Mathematics of Plott choice functions

This paper is devoted to the study of mathematical structures related to the class of choice functions satisfying the path independence property (Plott functions). The set of Plott functions has a natural lattice structure. We describe join-irreducible and meet-irreducible elements of this lattice. We introduce a convex structure on the set of simple words and show that Plott functions are in a natural one-to-one correspondence with convex subsets of simple words. In particular, this correspondence is compatible with the lattice structures on both sets. All these structures and relations are functorially dependent on a change of base sets.