The inference of consensus from a set of evolutionary trees is a funda
mental problem in a number of fields such as biology and historical li
nguistics, and many models for inferring this consensus have been prop
osed. In this paper we present a model for deriving what we call a loc
al consensus tree T from a set of trees T. The model we propose presum
es a function f, called a total local consensus function, which determ
ines for every triple A of species, the form that the local consensus
tree should take on A. We show that all local consensus trees, when th
ey exist, can be constructed in polynomial time and that many fundamen
tal problems can be solved in linear time. We also consider partial lo
cal consensus functions and study optimization problems under this mod
el. We present linear time algorithms for several variations. Finally
we point out that the local consensus approach ties together many prev
ious approaches to constructing consensus trees.