides a unified coherent narrative that leads from the fundamental first principles to practical recommendations.

On the Finding of an Equilibrium: Düpp e–Weintraub and the Problem of Scientific Credit

In this review article, I read a book that revolves around two papers published in 1954, one by Lionel McKenzie, and the other by Kenneth Arrow and Gérard Debreu—Till Düppe and E. Roy Weintraub’s Finding Equilibrium: Arrow, Debreu, McKenzie and the Problem of Scientific Credit (2014). Under a tripartite categorization of people, context, and credit, this book advances the claim that “by being applied, interpreted, shaped, and reshaped, [these] proofs came to symbolize a new intellectual culture in American economics and help reconstruct the body of economic knowledge” (Düppe and Weintraub 2014, p. 204). My reading leads me to contest this claim, and also to contest whether a history of economic analysis, much less a history of economic thought, can be written by taking refuge in the vernacular of ancillary discourses orthogonal to the subject matter whose history is being written, and without the disciplinary criteria that these discourses operate under. An unintended consequence of my reading is the identification of lacunae in the reception of these proofs, an underscoring of Paul A. Samuelson’s panoramic vision, and a reemphasis of the sterling contributions of David Gale, Thomas Kuhn, Hukukane Nikaido, and Hirofumi Uzawa. (JEL A14, B23, B30, C60)

Fundamentos teóricos de la Economía de la Salud

Es indiscutible y cada vez más aceptada la relación que existe entre la salud y la economía. A su vez, la importancia de esta última incide tanto en la prestación de servicios médicos como en el impacto social relacionado con el bienestar colectivo como motor de crecimiento y desarrollo, la disminución de la pobreza, el aumento de la esperanza de vida y la calidad de ésta. La Economía de la Salud es una disciplina relativamente nueva que comienza a surgir en la década de 1970, donde Kenneth Arrow sienta las bases con su conocido artículo “La incertidumbre y el análisis de bienestar de las prestaciones médicas” donde analiza las características que hacen que el mercado de servicios de salud se inserte dentro de los mercados llamados “imperfectos”. La Economía de la Salud busca ganancias en salud atendiendo a dos premisas: eficacia y eficiencia en la asignación de los recursos.

The Fuzzy Completeness Theory

The Two Incompleteness Theorems of Kurt Friedrich Gödel and the Impossibility Theorem of Kenneth Arrow claim that logic, the most reliable of human knowledge, is incomplete or can be inconsistent. The Fuzzy Completeness Theory states that the Fuzzy Logic of Lotfi A. Zadeh has resolved the incompleteness and impossibility in logic and made logic complete and knowledge reliable with the new concept of Range of Tolerance, within which logic is still complete and knowledge, valid. In the Age of Reason about 300 years ago just prior to the Age of Science, reasoning is free for all, without the constraint of the laws of nature, which would be discovered in the Age of Science. However, the Scientific Method of reasoning by empirical verification depends so much on faith that it is logically and empirically dismissed by mathematicians and logicians, especially, after the exposure by Thomas Kuhn and Paul Feyerabend that a scientific advancement is akin to a religious conversion. On the other hand, mathematicians and logicians have been working steadily to find the limit of reliable knowledge. In the current state of knowledge, Kurt Gödel has the last word with his Two Incompleteness Theorems, which conclude that the most reliable of human knowledge, logic, is incomplete, casting doubt whether knowledge is completely reliable. Gödel’s view is further supported by the Impossibility Theorem of Kenneth Arrow. However, Zadeh and the author of this paper extend Zadeh’s concept of Range of Value in Fuzzy Logic to that of Range of Tolerance. Accordingly, Fuzzy Logic deals with the sacrifice of precision in the process of expanding the Range of Tolerance of a creation in order for the creation to survive and flourish for all the possibility of an uncertain future. In knowledge, incompleteness in logic can be resolved by the Range of Tolerance covering the incomplete part or ignoring the infrequent impossibilities, and, thus, making logic valid, again. Knowledge is derived generally from reason. Technically, the Fuzzy Completeness Theory classifies 16 Methods of Reason. The 16 Methods are the combination of the 4 basic Methods of Reason: 1) Logic, 2) Mathematics, 3) Empirical Verification, and 4) Others, each of which has 2 forms: 1) Fuzzy and 2) Exact and two types: 1) Complete and 2) Incomplete. Gödel, Arrow, and the Author agree that no matter how rigorous is the Method of Reason the reason cannot be complete, when the reason is Exact. When a solution is newly defined as an answer within the Range of Tolerance of the solution, Fuzzy Logic resolves the incompleteness in logic and becomes the new foundation of knowledge, replacing Exact Logic. With this definition of a solution, Fuzzy Logic covers the incomplete or the impossible parts of the solution by expanding sufficiently the Range of Tolerance to make reason complete and knowledge reliable, but only within the Range of Tolerance. To summarize, even though the world’s leading intellectuals have proven, directly, that logic is incomplete and, indirectly, that knowledge is invalid, reality is still operating smoothly, and science has even demonstrated the power of knowledge. The conflict between the most reliable knowledge, namely, logic and the real world is resolved by Fuzzy Logic, which introduces the new concept of Range of Tolerance, within which reality can still operate in accordance with the laws discovered by knowledge. In sum, reality is fuzzy, not exact. The breakthrough impact of this paper centers around completeness theory and Fuzzy Logic. In the early 21st century, the mainstream knowledge is still not aware that the supply and demand model is incomplete, and that the DNA-protein system resembles computer science based on logic more than science based on experimentation. The current computer is based on exact logic and is designed for temporary existence, while the living system is design for permanent existence and must depend on the Range of Tolerance based on Fuzzy Logic to survive permanently in an uncertain future. Financial crises will be caused by the unstable investment return, which is the incomplete part in the supply demand model. Complexity crises will be caused by the lack of the requirement of permanence or complete automation, which is the ultimate solution to unlimited complexity. The 16 Methods of Reason correspond roughly to Culture Level Quotient (CLQ), which is a non-technical measure of a person, a people or a nation.

Dual Moments and Risk Attitudes

The well-known Pratt–Arrow approximation, developed independently by John W. Pratt and Kenneth Arrow, provides an insightful dissection of the risk premium under the expected utility (EU) model. It is given by one-half the product of the variance of the risk and the local index of absolute risk aversion of the decision maker. Quite surprisingly, despite many important developments on “global” risk aversion in non-EU models, the “local” approach to risk aversion has received little attention outside EU. By considering the first two dual moments, mean and maxiance, on equal footing with the first two primal moments, mean and variance, the authors develop a dissection of the risk premium under the popular rank-dependent utility (RDU) model. This yields a simple approximation to the risk premium and a local index of absolute risk aversion under the RDU model.

A Century of Economics and Engineering at Stanford

This article documents the disciplinary exchanges between economists and engineers at Stanford throughout the twentieth century. We outline the role of key scholars such as Kenneth Arrow and Robert Wilson, as well as engineers turned administrators like Frederick Terman. We show that engineers drew upon economic theories of decision and allocation to improve practical industrial management decisions. Reciprocally, economists found in engineering the tools that they needed to rethink production and growth theory (including linear programming, optimal control theory, an epistemology of “application” that emphasized awareness to institutional details, trials and errors and experiments). By the 2000s, they had turned into economic engineers designing markets and other allocation mechanisms. These cross-disciplinary exchanges were mediated by Stanford’s own institutional culture, notably its use of joint appointments, the development of multidisciplinary “programs” for students, the ability to attract a variety of visitors every year, the entrepreneurial and contract-oriented vision of its administrators, and the close ties with the industrial milieu that came to be called the Silicon Valley.

Research and Development, Testing, and the Economics of Information, 1937–63

American mathematicians’ contributions to the engineering and production of equipment in World War II included the exploration of ways to improve choices between competing designs and maximize the value of experimental testing of prototypes. After the war, these contributions were extended, particularly at the RAND Corporation. Working on such matters, Kenneth Arrow took a keen interest in testing as a paradigm for information gathering in economic decision-making and in encouraging investment in R&D as an information-gathering exercise essential to making informed choices in military systems acquisition. He later extended insights about the shortcomings of information gathering as a market activity to his touchstone analysis of disparities of information between physician and patient as a crucial aspect of the economics of medical care. While it is difficult to trace the precise influence of the work of Arrow and others around him on engineering and R&D management, the issues they grappled with have remained relevant for more than half a century.

The Origins of the CES Production Function

The CES production function was introduced to economics in the 1961 paper “Capital-Labor Substitution and Economic Efficiency,” by Kenneth Arrow, Hollis Chenery, Bagicha Minhas, and Robert Solow. The paper had an immediate and substantial impact on economic research, and the CES production function remains an important tool for both theoretical and empirical researchers. I review how the CES production function was derived and used in the paper, and, relying on archival sources, present a fine-grained account of the collaborative process that produced the paper. I also discuss the CES production function as an example of multiple simultaneous discovery and suggest reasons for its broad and rapid diffusion.

An Economist's Miscellany

The book ranges over a vast canvas of experience, from the world of economics, covering glimpses of life and thought in academe and universities, to policymaking and politics. The author comments on contemporary debates in economics and politics and presents his own ideas and criticisms. The book is interspersed with commentaries on personalities, places, and theories of economics. The personalities we encounter here range from Nobel laureates, Kenneth Arrow, Paul Samuelson, and Amartya Sen, to the author’s mother at the age of 90. The places described in the book range from Jerusalem and Florence, to the foothills of Mount Fuji in Japan to Monte Alban in Mexico. In this book, the author talks about his encounters both philosophical and comical. This expanded edition of An Economist’s Miscellany also contains author’s literary forays with translations of two Bengali short stories and a four-act play about a professor of philosophy. This book brings together an eclectic collection of writings on the world of academe, politics, policy, travel, and more.