Parameter interactions in cumulative prospect theory in relation to probability weighting

Tversky and Kahneman's cumulative prospect theory assumes symmetric probability cumulation with regard to the reference point in decision weights. Theoretically, this model should be fixed despite a change in the direction of probability cumulation. We investigate this phenomenon by proposing an alternative model with one-direction probability cumulation. By doing so, we create a reference model that allows us to verify the parameter interactions in cumulative prospect theory specifications. We apply the simultaneous parametric fitting of utility and weighting functions using binary choice data from our own incentivized choice experiment (N = 70). We consider two parametric forms of probability weighting functions, namely, the one-parameter Tversky–Kahneman and two-parameter Prelec functions. We find that the Prelec function is sufficiently flexible to make these two models equivalent, thereby preserving the stability of the utility parameters. We also observe parameter interactions in the other specifications, especially with the Tversky–Kahneman weighting function.