Relative uncertainty aversion and additively representable set rankings

This paper proposes a definition of relative uncertainty aversion for decision models under complete uncertainty. It is shown that, for a large class of decision rules characterized by a set of plausible axioms, the new criterion yields a complete ranking of those rules with respect to the relative degree of uncertainty aversion they represent. In addition, we address a combinatorial question that arises in this context, and we examine conditions for the additive representability of our rules.     

Ranking Committees,Income Streams or Multisets

Multisets are collections of objects which may include several copies of the same object. They may represent bundles of goods, committees formed of members of several political parties, or income streams. In this paper we investigate the ways in which a linear order on a finite set A can be consistently extended to an order on the set of all multisets on A of some given cardinality k and when such an extension arises from a utility function on A. The condition of consistency that we introduce is a close relative of the de Finetti’s condition that defines comparative probability orders. We prove that, when A has three elements, any consistent linear order on multisets on A of cardinality k arises from a utility function and all such orders can be characterised by means of Farey fractions. This is not true when A has cardinality four or greater. It is proved that, unlike linear orders that can be represented by a utility function, any non-representable order on the set of all multisets of cardinality k cannot be extended to a consistent linear order on multisets of cardinality K for sufficiently large K. We also discuss the concept of risk aversion arising in this context.A significant part of this work was written when both authors were visiting professors at Bilkent University, Ankara. Slinko thanks Semih Koray and Mefharet Kocatepe for making this possible and Serguei Stepanov for discussion about Farey fractions. Sertel thanks the Institut des Hautes Etudes Scientifiques (IHES), Bures-sur-Yvette, France, for a couple of invitations, in 1999 and 2000, during which he had a chance to elaborate on some of the questions addressed in this paper. The authors thank students of The University of Auckland Irene Peng and Mark Lui who participated at an early stage of this project and Marston Conder for checking the result of Theorem 6 with MAGMA and correcting it. Murat Sertel was deceased (1942 – 2003).An erratum to this article is available at .     

Exploratory Analysis of Similarities Between Social Choice Rules

Nurmi (1987) investigated the relationship between voting rules by determining the frequency that two rules pick the same winner. We use statistical techniques such as hierarchical clustering and multidimensional scaling to further understand the relationships between rules. We use the urn model with a parameter representing contagion to model the presence of social homogeneity within the group of agents and investigate how the classification tree of the rules changes when the homogeneity of the voting population is increased. We discovered that the topology of the classification tree changes quite substantially when the parameter of homogeneity is increased from 0 to 1. We describe the most interesting changes and explain some of them. Most common social choice rules are included, 26 in total. Jel Classification: D7     

Towards a General Theory of Good-Deal Bounds*

We consider an incomplete market in the form of a multidimensional Markovian factor model, driven by a general marked point process (representing discrete jump events), as well as by a standard multidimensional Wiener process. Within this framework, we study arbitrage-free good-deal pricing bounds for derivative assets, thereby extending the results by Cochrane and Saá Requejo (2000) to the point process case, while, at the same time, obtaining a radical simplification of the theory. To illustrate, we present numerical results for the classic Merton jump-diffusion model. As a by-product of the general theory, we derive extended Hansen-Jagannathan bounds for the Sharpe Ratio process in the point process setting. *We gratefully acknowledge financial support from the Jan Wallander and Tom Hedelius foundation. We thank Anders Forsgren, Krister Svanberg, and Jan Kallsen for a number of very helpful comments. We are very grateful to Mathias Stolpe for providing us with the optimization code used in our numerical example. A number of very helpful comments from the editor and an anonymous referee has greatly improved the paper.     

On complexity of lobbying in multiple referenda

In this paper we show that lobbying in conditions of “direct democracy” is virtually impossible, even in conditions of complete information about voters’ preferences, since it would require solving a very computationally hard problem. We use the apparatus of parametrized complexity for this purpose.      

ON FINITE DIMENSIONAL REALIZATIONS OF TWO-COUNTRY INTEREST RATE MODELS

This paper explores how consistent two-dimensional families of forward rate curves can be constructed on an international market. Applying the approach in Björk and Christenssen (1999) and Björk and Svensson (2001) , we study when a system of inherently infinite dimensional domestic and foreign forward rate processes in a two-country economy with spot (forward) exchange rate possesses finite dimensional realizations. In the system with the forward exchange rate, the forward interest rate equations are supplemented by a third infinite dimensional stochastic differential equation representing the forward exchange rate dynamics. We construct and fit consistent families to observed Euro and USD yields as well as the forward (spot) EUR/USD exchange rate.     

The Majoritarian Compromise in large societies

First, we dwell on the definition of the Majoritarian Compromise in the case of an odd number of alternatives. Then, assuming the Impartial Culture hypothesis we calculate the average maximum welfare achievable by the Majoritarian Compromise procedure and show that this social choice rule is asymptotically stable with the proportion of the number of unstable profiles to the total number of profiles being in the order of ,(¹We write in case there is a positive constant C such that for all sufficiently large values of ) where n is the total number of agents. I am grateful to Prof. Semih Koray for his invitation to visit the Center for Economic Design and the Department of Economics of Boğazi?i University in Turkey during the spring semester of 1999. I appreciate the stimulating discussions with Prof. Murat Sertel about the properties of the Majoritarian Compromise which I had during my stay there. I am also grateful to an anonymous referee whose remarks helped to significantly improve the exposition. A partial support from TüBİTAK NATO PC-B Programme is gratefully acknowledged.     

Equilibria on a circular market when consumers do not always buy from the closest firm

Review of Economic Design - We study spatial competition by firms which is often studied in the context of linear markets where customers always shop at the nearest firm. Here, customer behavior is...