Axiomatization and implementation via objections structures

In this article, we present a new formal framework called objections structures for the axiomatization and implementation of stable and/or desirable alternatives. This framework models the distribution of power within a society using the concept of an objection function, without explicitly revealing it to the agents. In addition to providing a general environment that encompasses a wide range of scenarios, including the modeling of rights structures and other institutional settings, a key advantage of the objection function is that it frees the social planner from the need to specify which agents or coalitions are authorized to change the status quo. This is particularly relevant in the context of increasingly complex and inefficient mechanisms, often referred to as legislative inflation. First, our axiomatization of the set of stable alternatives, known as the $$\Omega$$ Ω -equilibria set, incorporates a surjectivity property along with the well-established properties of monotonicity and attractivity. Second, we characterize implementable social choice rules using objections structures through a consistency principle, called $$\mathcal {O}$$ O -consistency. Our axiomatization and implementation results are then applied to the modeling of rights structures.