Stochastic monotonicity and realizable monotonicity (Q1872211): Difference between revisions

The authors explore and relate the notions of stochastic monotonicity and realizable monotonicity, for a system of probability measures on a common finite partially ordered set (poset) \(\mathcal{S}\) when the measures are indexed by another poset \(\mathcal{A}\). They give counterexamples to show that the two notions are not always equivalent. But for various large classes of \(\mathcal{S}\) they present conditions on the poset \(\mathcal{A}\) that are necessary and sufficient for equivalence.