Expected exponential discounting in inter-temporal decision making

We present a novel interpretation of delay discounting – a theoretical mechanism by which decision-makers discount the current value of reward if it is obtained at a future time rather than immediately. The theory proposes that decision-makers rationally account for the natural phenomenon of compounded interests (use exponential discounting) but need to take an average or expected value over some uncertainty distribution for the compound interest rate. Hence, the name Expected Exponential Discounting (EED) theory of inter-temporal choice. We show that EED provides a mechanism that unifies multiple empirically discovered descriptive discounting functions and fits to key qualitative findings about delay discounting in humans under non-sequential contexts, such as for hypothetical questions about delayed rewards. The general, falsifiable and comparatively minimal EED theory provides a good sanity check for more complex accounts of delay discounting, but also supports the derivation of new empirical predictions and reference points.