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.

In this note I consider a simple proof of Arrow's Impossibility Theorem (Arrow 1963). I start with the case of three individuals who have preferences on three alternatives. In this special case there are 133=2197 possible combinations of the three individuals' rational preferences. However, by considering the subset of linear preferences, and employing the full strength of the IIA axiom, I reduce the number of cases necessary to completely describe the SWF to a small number, allowing an elementary proof suitable for most undergraduate students.

Social choice and telling the truth

Perhaps the most influential result in social choice theory is Arrow’s impossibility theorem, which states that a seemingly modest set of desiderata cannot be satisfied when aggregating preferences [1]. While Arrow’s theorem might appear rather negative, it can also be interpreted in a positive way by identifying what can be achieved in preference aggregation.In this talk, I present a number of variations of Arrow’s theorem–such as those due to Mas-Colell and Sonnenschein [8] and Blau and Deb [2]–in their choice-theoretic version. The critical condition in all these theorems is the assumption of a rationalizing binary relation or equivalent notions of choice-consistency. The bulk of my presentation contains three escape routes from these results. The first one is to ignore consistency with respect to a variable set of alternatives altogether and require consistency with respect to a variable electorate instead. As Smith [12] and Young [14] have famously shown, this essentially characterizes the class of scoring rules, which contains plurality and Borda’s rule. For the second escape route, we factorize choice-consistency into two parts, contraction-consistency and expansions-consistency [11]. While even the mildest dose of the former has severe consequences on the possibility of choice, varying degrees of the latter characterize a number of appealing social choice functions, namely the top cycle, the uncovered set, and the Banks set [3,9,4]. Finally, I suggest to redefine choice-consistency by making reference to the set of chosen alternatives rather than individual chosen alternatives [6]. It turns out that the resulting condition is a weakening of transitive rationalizability and can be used to characterize the minimal covering set and the bipartisan set. Based on a two decades-old conjecture due to Schwartz [10], the tournament equilibrium set can be characterized by the same condition or, alternatively, by a weak expansion-consistency condition from the second escape route. Whether Schwartz’s conjecture actually holds remains a challenging combinatorial problem as well as one of the enigmatic open problems of social choice theory.Throughout the presentation I will discuss the algorithmic aspects of all considered social choice functions. While some of the mentioned functions can be easily computed, other ones do not admit an efficient algorithm unless P equals NP [13,5,7].

Extension of Arrow's theorem to symmetric sets of tournaments

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.

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.

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.

The specifics of pubic choice under representative democracy are considered in the seventh chapter of the textbook. The factors of forming of coalitions in parliament are analyzed. The methods of voting manipulation including the formulation of Arrow's impossibility theorem are described. The concept of logrolling is distinguished. The chapter also includes further readings, control tests and questions.

Now revised and updated, this introduction to decision theory is both accessible and comprehensive, covering topics including decision making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, with all concepts and results explained in non-technical and intuitive as well as more formal ways. There are now over 140 exercises with solutions, along with a glossary of key terms and concepts. This second edition includes a new chapter on risk aversion as well as updated discussions of numerous central ideas, including Newcomb's problem, prisoner's dilemmas, and Arrow's impossibility theorem. The book will appeal particularly to philosophy students but also to readers in a range of disciplines, from computer science and psychology to economics and political science.

Baryshnikov presented a remarkable algebraic topology proof of Arrow's impossibility theorem trying to understand the underlying reason behind the numerous proofs of this fundamental result of social choice theory. We present here a novel combinatorial topology approach that does not use advanced mathematics, while giving a geometric intuition of the impossibility. This exposes a remarkable connection with distributed computing techniques.

Now revised and updated, this introduction to decision theory is both accessible and comprehensive, covering topics including decision making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, with all concepts and results explained in non-technical and intuitive as well as more formal ways. There are now over 140 exercises with solutions, along with a glossary of key terms and concepts. This second edition includes a new chapter on risk aversion as well as updated discussions of numerous central ideas, including Newcomb's problem, prisoner's dilemmas, and Arrow's impossibility theorem. The book will appeal particularly to philosophy students but also to readers in a range of disciplines, from computer science and psychology to economics and political science.

Chapter 3 - First-Best and Second-Best Analyses and the Political Economy of Public Sector Economics

Welfare economics is the study of decision‐making with the aim of enhancing social welfare, in contrast to an individual's happiness or a firm's profit. This subject should be of value to government (since government is meant to be an agency for promoting social welfare); to an individual who is not committed solely to enhancing his or her own happiness; or even to the “enlightened” firm or business corporation that seeks not only to increase its profit but also has some commitment to the general well‐being of society. Welfare economics has two main concerns: (i) the abstract problem of deciding what constitutes social welfare; and (ii) the more mundane one of deciding how to choose between projects, taxation schemes, industrial regulation, environmental policy, and so on, given some agreed‐upon notion of social welfare. The most influential position has been a utilitarian one – however, it has been criticized. This analysis looks at Vilfredo Pareto's Pareto Optimality and Arrow's impossibility theorem; and it recognizes the place of welfare economics in the economist's repertoire.

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