A THEORY OF RATIONAL CHOICE UNDER COMPLETE IGNORANCE

This paper contributes to a theory of rational choice under uncertainty for decision-makers whose preferences are exhaustively described by partial orders representing ""limited information."" Specifically, we consider the limiting case of ""Complete Ignorance"" decision problems characterized by maximally incomplete preferences and important primarily as reduced forms of general decision problems under uncertainty. ""Rationality"" is conceptualized in terms of a ""Principle of Preference-Basedness,"" according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called ""Simultaneous Expected Utility Maximization"" which in particular satisfies a choice-functional independence and a context-dependent choice-consistency condition; it can be interpreted as the fair agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the different possible states (respectively extermal priors in the general case).

Choice by lexicographic semiorders

In Tversky's (1969) model of a lexicographic semiorder, preference is generated by the sequential application of numerical criteria, by declaring an alternative x better than an alternative y if the first criterion that distinguishes between x and y ranks x higher than y by an amount exceeding a fixed threshold. We generalize this idea to a fully-fledged model of boundedly rational choice. We explore the connection with sequential rationalizability of choice (Apesteguia and Ballester 2009, Manzini and Mariotti 2007), and we provide axiomatic characterizations of both models in terms of observable choice data.Lexicographic semiorders, bounded rationality, revealed preference, choice

A Homological Approach to Factorization

Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated localizations of D and projections onto partially ordered quotient groups of G(D). We use this functor to construct many cochain complexes of o-homomorphisms of po-groups. These complexes naturally lead to some fundamental structure theorems and some natural homology theory that provide insight into the factorization behavior of D.Comment: Submitted for publication 12/15/201

Where do preferences come from?

Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Preferences are usually assumed to be fixed and exogenously given. Building on related work on reasons and rational choice (Dietrich and List, Nous, forthcoming), we describe a framework for conceptualizing preference formation and preference change. In our model, an agent’s preferences are based on certain ‘motivationally salient’ properties of the alternatives over which the preferences are held. Preferences may change as new properties of the alternatives become salient or previously salient properties cease to be salient. Our approach captures endogenous preferences in various contexts and helps to illuminate the distinction between formal and substantive concepts of rationality, as well as the role of perception in rational choice

Expressing advanced user preferences in component installation

State of the art component-based software collections - such as FOSS distributions - are made of up to dozens of thousands components, with complex inter-dependencies and conflicts. Given a particular installation of such a system, each request to alter the set of installed components has potentially (too) many satisfying answers. We present an architecture that allows to express advanced user preferences about package selection in FOSS distributions. The architecture is composed by a distribution-independent format for describing available and installed packages called CUDF (Common Upgradeability Description Format), and a foundational language called MooML to specify optimization criteria. We present the syntax and semantics of CUDF and MooML, and discuss the partial evaluation mechanism of MooML which allows to gain efficiency in package dependency solvers