New designs for research in delay discounting

The two most influential models in delay discounting research have been the exponential (E) and hyperbolic (H)
models. We develop a new methodology to design binary choice questions such that exponential and hyperbolic discount rates can be purposefully manipulated to make their rate parameters orthogonal (Pearson’s R = 0), negatively correlated (R = –1), positively correlated (R = +1), or to hold one rate constant while allowing the other to vary. Then we extend the method to similarly contrast different versions of the hyperboloid model. The arithmetic discounting model (A), which is based on differences between present and future rewards rather than their ratios, may easily be made orthogonal to any other pair of models. Our procedure makes it possible to design choice stimuli that precisely vary the relationship between different discount rates. However, the additional control over the correlation between different discount rate parameters may require the researcher to either restrict the range that those rate parameters can take, or to expand the range of times the participant must wait for future rewards.