Аннотация:In the paper we study choice functions on posets satisfying the conditions of heredity and outcast. For every well-ordered sequence of elements of a poset, we define the corresponding ‘elementary’ choice function. Every such choice function satisfies the conditions of heredity and outcast. Inversely, every choice function satisfying the conditions of heredity and outcast can be represented as a union of several elementary choice functions. This resultgeneralizes the Aizerman-Malishevski theorem about the structure of path-independent choice functions.Keywords Order ideal · Filter · Well order · Path independence · Stable contract