Compound invariance implies prospect theory for simple prospects

Behavioral conditions such as compound invariance for risky choice and constant decreasing relative impatience for intertemporal choice have surprising implications for the underlying decision model. They imply a multiplicative separability of outcomes and either probability or time. Hence the underlying model must be prospect theory or discounted utility on the domain of prospects with one nonzero outcome. We indicate implications for richer domains with multiple outcomes, and with both risk and time involved.