A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market

We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities.Comment: Preliminary version in ICALP 201

Migration with local public goods and the gains from changing places

Without public goods and under fairly standard assumptions, in Hammond and Sempere (J Pub Econ Theory, 8: 145–170, 2006) we show that freeing migration enhances the potential Pareto gains from free trade. Here, we present a generalization allowing local public goods subject to congestion. Unlike the standard literature on fiscal externalities, our result relies on fixing both local public goods and congestion levels at their status quo values. This allows constrained efficient and potentially Pareto improving population exchanges regulated only through appropriate residence charges, which can be regarded as Pigouvian congestion taxes

Sen and the art of educational maintenance: evidencing a capability, as opposed to an effectiveness, approach to schooling

There are few more widely applied terms in common parlance than ‘capability’. It is used (inaccurately) to represent everything from the aspiration to provide opportunity to notions of innate academic ability, with everything in between claiming apostolic succession to Amartya Sen, who (with apologies to Aristotle) first developed the concept. This paper attempts to warrant an adaptation of Sen’s capability theory to schooling and schooling policy, and to proof his concepts in the new setting using research involving 100 pupils from 5 English secondary schools and a schedule of questions derived from the capability literature. The findings suggest that a capability approach can provide an alternative to the dominant Benthamite school effectiveness paradigm, and can offer a sound theoretical framework for understanding better the assumed relationship between schooling and well-being

Sorted-pareto dominance and qualitative notions of optimality

Pareto dominance is often used in decision making to compare decisions that have multiple preference values – however it can produce an unmanageably large number of Pareto optimal decisions. When preference value scales can be made commensurate, then the Sorted-Pareto relation produces a smaller, more manageable set of decisions that are still Pareto optimal. Sorted-Pareto relies only on qualitative or ordinal preference information, which can be easier to obtain than quantitative information. This leads to a partial order on the decisions, and in such partially-ordered settings, there can be many different natural notions of optimality. In this paper, we look at these natural notions of optimality, applied to the Sorted-Pareto and min-sum of weights case; the Sorted-Pareto ordering has a semantics in decision making under uncertainty, being consistent with any possible order-preserving function that maps an ordinal scale to a numerical one. We show that these optimality classes and the relationships between them provide a meaningful way to categorise optimal decisions for presenting to a decision maker

Trade uncertainty and the two-step procedure: The choice of numeraire and exact indexation

In a small open economy it is optimal to first maximize national income and second choose the best consumption point. The same two-step procedure under (quantitative) uncertainty is suboptimal if one of the goods is used as numéraire. Optimality is restored however, if nominal prices are deflated by the exact price index. Hence there is equivalence between the appropriate two-step procedure and the introduction of a stock market under uncertainty (Diamond 1967) under ideal circumstances

Index tracking with utility enhanced weighting

Passive index investing involves investing in a fund that replicates a market index. Enhanced indexation uses the returns of an index as a reference point and aims at outperforming this index. The motivation behind enhanced indexing is that the indices and portfolios available to academics and practitioners for asset pricing and benchmarking are generally inefficient and, thus, susceptible to enhancement. In this paper we propose a novel technique based on the concept of cumulative utility area ratios and the Analytic Hierarchy Process (AHP) to construct enhanced indices from the DJIA and S&P500. Four main conclusions are forthcoming. First, the technique, called the utility enhanced tracking technique (UETT), is computationally parsimonious and applicable for all return distributions. Second, if desired, cardinality constraints are simple and computationally parsimonious. Third, the technique requires only infrequent rebalancing, monthly at the most. Finally, the UETT portfolios generate consistently higher out-of-sample utility profiles and after-cost returns for the fully enhanced portfolios as well as for the enhanced portfolios adjusted for cardinality constraints. These results are robust to varying market conditions and a range of utility functions

Relationships Between Archimedean Copulas and Morgenstern Utility Functions

The (additive) generator of an Archimedean copula is a strictly decreasing and convexfunction, while Morgenstern utility functions (applying to risk aversion decision makers) arenondecreasing and concave. In this presentation, relationships between generators and utilityfunctions are established. For some well known Archimedean copula families, links betweenthe generator and the corresponding utility function are demonstrated.Some new copulafamilies are derived from classes of utility functions which appeared in the literature, andtheir properties are discussed. It is shown how dependence properties of an Archimedeancopula translate into properties of the utility function from whichthey are constructed

More light and less heat Mirowski on economics and the energy metaphor

I initially approached More Heat than Light with some apprehension. This is not because I suspected that I would disagree with its main thesis but because I feared that I would find the book anticlimactic. Over the past few years, Phil Mirowski has served us a number of delightful appetizers’-so many in fact that I suspected I might tire of the taste before the main entrée appeared. These concerns were wholly unfounded. The main entrée has finally arrived and is of such depth and complexity that it makes the appetizers, well, just appetizers. Mirowski’s central thesis is that neoclassical economics-initially developed during the 1870s and currently the dominant paradigm in economic theory-amounts to little more than a &dquo;brazen daylight robbery&dquo; (p. 4)2 of nineteenth-century energy physics. Motivated by the desire to achieve the status and prestige of the physical sciences, early neoclassical economists created their &dquo;revolution&dquo; by simply substituting &dquo;utility&dquo; for &dquo;energy&dquo; in the physics of their day. In a limited respect, this project was successful-the mathematical formalism of energy physics did (and does) contribute to the scientific respectability of the neoclassical research program-but this status was achieved at substantial cost. Mirowski argues that there were (and are) deep problems associated with the economic appropriation of the energy metaphor; physical systems have properties that make the mathematics appropriate, but these properties are not shared by economic systems. For example, the physical requirement that potential energy and kinetic energy sum to a constant translates into the economic requirement that utility and income sum to a constant. This is a problem because utility and income are measured in entirely different units. Mirowski argues that such difficulties were exacerbated by the scientific naivete of the early neoclassical economists who were trained in science and engineering-they had been exposed to the basic ideas of energy physics-but their knowledge was relatively rudimentary (p. 250). The result was energy physics appropriated in a &dquo;shoddy and slipshod manner&dquo; (p. 108). Mirowski provides a detailed discussion of how this misappropriation of the energy metaphor has surreptitiously influenced the development of modern economic thought. He reconstructs and explains certain generally accepted facts of theoretical life in economics (such as the problems of neoclassical production theory) and exposes some of the fundamental weaknesses of neoclassical theory (such as its inability to explain preference changes). Mirowski also argues that the dominance of the energy metaphor from nineteenth-century physics has prevented economists from taking advantage of more recent developments in physical theory, such as quantum mechanics and the theory of relativity. The result, according to Mirowski, is a tale reminiscent of Dorian Gray .... Neoclassicals, by imbibing some mystical elixir of modern mathematical techniques, have maintained the figure of vibrant youth, while hidden away somewhere in the attic is the real portrait, the original metaphor of a conserved preference field in an independently constituted commodity space, growing progressively desiccated and decrepit. (p. 374) My overall evaluation of Mirowski’s thesis is quite positive. I believe that he is entirely correct about the role of the energy metaphor in early neoclassical economics (probably reaching an apogee in Irving Fisher), and he is also correct that the metaphor has been lurking ever since in the background of neoclassical economics. The energy metaphor and its mathematics have been actively influential in the development of modem neoclassical theory, although I would probably weaken its impact from Mirowski’s story by saying &dquo;influenced&dquo; whereas Mirowski would say &dquo;dominated.&dquo; Where I mainly differ from Mirowski is on the implications of his thesis. For Mirowski, uncovering this hidden influence amounts to a scathing critique of modern neoclassical economics (and given the neoclassical dominance of the profession, this means most of modem economics). For him, the metaphor and its mathematics have been both dominant and pernicious. I disagree. While I am convinced that Mirowski has uncovered something important that can be used to further our understanding of the development of modem economic theory, I am not convinced that his thesis entails the kind of critical bite that he would like it to have. Given this overall evaluation of More Heat than Light, I will divide my comments into two sections. The first-more light-lends additional support to Mirowski’s general historical thesis by using it to illuminate two areas of modem neoclassical economics that Mirowski does not emphasize. The second-less heat-offers some arguments against Mirowski’s critical interpretation of his general thesis

How brains make decisions

This chapter, dedicated to the memory of Mino Freund, summarizes the Quantum Decision Theory (QDT) that we have developed in a series of publications since 2008. We formulate a general mathematical scheme of how decisions are taken, using the point of view of psychological and cognitive sciences, without touching physiological aspects. The basic principles of how intelligence acts are discussed. The human brain processes involved in decisions are argued to be principally different from straightforward computer operations. The difference lies in the conscious-subconscious duality of the decision making process and the role of emotions that compete with utility optimization. The most general approach for characterizing the process of decision making, taking into account the conscious-subconscious duality, uses the framework of functional analysis in Hilbert spaces, similarly to that used in the quantum theory of measurements. This does not imply that the brain is a quantum system, but just allows for the simplest and most general extension of classical decision theory. The resulting theory of quantum decision making, based on the rules of quantum measurements, solves all paradoxes of classical decision making, allowing for quantitative predictions that are in excellent agreement with experiments. Finally, we provide a novel application by comparing the predictions of QDT with experiments on the prisoner dilemma game. The developed theory can serve as a guide for creating artificial intelligence acting by quantum rules.Comment: Latex file, 20 pages, 3 figure

Endogenous Risks and Learning in Climate Change Decision Analysis

We analyze the effects of risks and learning on climate change decisions. A two-stage, dynamic, climate change stabilization problem is formulated. The explicit incorporation of ex-post learning induces risk aversion among ex-ante decisions, which is characterized in linear models by VaR- and CVaR-type risk measures. Combined with explicit introduction of "safety" constraints, it creates a "hit-or-miss" type decision-making situation and shows that, even in linear models, learning may lead to either less-or more restrictive ex-ante emission reductions. We analyze stylized elements of the model in order to identify the key factors driving outcomes, in particular, the critical role of quantiles of probability distributions characterizing key uncertainties