Solidarity and efficiency in preference aggregation: a tale of two rules

This paper is concerned with preference-aggregation rules satisfying desirable efficiency and solidarity requirements. We formulate weaker versions of existing solidarity axioms and show how they imply, in conjunction with strategy-proofness, the existence of reference outcomes holding privileged status. We propose a new class of rules, fixed order status-quo rules, that can be productively contrasted to their closest counterparts in the literature, status-quo rules based on the least upper bound of a lattice. Fixed order status-quo rules satisfy stronger efficiency requirements than lattice status-quo rules but have weaker, though still significant, solidarity properties. A subfamily based on lexicographic orders is analyzed further. Fixed order status-quo rules are characterized by strategy-proofness, strong efficiency, and a third axiom, unanimity-basedness.