A two-valued function f defined on the vertices of a graph G = (V,E), f : V --~ {-1, 1}, is an opinion function. The positive value of f, denoted by pos f, is the number of vertices that are assigned the value +1 under f. For each vertex v of G, the vote(v) is the sum of the function values of f over the closed neighborhood of v. If vote(v) >~ 1, then we say that the vote of v is aye. A unanimous function of G is an opinion function for which every vertex votes aye. The unanimity index of G is unan(G) = min{pos f I f is a unanimous function of G}. We show that the maximum number of ayes that can occur in a tree with an opinion function of positive value n/> 2 is L~J -1. We then determine which trees have unanimous functions with positive value n (>i 2) attaining this value. We show that the range of values for the unanimity index of trees of order p > 1 is L2(p+2)J to p, and we characterize those trees with unanimity index reaching the lower bound. A majority function of a graph G is an opinion function for which more than half the vertices vote aye. The majority index of G, denoted by maj(G), is maj(G) = min{posfl f is a majority function of G}. For any tree of order p >t 2, we show that ~2 L2ej j + 2 ~< maj(T) ~< L2eJ + 2. We establish the majority index for the class of trees called comets.