Stochastic Dominance
Understand First-Order Stochastic Dominance by comparing distribution pairs and their cumulative distribution functions.
Free theory articleUnderstand First-Order Stochastic Dominance by comparing distribution pairs and their cumulative distribution functions.
Concept & interpretation
Stochastic dominance is a partial order on probability distributions. It is widely used in decision theory and economics to compare random variables. First-Order Stochastic Dominance (FSD) occurs when one distribution unambiguously yields higher values than another, meaning that any decision-maker with an increasing utility function would prefer it.
Experiment
You can use the Stochastic Dominance interactive module to visualize CDF comparisons and expected utilities.
- Select the Crossing option in the Distribution pair control.
- Observe that the CDF step lines cross.
F_A(0) = 0.5is greater thanF_B(0) = 0, butF_A(1) = 0.5is less thanF_B(1) = 1.0. Thus, neither dominates. - Adjust the Threshold x control to
1.0. Read F_A(1) = 1/2 and F_B(1) = 1 in the visible readouts and complete CDF table. - Change the Utility control from Linear to Square. Read E[u(A)] = 2 and E[u(B)] = 1. Although these expected utilities change, this cannot establish dominance on its own since the full CDF check showed they cross.
- Select Distribution pair = Equal, keep Threshold x = 1, and choose Utility = Square. Both means of the utility are (02 + 12 + 22)/3 = 5/3 ≈ 1.666667. The CDFs remain equal; changing the utility does not change the distributions.