Mechanism design for preference aggregation over coalitions

Abstract

Mechanisms are decision functions that map the individual preference orderings of separate parties into a single ordering over the group outcome. Unfortunately, classical impossibility results, readily extended to preferences, show that no mechanism can be "fair" for all scenarios [1]. Further, any positive results typically assume that agents do not form coalitions or other such partnerships. While coalitions can complicate both theoretical analysis and underlying paradigms of rationality, in a particular setting they can serve to constrain a problem to the point of circumventing traditional impossibility results. Automated mechanism design (AMD) [2] attempts to overcome such results by designing specific mechanisms for specific situations on the spot. No perfect mechanism exists that works in every context, but whenever there is information about the players, a fair mechanism can exist for that specific setting. Our goal is mechanism design for preference aggregation over coalitions. While AMD research has focused on auction and continuous domains, we seek to model preferences in logic and operate over discrete domains. To do so we use a recently-proposed logic for extensive games, based in turn on Alternating Time (ATL) temporal logic [3,4]. While such efforts seek to express desirable properties, and verify whether a provided mechanism satisfies them, our approach aspires to automatically generate satisfying mechanisms. Using a standard CSP solver, we have implemented a preliminary system that does so for an extremely simplified variant of these languages. The general approach is to establish variables representing a blank template game tree, and then instantiate them with the names of players, subject to constraints representing the specified properties. The space of possible trees is combinatorially large, and even tighter control of variable ordering and propagation will be necessary to meet this challenge. © Springer-Verlag Berlin Heidelberg 2005.