Convergence of preference functions

A preference function is a function which selects a subset of objects based on (partial) information. As information increases, different objects may be selected. We examine conditions under which the selection of objects converges to the choice that would be made if full information were available, making use of tools from domain theory. The work is motivated by previous research on co-evolutionary algorithms in which an evolving population of agents interact with each other and, it is hoped, produce better and better quality behaviour. The formalisation of how quality can be measured in this context has introduced the concept of a convex preference function (or “solution concept”). We simplify and extend the scope of this previous work, examining the relationship between convexity and convergence properties.