Rational choice and revealed preference without binariness

 This paper attempts to provide a unified account of the rationalization of possibly non-binary choice-functions by “Extended Preference Relations” (relations between sets and elements). The analysis focuses on transitive EPRs for which three choice-functional characterizations are given, two of them based on novel axioms. Transitive EPRs are shown to be rationalizable by sets of orderings that are “closed under compromise”; this novel requirement is argued to be the key to establish a canonical relationship between sets of orderings and choice-functions. The traditional assumption of “binariness” on preference relations or choice functions is shown to be analytically unhelpful and normatively unfounded; non-binariness may arise from “unresolvedness of preference”, a previously unrecognized aspect of preference incompleteness. Received: 28 August 1995/Accepted: 14 February 1996     

现象学的意向性伦理学

从胡塞尔与海德格尔的现象学中是否能够引出一门现象学的意向伦理学？这个问题可分成三个步骤来论述：首先,胡塞尔的“充实”概念对整个哲学都具有基本的意义,但它带有一个胡塞尔无法解决的困难。其次,这个困难在海德格尔这里得到了某种解决,他用实践的“充实”概念取代了理论的“充实”概念。最后,借助于海德格尔而获得的对情感满足的理解可以用来建构一门现象学的意向性伦理学。     

The mixed economy, the neoliberal challenge, and the negotiated economy

In recent years the ideal of the mixed economy has been challenged by neoliberal theories. This article reviews the debate. A better definition of the concept is presented and used to clarify what is at stake in the debate.     

An Approximation Scheme for Bin Packing with Conflicts

In this paper we consider the following bin packing problem with conflicts. Given a set of items V = {1,..., n} with sizes s₁,..., s (0,1) and a conflict graph G = (V, E), we consider the problem to find a packing for the items into bins of size one such that adjacent items (j, j) E are assigned to different bins. The goal is to find an assignment with a minimum number of bins. This problem is a natural generalization of the classical bin packing problem.We propose an asymptotic approximation scheme for the bin packing problem with conflicts restricted to d-inductive graphs with constant d. This graph class contains trees, grid graphs, planar graphs and graphs with constant treewidth. The algorithm finds an assignment for the items such that the generated number of bins is within a factor of (1 + ) of optimal provided that the optimum number is sufficiently large. The running time of the algorithm is polynomial both in n and in .     

A Theory of Diversity

How can diversity be measured? What does it mean to value biodiversity? Can we assist Noah in constructing his preferences? To address these questions, we propose a multi‐attribute approach under which the diversity of a set of species is the sum of the values of all attributes possessed by some species in the set. We develop the basic intuitions and requirements for a theory of diversity and show that the multi‐attribute approach satisfies them in a flexible yet tractable manner. A natural starting point is to think of the diversity of a set as an aggregate of the pairwise dissimilarities between its elements. The multi‐attribute framework allows one to make this program formally precise. It is shown that the program can be realized if and only if the family of relevant attributes is well‐ordered (“acyclic”). Moreover, there is a unique functional form aggregating dissimilarity into diversity, the length of a minimum spanning tree. Examples are taxonomic hierarchies and lines representing uni‐dimensional qualities. In multi‐dimensional settings, pairwise dissimilarity information among elements is insufficient to determine their diversity. By consequence, the qualitative and quantitative behavior of diversity differs fundamentally.     

Preference for Flexibility in a Savage Framework

We study preferences over Savage acts that map states to opportunity sets and satisfy the Savage axioms. Preferences over opportunity sets may exhibit a preference for flexibility due to an implicit uncertainty about future preferences reflecting anticipated unforeseen contingencies. The main result of this paper characterizes maximization of the expected indirect utility in terms of an ‘Indirect Stochastic Dominance’ axiom that expresses a preference for ‘more opportunities in expectation.’ The key technical tool of the paper, a version of Möbius inversion, has been imported from the theory of nonadditive belief functions; it allows an alternative representation using Choquet integration, and yields a simple proof of Kreps' (1979) classic result.