An axiomatic study of Majority-rule (+ ) and associated consensus functions on hierarchies

Consensus trees have been used routinely in systematic biology for over 30 years with the majority-rule consensus tree among the most popular. In this paper we give axioms that characterize a new consensus function, called majority-rule (+), that is based on a generalization of majority-rule to the supertree case. In addition, two other related consensus functions are characterized.

► The new majority-rule (+) consensus function on hierarchies is characterized.
► We present axioms that characterize the loose consensus function on hierarchies.
► The function that is the union of majority-rule and loose consensus is characterized.