Arrow's Impossibility Research Articles

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.

Arrovian Aggregation of Convex Preferences

We consider social welfare functions that satisfy Arrow's classic axioms ofindependence of irrelevant alternativesandPareto optimalitywhen the outcome space is the convex hull of some finite set of alternatives. Individual and collective preferences are assumed to be continuous and convex, which guarantees the existence of maximal elements and the consistency of choice functions that return these elements, even without insisting on transitivity. We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation. The domains admit arbitrary preferences over alternatives, which completely determine an agent's preferences over all mixed outcomes. On these domains, Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings involving divisible resources such as probability, time, or money.

The importance of social learning for non-market valuation

Neoclassical valuation methods often measure the contribution that non-market goods make to utility as income compensations. This circumvents Arrow's impossibility (AI) –a theoretical proof establishing the impossibility of social preferences – but those methods cannot be used in all settings. We build on Arrow's original proof, showing that with two additional axioms that allow for social learning, a second round of preference elicitation with a social announcement after the first, generates logically consistent social preferences. In short: deliberation leads to convergence. A ‘web-game’ aligning with this is trialed to select real world projects, in a deliberative way, with the board of an Australian Aboriginal Corporation. Analysis of the data collected in the trial validates our theory; our test for convergence is statistically significant at the 1% level. Our results also suggest complex social goods are relatively undervalued without deliberation. Most non-market valuation methods could be easily adapted to facilitate social learning.

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.

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.

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.

Deflecting Arrow by Aggregating Rankings of Multiple Correlated Criteria According to Borda

AbstractThis paper has two objectives. The first is to review and address concerns raised by Hazelrigg that Arrow's impossibility theorem prevents the selection of rational aggregation methods for use in engineering trade studies. In addressing these concerns, the work of Saari is cited to establish the fact that the Borda count is the only ‘non‐dictatorial’ positional voting method that satisfies the criteria for a rational decision procedure while using complete information. Hence, the resulting rank ordering of the alternatives is the most reliable outcome. Several previous studies that use other aggregation methods are critiqued, and Borda is applied to examples to illustrate the differences in the outcomes. The second objective is to extend the applicability of Borda to include attributes such as cost, schedule duration, and certain technical and performance measures that are generally more reasonably described as correlated random variables. Exact Probabilities by Simulation with Borda, a method introduced by Hulkower that improves a technique by Book for determining which candidate in a trade study is the probable lowest‐cost alternative, is generalized to include multiple correlated criteria, each of which is expressed as a random variable and thus incorporates probabilistic uncertainty. Copyright © 2016 John Wiley & Sons, Ltd.

Natural Deduction for Modal Logic of Judgment Aggregation

We can formalize judgments as (consistent sets of) logical formulas. Judgment aggregation deals with judgments of several agents, which need to be aggregated to a collective judgment. There are several logical formalizations of judgment aggregation. This paper focuses on a modal formalization which nicely expresses classical properties of judgment aggregation rules and famous results of social choice theory, like Arrow's impossibility theorem. A natural deduction system for modal logic of judgment aggregation is presented in this paper. The system is sound and complete. As an example of derivation, a formal proof of Arrow's impossibility theorem is given.

The Parliament and the efficient allocation of budget funds

The paper provides an in-depth analysis of a parliamentary procedure of making decisions concerning the budget funds distribution. The author was the first who gave legal interpretation of the classical economic Arrow's impossibility theory. Applying these ideas to analyze budget distribution procedure, the author proves that the Parliament cannot make effective decisions concerning the distribution of budget funds. Thus, the exclusive power of the Parliament to approve the budget is brought into question.

Crítica de la teoría de la elección racional. Esquema administrativo de competencia y cooperación

This research concerns how the notion of rationality, the representative individual of the rational choice theory, which elects administrative environment, is incapable of social-solidarity interaction generalizations: reflected in game theory and theorem Arrow's impossibility. Which is explained by the type of axioms of a rational individual, a condition that brings inconsistencies between competitive and cooperative strategies. Instead, a place culturalist context if the combination is competitive and cooperative strategies, leading to collective action or social interaction.

Information Support of Management Control in Information Asymmetry and Modern Instability

Information support model of management control is provided for building an integrated information system which collects detailed information about the state of the company on the strategic, tactical and operational levels of management and directions. Its construction is based on the concept of 4Ms and the pyramid of efficiency. The exact model designed for information support of management control has been formed by assessing 3 alternative models (conviction, cooperation and pragmatism) and selected on the basis of the strategy of the company, its specifics and existing features of the environment in which it functions. Taking into account the factors of instability in the formation of information support of management control for managerial decision-making it is reasonable to rely on such methods as adjustments, risk analysis and sensitivity analysis. Based on Arrow's impossibility theorem and the existing state of the management control systems regarding determination of groups of indicators, which will be monitoring effectiveness, it is expedient to introduce a dictatorial approach.