Before revision: For any matching market where the set of stable matchings has a lattice structure, if the binary operations ( l.u.b. and g.l.b. ) are computed via a "pointing function", then the set of random matchings (lotteries of stable matchings) has a lattice structure .
After revision: For any matching market where the set of stable matchings has a lattice structure, if the binary operations ( l.u.b. and g.l.b. ) are computed via a "pointing function", then the set of random matchings has two dual lattices .