Results for 'Pareto efficiency'

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  1.  57
    Pareto efficiency in multiple referendum.Tuğçe Çuhadaroğlu & Jean Lainé - 2012 - Theory and Decision 72 (4):525-536.
    We consider situations of multiple referendum: finitely many yes-or-no issues have to be socially assessed from a set of approval ballots, where voters approve as many issues as they want. Each approval ballot is extended to a complete preorder over the set of outcomes by means of a preference extension. We characterize, under a mild richness condition, the largest domain of top-consistent and separable preference extensions for which issue-wise majority voting is Pareto efficient, i.e., always yields out a (...)-optimal outcome. Top-consistency means that voters’ ballots are their unique most preferred outcome. It appears that the size of this domain becomes negligible relative to the size of the full domain as the number of issues increases. (shrink)
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  2.  36
    The pareto efficiency and expected costs of k-majority rules.Keith L. Dougherty & Julian Edward - 2004 - Politics, Philosophy and Economics 3 (2):161-189.
    Florida International University, USA edwardj{at}fiu.edu ' + u + '@ ' + d + ' '/ /- -> Several authors have analyzed the optimal k -majority rule based on a variety of criteria. Buchanan and Tullock argued that, in constitutional settings, the criterion should be that all changes meet the Pareto criterion; otherwise the status quo should be preferred. They then asserted that unanimity rule would be the preferred voting rule in this setting. In parliamentary settings, they claimed that (...)
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  3. The Pareto efficiency and expected cost of k-majority rules: a probabilistic study of 'The Calculus of Consent'.Keith L. Dougherty & Julian Edward - forthcoming - Politics, Philosophy and Economics.
     
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  4.  39
    Pareto Efficiency, Egalitarianism, and Difference Principles.Julian Lamont - 1994 - Social Theory and Practice 20 (3):311-325.
  5.  89
    Welfare, Justice, and Pareto Efficiency.Sven Ove Hansson - 2004 - Ethical Theory and Moral Practice 7 (4):361-380.
    In economic analysis, it is usually assumed that each individuals well-being (mental welfare) depends on her or his own resources (material welfare). A typology is provided of the ways in which one persons well-being may depend on the material resources of other persons. When such dependencies are taken into account, standard Paretian analysis of welfare needs to be modified. Pareto efficiency on the level of material resources need not coincide with Pareto efficiency on the level of (...)
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  6.  72
    Legal Necessity, Pareto Efficiency & Justified Killing in Autonomous Vehicle Collisions.Geoff Keeling - 2018 - Ethical Theory and Moral Practice 21 (2):413-427.
    Suppose a driverless car encounters a scenario where harm to at least one person is unavoidable and a choice about how to distribute harms between different persons is required. How should the driverless car be programmed to behave in this situation? I call this the moral design problem. Santoni de Sio defends a legal-philosophical approach to this problem, which aims to bring us to a consensus on the moral design problem despite our disagreements about which moral principles provide the correct (...)
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  7.  23
    Optimization of multiple criteria: Pareto efficiency and fast heuristics should be more popular than they are.Peter Schuster - 2013 - Complexity 18 (2):5-7.
  8.  45
    A Contractarian Approach to Pareto Efficiency in Teams: A Note.Raul V. Fabella - 2000 - Theory and Decision 48 (2):139-149.
    We show that if identical members first decide on the sharing technology (stage I) taking into account their subsequent effort supply (stage II) decisions, the resulting contractarian sharing technology (constitution) channels individual self-seeking towards team (Pareto) optimum. Voting with one's feet and open entry can ensure symmetry and majoritarian decision making in the real world teams. The model helps explain the differential performance of the Israeli Kibbutz and the Russian Kolkhoz.
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  9.  44
    Generalized sharing, membership size and pareto efficiency in teams.Raul V. Fabella - 2000 - Theory and Decision 48 (1):47-60.
    We first show that the Generalized Sharing mechanism which is exhaustive, allows a team of identical members voluntarily supplying the observable effort to attain Pareto efficient production under increasing returns provided team size is allowed to vary. We then show that where true effort is imperfectly observable (moral hazard) Pareto efficient production under nonconstant returns to scale is still attainable by varying team size.
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  10.  41
    An Evolutionary Efficiency Alternative to the Notion of Pareto Efficiency.Irene van Staveren - 2012 - Economic Thought 1 (1).
    The paper argues that the notion of Pareto efficiency builds on two normative assumptions: the more general consequentialist norm of any efficiency criterion, and the strong no-harm principle of the prohibition of any redistribution during the economic process that hurts at least one person. These normative concerns lead to a constrained and static notion of efficiency in mainstream economics, ignoring dynamic efficiency gains from more equal allocations of resources. The paper argues that a weak no-harm (...)
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  11.  25
    Justice-constrained libertarian claims and pareto efficient collective decisions.Wulf Gaertner - 1985 - Erkenntnis 23 (1):1 - 17.
    This paper discusses justice-constrained libertarian claims that were proposed as a way to circumvent the impossibility of the Paretian liberal. Since most of the results are negative in character, we suggest an alternative route: A requirement on the structure of individual orderings should be combined with the idea that under particular circumstances individual decisiveness should be controlled by higher-order principles.
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  12.  83
    Is the “Point” of the Market Pareto or Kaldor-Hicks Efficiency?Heath Joseph - 2019 - Business Ethics Journal Review 7 (4):21-26.
    Moriarty argues that the Market Failures Approach to business ethics is inapplicable to “real world” problems, because it treats “market failure” as a failure to achieve Pareto efficiency. Depending upon how it is applied, Pareto efficiency is either trivially easy to satisfy or else so demanding that no real-world market could ever satisfy it. In this Commentary, I argue that Moriarty overstates these difficulties. The regulatory structure governing markets is best understood as an attempt to maximize (...)
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  13.  50
    The pareto argument and inequality.Patrick Shaw - 1999 - Philosophical Quarterly 49 (196):353-368.
    The Pareto argument for inequality holds that any change from a position of equality to one of inequality is justified so long as everyone benefits from the change. G.A. Cohen criticizes this argument (which he attributes to Rawls) on the ground that changes can normally be found which preserve both equality and Paretoefficiency. However, this does not resolve the basic conflict between the two desiderata. Strong egalitarians hold that Pareto changes are not for the better if (...)
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  14. What’s the Point of Efficiency? On Heath’s Market Failures Approach.Richard Endörfer & Louis Larue - 2024 - Business Ethics Quarterly 34 (1):35 - 59.
    This article reviews and criticizes Joseph Heath’s market failures approach (MFA) to business ethics. Our criticism is organized into three sections. First, we argue that, even under the ideal assumptions of perfect competition, when markets generate Pareto-efficient distributions, Heath’s approach does not rule out significant harms. Second, we show that, under nonideal conditions, the MFA is either too demanding, if efficiency is to be attained, or not sufficiently demanding, if the goal of Pareto efficiency is abandoned. (...)
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  15.  42
    Efficiency and Ethically Responsible Management.Jeffery Smith - 2018 - Journal of Business Ethics 150 (3):603-618.
    One common justification for the pursuit of profit by business firms within a market economy is that profit is not an end in itself but a means to more efficiently produce and allocate resources. Profit, in short, is a mechanism that serves the market’s purpose of producing Pareto superior outcomes for society. This discussion examines whether such a justification, if correct, requires business managers to remain attentive to how their firm’s operation impacts the market’s purpose. In particular, it is (...)
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  16. Chapter 3 Efficiency and Wellbeing.Douglas MacKay - manuscript
    A principal rationale for public policy is to address market failures. Pareto efficiency is therefore a highly common and relatively non-controversial evaluative criterion for many policy analyses and is discussed at length in policy analysis texts. This makes sense, for Pareto improvements involve making at least one person better off without making anyone worse off. Who could object to that? But does efficiency deserve the prominence it enjoys in public policy? Is one policy option better than (...)
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  17. The choice of efficiencies and the necessity of politics.Michael Bennett - 2023 - Critical Review of International Social and Political Philosophy 26 (6):877-896.
    Efficiency requires legislative political institutions. There are many ways efficiency can be promoted, and so an ongoing legislative institution is necessary to resolve this choice in a politically sustainable and economically flexible way. This poses serious problems for classical liberal proposals to constitutionally protect markets from government intervention, as seen in the work of Ilya Somin, Guido Pincione & Fernando Tesón and others. The argument for the political nature of efficiency is set out in terms of both (...)
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  18.  5
    Efficiency.Russell Hardin - 2017 - In Robert E. Goodin, Philip Pettit & Thomas Pogge (eds.), A Companion to Contemporary Political Philosophy. Oxford, UK: Blackwell. pp. 563–571.
    In the vernacular, ‘efficiency’ typically concerns means. I can choose efficient rather than inefficient means to accomplish my ends. Or more generally, I can be efficient or inefficient in allocating my limited resources. If we could measure the aggregate utility or welfare of a society, as in Benthamite utilitarianism, we could say that a society is efficient in an analogous sense: it uses effective institutions to achieve the greatest possible welfare. But the normative notion of efficiency commonly in (...)
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  19.  41
    Stability and efficiency in perfect foresight situation.Yoshio Kamijo - 2013 - Theory and Decision 75 (3):339-357.
    We study the stable standard of behavior in a perfect foresight situation that was introduced by Xue. We assume that the inducement relations are invertible and coalition free. We show that the conditions are sufficient for the existence of the nonempty-valued optimistic/conservative stable standard of behavior for perfect foresight situation. Moreover, we find that an OSSB-PF supports a Pareto-efficient outcome as a stable outcome; if the preference relations are strict, only the Pareto-efficient outcomes are supported by the OSSB-PF.
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  20.  21
    Efficient Conical Area Differential Evolution with Biased Decomposition and Dual Populations for Constrained Optimization.Weiqin Ying, Bin Wu, Yu Wu, Yali Deng, Hainan Huang & Zhenyu Wang - 2019 - Complexity 2019:1-18.
    The constraint-handling methods using multiobjective techniques in evolutionary algorithms have drawn increasing attention from researchers. This paper proposes an efficient conical area differential evolution algorithm, which employs biased decomposition and dual populations for constrained optimization by borrowing the idea of cone decomposition for multiobjective optimization. In this approach, a conical subpopulation and a feasible subpopulation are designed to search for the global feasible optimum, along the Pareto front and the feasible segment, respectively, in a cooperative way. In particular, the (...)
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  21.  8
    A Limited Defense of Efficiency Against Charges of Incoherency and Bias.Jonathan H. Choi - 2022 - Social Philosophy and Policy 39 (1):252-267.
    Scholars have long debated the appropriate balance between efficiency and redistribution. But recently, a wave of critics has argued not only that efficiency is less important, but that efficiency analysis itself is fundamentally flawed. Some say that efficiency is incoherent because there is no neutral baseline from which to judge inefficiency. Others say that efficiency is biased toward those best able to pay (generally, the rich). This essay contends that efficiency is not meaningfully incoherent (...)
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  22.  35
    Stability and Efficiency of Partitions in Matching Problems.İpek Özkal-Sanver - 2005 - Theory and Decision 59 (3):193-205.
    We define two versions of stability and efficiency of partitions and analyze their relationships for some matching rules. The stability and efficiency of a partition depends on the matching rule φ. The results are stated under various membership property rights axioms. It is shown that in a world where agents can freely exit from and enter coalitions, whenever the matching rule is individually rational and Pareto optimal, the set of φ-stable and φ-efficient partitions coincide and it is (...)
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  23.  14
    Does collective rationality entail efficiency?Paul Weirich - 2010 - Logic Journal of the IGPL 18 (2):308-322.
    Collective rationality in its ordinary sense is rationality’s extension to groups. It does not entail efficiency by definition. Showing that it entails efficiency requires a normative argument. Game theorists treating cooperative games generally assume that collective rationality entails efficiency, but formulating the reasoning that leads individuals to efficiency, and verifying the rationality of its steps, presents challenging philosophical issues. This paper constructs a framework for addressing those issues and reaches some preliminary results about the prospects of (...)
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  24. Envy and efficiency.Joseph Heath - 2006 - Revue de Philosophie Économique 13.
    Joseph Heath1 The Pareto principle states that if a proposed change in the condition of society makes at least one person better off, and does not make anyone else worse off, then that change should be regarded as an improvement. This principle forms the conceptual core of modern welfare economics, and exercises enormous influence in contemporary discussions of justice and equality. It does, however, have an Achilles’ heel. When an individual experiences envy, it means that improvements in the condition (...)
     
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  25.  55
    Can economics rank slavery against free labor in terms of efficiency?Lawrence H. White - 2008 - Politics, Philosophy and Economics 7 (3):327-340.
    The standard allocative efficiency criteria used by economists (Pareto efficiency and Kaldor-Hicks efficiency) are fundamentally unable to rank a slave-labor system against a free-labor system. Given either set of initial property rights assignments the market can reach (or fail to reach) allocative efficiency (that is, allocate resources to their highest-valued uses), but welfare economics provides no meta-framework for ranking initial assignments. This finding underscores the limits to the usefulness of efficiency criteria: they cannot settle (...)
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  26. Scritti politici.Vilfredo Pareto - 1974 - [Torino]: Unione tipografico editrice torinese.
    v. 1. Lo sviluppo del capitalismo (1872-1895).--v. 2. Reazione, liberta, fascismo (1896-1923).
     
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  27.  4
    Shakaigaku taikō.Vilfredo Pareto - 1987 - Tōkyō: Aoki Shoten. Edited by Takayoshi Kitagawa, Akira Hirota & Tatsubun Itakura.
  28. How to Have your Cake and Eat it Too: Resolving the Efficiency- Equity Trade-off in Minimum Wage Legislation.Nikil Mukerji & Christoph Schumacher - 2008 - Journal of Interdisciplinary Economics 19:315-340.
    Minimum wages are usually assumed to be inefficient as they prevent the full exploitation of mutual gains from trade. Yet advocates of wage regulation policies have repeatedly claimed that this loss in market efficiency can be justified by the pursuit of ethical goals. Policy makers, it is argued, should not focus on efficiency alone. Rather, they should try to find an adequate balance between efficiency and equity targets. This idea is based on a two-worlds-paradigm that sees ethics (...)
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  29.  4
    Pages retrouvées.Vilfredo Pareto - 1988 - Genève: Libr. Droz. Edited by Giovanni Busino.
  30.  23
    Mind and society.Vilfredo Pareto - unknown
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  31.  8
    Punishing the weakest link - Voluntary sanctions and efficient coordination in the minimum effort game.Fabrice Le Lec, Astrid Matthey & Ondřej Rydval - 2023 - Theory and Decision 95 (3):429-456.
    Using a laboratory experiment, we examine whether voluntary sanctions induce subjects to coordinate more efficiently in a repeated minimum-effort game. While most groups first experience Pareto inferior coordination in a baseline treatment, the level of effort increases substantially once ex post sanctioning opportunities are introduced, that is, when one can assign costly punishment points to other group members to reduce their payoffs. We compare the effect of this voluntary punishment possibility with the effect of ex post costless communication, which (...)
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  32.  44
    Manual of Political Economy: A Variorum Translation and Critical Edition.Vilfredo Pareto - 2014 - Oxford University Press UK.
    Vilfredo Pareto's Manual of Political Economy is a 'classic' study in the history of economic thought. It is not only one of the leading works in the Lausanne tradition of economics, which centres on the theory of general equilibrium, it is one of the most important books in the history of neoclassical economics. This 'critical edition' of Pareto's Manual of Political Economy is a very significant work for two main reasons. First, it is the only variorum translation of (...)
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  33.  23
    Against Paretianism: A Wealth Creation Approach to Business Ethics.Carson Young - 2022 - Business Ethics Quarterly 32 (3):475-501.
    How should we distinguish between ethical and unethical ways of pursuing profit in a market? The market failures approach (MFA) to business ethics purports to provide an answer to this question. I argue that it fails to do so. The source of this failure is the MFA’s reliance on Pareto efficiency as a core ethical principle. Many ethically “preferred” tactics for seeking profit cannot be justified by appeal to Pareto efficiency. One important reason for this is (...)
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  34.  24
    Prolegómenos a una ética para la robótica social.Júlia Pareto Boada - 2021 - Dilemata 34:71-87.
    Social robotics has a high disruptive potential, for it expands the field of application of intelligent technology to practical contexts of a relational nature. Due to their capacity to “intersubjectively” interact with people, social robots can take over new roles in our daily activities, multiplying the ethical implications of intelligent robotics. In this paper, we offer some preliminary considerations for the ethical reflection on social robotics, so that to clarify how to correctly orient the critical-normative thinking in this arduous task. (...)
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  35.  66
    Target Rules for Public Choice Economies on Tree Networks and in Euclidean Spaces.Bettina Klaus - 2001 - Theory and Decision 51 (1):13-29.
    We consider the problem of choosing the location of a public facility either (a) on a tree network or (b) in a Euclidean space. (a) (1996) characterize the class of target rules on a tree network by Pareto efficiency and population-monotonicity. Using Vohra's (1999) characterization of rules that satisfy Pareto efficiency and replacement-domination, we give a short proof of the previous characterization and show that it also holds on the domain of symmetric preferences. (b) The result (...)
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  36. Agrifood systems for competent, ordinary people.Jane Adams & Efficiency Individualism - 1998 - Agriculture and Human Values 15:391-403.
     
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  37. Costs Law Expertise.Dgt Costs Lawyers Approachable Efficient Progressive - forthcoming - Ethos: Journal of the Society for Psychological Anthropology.
     
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  38.  53
    The Responsibilities and Role of Business in Relation to Society: Back to Basics?Nien-hê Hsieh - 2017 - Business Ethics Quarterly 27 (2):293-314.
    ABSTRACT:In this address, I outline a “back to basics” approach to specifying the responsibilities and role of business in relation to society. Three “basics” comprise the approach. The first is arguing that basic principles of ordinary morality, such as a duty not to harm, provide an adequate basis for specifying the responsibilities of business managers. The second is framing the role of business in society by looking to the values realized by the basic building blocks of contemporary economic activity, i.e., (...)
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  39. A market failures approach to justice in health.L. Chad Horne & Joseph Heath - 2022 - Politics, Philosophy and Economics 21 (2):165-189.
    Politics, Philosophy & Economics, Volume 21, Issue 2, Page 165-189, May 2022. It is generally acknowledged that a certain amount of state intervention in health and health care is needed to address the significant market failures in these sectors; however, it is also thought that the primary rationale for state involvement in health must lie elsewhere, for example in an egalitarian commitment to equalizing access to health care for all citizens. This paper argues that a complete theory of justice in (...)
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  40. First Come, First Served?Tyler M. John & Joseph Millum - 2020 - Ethics 130 (2):179-207.
    Waiting time is widely used in health and social policy to make resource allocation decisions, yet no general account of the moral significance of waiting time exists. We provide such an account. We argue that waiting time is not intrinsically morally significant, and that the first person in a queue for a resource does not ipso facto have a right to receive that resource first. However, waiting time can and sometimes should play a role in justifying allocation decisions. First, there (...)
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  41.  69
    The Implicit Morality of the Market and Joseph Heath’s Market Failures Approach to Business Ethics.Marc A. Cohen & Dean Peterson - 2019 - Journal of Business Ethics 159 (1):75-88.
    Joseph Heath defends competitive markets and conceptualizes business ethics with reference to Pareto efficiency, which he takes to be the “implicit morality of the market.” His justification for markets is that they generate Pareto efficient outcomes, meaning that markets optimally satisfy consumer preferences. And, for Heath, business ethics is the set of normative constraints—regulation and beyond-compliance norms—needed to preserve that outcome. The present paper accepts Heath’s claim that the economic justification for markets is ethical, in that satisfying (...)
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  42.  52
    The Inapplicability of the Market-Failures Approach in a Non-Ideal World.Etye Steinberg - 2017 - Business Ethics Journal Review 5 (5):28-34.
    Joseph Heath (2014) argues that the contribution of competitive markets to Pareto-efficiency generates moral constraints that apply to business managers. Heath argues that ethical behavior on the part of management consists in avoiding profit-seeking strategies which, under conditions of perfect competition, would decrease Pareto-efficiency. I argue that because (1) such conditions do not obtain; and (2) the most efficient result – under imperfect conditions – is not achieved by satisfying the largest possible set of the remaining (...)
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  43. The Benefits of Cooperation.Joseph Heath - 2006 - Philosophy and Public Affairs 34 (4):313-351.
    There is an idea, extremely common among social contract theorists, that the primary function of social institutions is to secure some form of cooperative benefit. If individuals simply seek to satisfy their own preferences in a narrowly instrumental fashion, they will find themselves embroiled in collective action problems – interactions with an outcome that is worse for everyone involved than some other possible outcome. Thus they have reason to accept some form of constraint over their conduct, in order to achieve (...)
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  44.  26
    Welfare Economic Dogmas: A Reply to Sagoff.Richard Cookson - 1996 - Environmental Values 5 (1):59-74.
    This article examines Sagoff's criticisms of 'Four Dogmas of Environmental Economies' and argues that none of them are fatal. Many of the criticisms appear to rest on general misunderstandings about welfare economics. One misunderstanding is that transaction costs are theoretically indistinguishable from regular production costs. The theoretical distinction is that transaction costs vary under alternative policies and institutions whereas production costs are fixed by tastes, technology and endowments. Another misunderstanding is that market failure concerns only Pareto efficiency. Market (...)
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  45. Political Egalitarianism.Joseph Heath - 2008 - Social Theory and Practice 34 (4):485-516.
    The term “political” egalitarianism is used here, not to refer to equality within the political sphere, but rather in John Rawls’s sense, to refer to a conception of egalitarian distributive justice that is capable of serving as the object of an overlapping consensus in a pluralistic society.1 Thus “political” egalitarianism is political in the same way that Rawls’s “political” liberalism is political. The central task when it comes to developing such a conception of equality is to determine what constraints a (...)
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  46.  8
    Freedom, Markets and Moral Motivation: Towards a More Adequate Account of the Implicit Morality of the Market.Caleb Bernacchio - 2024 - Journal of Human Values 30 (1):59-74.
    The market failures approach is amongst the most influential theories of business ethics. Its interest within the field is, in large part, a result of its rejection of moralism and any sort of applied ethics approach, favouring, in contrast, a focus on the institutionally embodied goal of economic activity, which it takes to be that of Pareto efficiency. From this articulation of the goal, or purpose, of markets, a set of efficiency imperatives are derived that are taken (...)
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  47.  15
    Elements for a Normative Theory of Privatization.Rutger Claassen - 2024 - Erasmus Journal for Philosophy and Economics 16 (2):107-135.
    Heath’s paper on privatization defends a broadly welfarist-economic approach in thinking about the legitimacy of privatizations. This approach is ‘instrumentalist’ (in contrast to deontological approaches). In this response, I accept the value of an instrumentalist approach to privatization, but argue against Heath’s welfarist version of it, and argue in favor an alternative. First, the ends we seek when thinking about socially vital goods (our theory of public interests) should go beyond Pareto-efficiency. Second, as to the means we employ (...)
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  48.  24
    Corporate responsibility and the plurality of market aims.Jeffery Smith - 2019 - Business and Society Review 124 (2):183-199.
    A number of recent authors, most notably Joseph Heath, have persausively defended a market‐centered account of corporate responsibility that grounds standards of business conduct upon the normative presuppositions of the market. They have us focus on two important items: first, the value of welfare, or Pareto efficient outcomes, which underwrites the legitimacy of market arrangements; and second, the behavioral requirements needed to assure that corporations conduct business in a manner consistent with this value. This article critically examines the aspirations (...)
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  49. General Equilibrium Theory: An Introduction.Ross M. Starr - 2012 - Cambridge University Press.
    General Equilibrium Theory: An Introduction treats the classic Arrow-Debreu general equilibrium model in a form accessible to graduate students and advanced undergraduates in economics and mathematics. Topics covered include mathematical preliminaries, households and firms, existence of general equilibrium, Pareto efficiency of general equilibrium, the First and Second Fundamental Theorems of Welfare Economics, the core and core convergences, future markets over time and contingent commodity markets under uncertainty. Demand, supply, and excess demand appear first as functions, then optionally as (...)
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  50.  14
    Folk theorems in a bargaining game with endogenous protocol.Shiran Rachmilevitch - 2019 - Theory and Decision 86 (3-4):389-399.
    Two players bargain to select a utility allocation in some set X⊂R+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\subset {\mathbb {R}}_+^2$$\end{document}. Bargaining takes place in infinite discrete time, where each period t is divided into two sub-periods. In the first sub-period, the players play a simultaneous-move game to determine that period’s proposer, and bargaining takes place in the second sub-period. Rejection triggers a one-period delay and move to t+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t+1$$\end{document}. For (...)
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