Three new tests of independence that differentiate models of risky decision making

This paper tests new ‘independence’ properties to compare three models of risky decision making. According to the rank-affected multiplicative (RAM) weights model, all three properties should be satisfied; according to the transfer of attention exchange (TAX) model, two should be satisfied and one can be violated. However, according to cumulative prospect theory (CPT), all three properties will be violated if the probability weighting function is nonlinear. Although CPT is flexible enough to accommodate violations of these properties, its predicted violations based on previously estimated parameters failed to materialize. In 14 choices for which the CPT model disagreed with TAX, CPT correctly predicted the modal choice in only one case and TAX predicted the modal choice in the other 13. New versions of three other paradoxes were also tested and found to refute CPT.