Stability conditions for consensus functions defined on n-trees

Eight natural extensions of K. Arrowʹs “independence of irrelevant alternatives” axiom (which are called “stability” conditions in this paper) for consensus functions on weak orders are identified for n-trees, and the complete relationships among these eight axioms are determined. The behavior of consensus functions that satisfy the classical Pareto condition, in addition to one of the stability axioms, is also studied.