Reference-dependent discounting

Reference-dependence has become a widely established phenomenon in decision making under risk, not only for monetary outcomes but also for other outcomes, e.g., related to health. However, when the prospects involve risk about timing (the time of receipt of outcomes), rather than the outcomes themselves, much less is known about reference-dependence. This study extends discounted utility to incorporate reference-dependence and is the first to test it in timing prospects. We are also the first to estimate the probability weighting function for timing prospects. For both timing and outcome risk tasks, we replicate the typical fourfold pattern of risk attitudes: risk seeking for low-probability gains, risk aversion for high-probability gains, risk aversion for low-probability losses and risk seeking for high-probability losses. In other words, we find substantial pessimism with regard to high probabilities in the gain domain and low probabilities in the loss domain, and probabilistic optimism for low probabilities in the gain domain and high probabilities in the loss domain. Furthermore, we report loss aversion for outcome risks, while for timing risks, we find the opposite result, which we term earliness seeking. In sum, we find substantial empirical support for reference-dependent discounting. Our results show that psychological biases are also important when timing is risky, although the direction of bias may differ.