Violations of Branch Independence in Choices between Gambles

Abstract

Branch Independence is weaker than Savage's independence axiom; it holds that if two gambles have a common outcome for an event of known probability, the value of that common outcome should have no effect on the preference order induced by other probability-outcome branches. Systematic violations of branch independence were obtained in two experiments with choices between gambles composed of three equally likely, positive outcomes. Most people prefer ($2, $40, $44) over ($2, $10, $98); however, most people prefer ($10, $98, $136) over ($40, $44, $136). These results refute Expected Utility theories. They also refute the theory that people edit and cancel common components in choice. The pattern is opposite that predicted by the weighting function of cumulative prospect theory. Results are consistent with rank dependent, configural weight theory, with wL> wM> wH, where wL, wM, and wHare the weights of the lowest, medium, and highest outcomes, respectively. In this theory, violations of branch independence depend on relations among weights: results indicate that wL/wM< wM/wH.