Decidability and manipulability in social choice

We present a geometric model of social choice when the latter takes place among bundles of interdependent elements, that we will call objects. We show that the outcome of the social choice process is highly dependent on the way these bundles are formed. By bundling and unbundling the same set of constituent elements an authority enjoys a vast power of determining the social outcome, as locally or globally stable social optima can be created or eliminated. At the same time, by bundling and unbundling elements, it is also possible to greatly increase or decrease decidability both because the likelihood of intransitive cycles varies and because the time required to reach a social optimum varies. In this paper we present a rigorous framework which allow us to study this trade-off between decidability and manipulability.