Three related papers on autonomy, recursive preferences, and continuous preferences

[marcus...@gmail.com]

Dear all,

I am please to announce three working papers on closely related themes.   (Some of you may have already seen earlier drafts of some of these papers.)   The first paper develops two models of "autonomy":  one based on higher-order preferences, and one based on recursive preferences.  The second paper builds on the framework of the first paper, and constructs a "universal" recursive preference structure (somewhat analogous to a universal type space).  The third paper studies the topological properties of spaces of continuous preferences; it develops some technical results that play a key role in the second paper, but it also contains many other results which may be of independent interest to researchers in topological preference theory.

The papers are available on SSRN;  the links (along with titles and abstracts) appear below.   Of course I would be delighted to receive comments about any of these papers.

Best wishes,
  Marcus

Autonomy and Metapreferences

To adequately describe notions like "autonomy" or "responsibility" within the standard economic model of rational choice, it is necessary to introduce metapreferences ---that is, preferences over preferences. This paper develops two models of metapreferences: a "hierarchical" model, involving second-order preferences, third-order preferences, etc., and a "recursive" model, involving a type space where each type determines preferences over type-outcome pairs. For each model, the paper introduces concepts of internal coherence and rational choice. It then studies the relationship between the two models. 

Universal Recursive Preference Structures

Given a set X of "outcomes" and a set T of "types", a recursive preference structure (RPS) is a function that assigns a continuous partial order over T x X to every element of T. This describes an agent who has preferences not only over the outcomes in X , but also over her own preferences (as encoded by the types). We prove the existence of a universal RPS ---one into which any other RPS can be mapped in a unique way. Formally, this universal RPS is a terminal coalgebra of a suitably defined endofunctor on the category of compact Hausdorff spaces. 

Compact Spaces of Continuous Preferences

Let X be a topological space. We consider two spaces of continuous preference relations on X. A local continuous quasiorder is a continuous, complete, quasitransitive binary relation defined on a closed subset of X. Let Q(X) be the set of all such relations. A local continuous strict partial order is a continuous partial order (with no indifference) defined on a closed subset of X. Let P(X) be the set of all such relations. There is a natural bijection ("duality") between Q(X) and P(X). We endow both sets with the Fell topology (also called the topology of closed convergence, the Vietoris topology, or the Hausdorff metric topology, depending on context), and show that under mild conditions, they are compact Hausdorff spaces, compact metrizable spaces, continua, or even contractible continua. (In contrast, most "preference spaces" in the literature have none of these nice properties.)  If X is a compact metric space, then duplex multiutility representations define continuous functions into Q(X) and P(X) from a space of compact collections of utility functions, endowed with its own Fell topology.  Furthermore, any continuous function F: X → Y induces continuous functions  QF : Q(X) → Q(Y) and PF : P(X) → P(Y). We thus obtain two endofunctors Q and P on the category of compact Hausdorff spaces, which are naturally isomorphic to each other. Finally, we show that these endofunctors are "continuous": if X is the limit of a chain X_1 ← X_2 ← X_3 ← .... of compact Hausdorff spaces, then Q(X) is the limit of the corresponding chain Q(X_1) ← Q(X_2) ← Q(X_3) ← ..... (and likewise for P(X)).