Arrow's Impossibility Theorem Research Articles

아마르티아 센의 파레토적 자유주의 불가능성에 대한 공공선택학파의 반론

Kenneth’s Arrow Impossibility Theorem revealed dismal prospect to democracy, Amartya Sen’s Impossibility Theorem of Paretian Libertarianism provoked deep pessimism to Libertarianism. This paper synthesize critique by Public Choice School on Sen’s theorem comprising three points. Firstly, Sen misunderstood individuals as picking ‘social states’, which he regarded as complete description of society including all individual positions on it. Actually, however, individuals just choose particular aspect. Secondly, Sen’s impossibility basically comes from externality of individual’s preference. Public Choice scholars revealed, by designing proper game model under externality, Pareto optimality comes along with libertarian choice. Thirdly, Sen’s Impossibility Theorem is just short-term equilibrium showing contradiction between Pareto principle and Libertarian principle. Buchanan proves that paradox can be resolved through mutual coordination between individuals who are under Paretian inferior equilibrium. This paper suggests some implication as follows. Firstly, Libertarianism in Sen’s sense is far from normal meaning of liberty. Without proper conceptual modification, his theorem needs to be renamed. Secondly, If Sen’s Impossibility Theorem under U-condition can never exclude some cases in which two principles can coexist, then his theorem can be renamed as “Impossibility of Sen’s Impossibility of Paretian Libertarianism”. Thirdly, Public Choice theorists properly proved Paretian Libertarianism is possible, showing Sen exaggerated the paradox. Then, as Arrow’s theorem can be interpreted as ‘Possibility’ Theorem, considering substantial stability of actual collective choice situation, Sen’s theorem also can be re-interpreted as ‘Possibility’ Theorem of Paretian Libertarianism. Two camps needs to confront each other again towards the empirical proof on it.

Incomparability and Incommensurability in Choice: No Common Currency of Value?

Models of decision-making typically assume the existence of some common currency of value, such as utility, happiness, or inclusive fitness. This common currency is taken to allow comparison of options and to underpin everyday choice. Here we suggest instead that there is no universal value scale, that incommensurable values pervade everyday choice, and hence that most existing models of decision-making in both economics and psychology are fundamentally limited. We propose that choice objects can be compared only with reference to specific but nonuniversal "covering values." These covering values may reflect decision-makers' goals, motivations, or current states. A complete model of choice must accommodate the range of possible covering values. We show that abandoning the common-currency assumption in models of judgment and decision-making necessitates rank-based and "simple heuristics" models that contrast radically with conventional utility-based approaches. We note that if there is no universal value scale, then Arrow's impossibility theorem places severe bounds on the rationality of individual decision-making and hence that there is a deep link between the incommensurability of value, inconsistencies in human decision-making, and rank-based coding of value. More generally, incommensurability raises the question of whether it will ever be possible to develop single-quantity-maximizing models of decision-making.

Ethics without numbers

AbstractThis paper develops and explores a new framework for theorizing about the measurement and aggregation of well‐being. It is a qualitative variation on the framework of social welfare functionals developed by Amartya Sen. In Sen's framework, a social or overall betterness ordering is assigned to each profile of real‐valued utility functions. In the qualitative framework developed here, numerical utilities are replaced by the properties they are supposed to represent. This makes it possible to characterize the measurability and interpersonal comparability of well‐being directly, without the use of restrictive invariance conditions, and to distinguish between real changes in well‐being and merely representational changes in the unit of measurement. The qualitative framework is shown to have important implications for a range of issues in axiology and social choice theory, including the characterization of welfarism, axiomatic derivations of utilitarianism, the meaningfulness of prioritarianism, the informational requirements of variable‐population ethics, the impossibility theorems of Arrow and others, and the metaphysics of value.

Definition of conceptual basics of nanoeconomics as inclusive society environment

The definition of nanoeconomics can relate to different levels and areas of economic life. First of all, this is the nanolevel of the economic system. As a human economy, nanoeconomics provides for the allocation of an individual factor within the framework of a socio-economic phenomenon. The nanoeconomic aspect is central to the definition of inclusion. So, the inclusion of a person, as the main subject of nanoeconomics, to the formation and stabilization of economic systems is the initial one in the integration of an individual in relation to production processes and economic development. A person is involved in academic and social life by making decisions about their own business and integrating it into the sectoral and national economic space. It is proved that its indicators are the conditions for clustering the economic system. The study carried out a cluster analysis of the innovation system in a country with an economy in transition. In addition, the study outlined that inclusive phenomena in the economy are close to integration and are the opposite of segregation and isolation. It is noted that different institutions of integration can be used to form objective conditions for the development of babyeconomics. Public decisions of inclusion involve the use of Arrow's impossibility theorem. The research results can be used: – the individualistic functions of inclusion should be used in the formation of the babyeconomics, the human economy and the economy of nanotechnology; – states of inclusion must be created at all levels of the economic system; – a person and wealth are an individualistic aspect of an inclusive economy, because national wealth consists of individual wealth. Nanoeconomics is just beginning to be included in the systemic processes of inclusive economic phenomena, especially in countries with economies in transition

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.

COVID-19 Vaccine Mandates and Arrow's Impossibility Theorem

COVID-19 Vaccine Mandates and Arrow's Impossibility Theorem

Aggregating multiple ordinal rankings in engineering design: the best model according to the Kendall\u2019s coefficient of concordance

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.

Editorial

Editorial

Kenneth Joseph Arrow. 23 August 1921—21 February 2017

Kenneth Arrow was a mathematical economist and political scientist who made many ground-breaking contributions to the theory of economics and social values. His great mathematical ability led him to introduce new approaches to theoretical economics and in particular to a series of fundamental theorems in the discipline. These included the Arrow Impossibility Theorem, the two fundamental theorems of welfare economics and the existence of a competitive equilibrium. For these and many other contributions he was awarded the 1972 Nobel Prize in Economics shared with Sir John Hicks. He took a particular interest in computation and computability in economics. He was active and very productive as a researcher for over seven decades and was renowned as a generous and inspiring teacher and colleague.

Radical Interpretation and The Aggregation Problem

This paper takes issue with Lewis’ influential argument for the supervenience of the semantic on the non‐semantic based on the possibility of radical interpretation. Radical interpretation is possible only if an ideal being, who is omniscient about the non‐semantic truths, can deduce the semantic truths a priori. The radical interpreter appeals to a set of criteria of interpretation choice, such as most notably some kind of Principle of Charity.It is argued in this paper that the radical interpreter faces an insoluble aggregation problem: the radical interpreter must jointly apply several criteria for evaluating interpretations in order to determine which interpretation is best overall. First, the situation of the radical interpreter is formally modeled using the machinery of social choice theory. Second, it is argued that either Arrow's impossibility theorem or a variant of it applies to the situation of the radical interpreter. The upshot is that radical interpretation is impossible, and Lewis’ argument for semantic supervenience fails.

How mathematical impossibility changed welfare economics: A history of Arrow's impossibility theorem

During the 20th century, impossibility theorems have become an important part of mathematics. Arrow's impossibility theorem (1950) stands out as one of the first impossibility theorems outside of pure mathematics. It states that it is impossible to design a welfare function (or a voting method) that satisfies some rather innocent looking requirements. Arrow's theorem became the starting point of social choice theory that has had a great impact on welfare economics. This paper will analyze the history of Arrow's impossibility theorem in its mathematical and economic contexts. It will be argued that Arrow made a radical change of the mathematical model of welfare economics by connecting it to the theory of voting and that this change was preconditioned by his deep knowledge of the modern axiomatic approach to mathematics and logic.

Cycles and Intractability in a Large Class of Aggregation Rules

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.

A difficulty in Arrow’s impossibility theorem

PurposeThe purpose of this paper is twofold. First, it evaluates the impossibility proposition, called the “Arrow impossibility theorem” (AIT), which is widely attributed to Arrow’s social choice theory. This theorem denies the possibility of arriving at any collective majority resolution in any group voting system if the social choice function must satisfy “certain natural conditions”. Second, it intends to show the reasons behind the proliferation of this impossibility impression.Design/methodology/approachTheoretical and philosophical.FindingsArrow’s mathematical model does not seem to suggest or support his impossibility thesis. He has considered only one voting outcome, well known by the phrase “the Condorcet paradox”. However, other voting results are equally likely from his model, which might suggest unambiguous majority choice. This logical dilemma has been created by Arrow’s excessive dependence on the language of mathematics and symbolic logic.Research limitations/implicationsThe languages of mathematics and symbolic logic – numbers, letters and signs – have definite advantages in scientific argumentation and reasoning. These numbers and letters being invented however do not have any behavioural characteristics, which suggests that conclusions drawn from the model merely reflect the author’s opinions. The AIT is a good example of this logical dilemma.Social implicationsThe modern social choice theory, which is founded on the AIT, seems to be an academic assault to the system of democratic governance that is dominating current global village. By highlighting weaknesses in the AIT, this paper attempts to discredit this intellectual omission.Originality/valueThe paper offers a counter example to show that the impossibility of social choice is not necessarily implied by the Arrow’s model. Second, it uses Locke’s theory of human understanding to explain why the concerned social scientists are missing this point. This approach is probably entirely novel in this area of research.

El espacio público en la ciudad: Una aproximación desde los precios hedónicos

Esta es una investigación aplicada al sistema de parques de Bogotá, la cual tiene como objetivo proponer un modelo econométrico de determinación del valor del suelo del espacio público. Dada la complejidad para valorar el suelo público, la investigación se desarrolla a partir de combinar las determinantes de la teoría de la elección social por medio del teorema de la imposibilidad de Arrow y el modelo de precios (haciendo énfasis en la estructura urbana). Frente a lo anterior, la Defensoría del Espacio Público de Bogotá ha obtenido, como principal resultado, la evidencia de que existe una alta valoración social del espacio público, poniendo como reto la incorporación de análisis económicos más refinados que describan las diferentes valoraciones que hace la sociedad del espacio público. Así mismo, se encontró que la presencia de espacios públicos en el contexto urbano influye altamente en la determinación de los precios del suelo privado.

Impossibility in belief merging

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 Pérez. 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.

Quantum voting and violation of Arrow's impossibility theorem

We propose a quantum voting system, in the spirit of quantum games such as the quantum Prisoner's Dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's Impossibility Theorem. Arrow's Theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's Theorem. A quantum version of majority rule, we show, violates this Quantum Arrow Conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.

A Very Easy Proof of Arrow's Impossibility Theorem Using Social Welfare Functionals

In this paper we provide Impossibility Theorems for social welfare functionals. We adapt the method of proving the inevitability of dictatorial Bergson-Samuelson social welfare functions for fixed utility profiles developed in a paper by Robert P. Parks in 1976. With a little more from results already available in the literature we are able to prove impossibility under conditions on the admissible set which are milder than the ones existing in the literature.

The Austrians and the Arrow Impossibility Theorem

Some economists in the Austrian tradition interpret the Arrow Impossibility Theorem (AIT) as support for their laissez-faire standpoint. They presume that the AIT cannot be applied in market settings, but in the context of voting,it adds weight to their arguments against the possibility of socialism and planning.The examples of Boettke (2001) and Boettke and Leeson (2002)are taken as examples. It is shown that their stance is founded on a misinterpretation of Arrow, and no compelling case for exempting markets from the AITis found. The Austrian writers draw on Buchanan’s critique of Arrow, which critique is in turn shown to be faulty and unreliable. Finally a possible avenue for future Austrian research is identified, showing that the AIT might not apply to markets.

How well does theory explain reality? - A case of Arrow's impossibility theorem

In this paper, we investigate how well Arrow's impossibility theorem, a typical no-existence proof, can explain real human decision-making. Since the conclusion of a no-existence proof is universal, it may also be useful to examine instances of illogical decision-making which are actually handled in reality if an Arrovian approach is seriously considered. Then, we try to modify the framework to reflect the actual decision-making situation as much as possible by allowing individuals to have their own sets of alternatives. Since individual sets of alternatives are varied in nature, Arrow's framework is not satisfied in general because a social ordering of all alternatives does not normally exist. Therefore, it may be concluded that Arrow's impossibility result holds not only in theory but also in reality. This conclusion may open up a way to manage an illogical social decision such as cyclical decision-making and strategic negotiation, among others which are popular and effective in actual decision-making.

How well does theory explain reality? - A case of Arrow's impossibility theorem

In this paper, we investigate how well Arrow's impossibility theorem, a typical no-existence proof, can explain real human decision-making. Since the conclusion of a no-existence proof is universal, it may also be useful to examine instances of illogical decision-making which are actually handled in reality if an Arrovian approach is seriously considered. Then, we try to modify the framework to reflect the actual decision-making situation as much as possible by allowing individuals to have their own sets of alternatives. Since individual sets of alternatives are varied in nature, Arrow's framework is not satisfied in general because a social ordering of all alternatives does not normally exist. Therefore, it may be concluded that Arrow's impossibility result holds not only in theory but also in reality. This conclusion may open up a way to manage an illogical social decision such as cyclical decision-making and strategic negotiation, among others which are popular and effective in actual decision-making.