The curse of hope

In Kőszegi and Rabin's (Q J Econ 1133–1165, 2006, Am Econ Rev 97:1047–1073, 2007) reference-dependent model of preferences, the chance of obtaining a better outcome can reduce an agent's expected utility through an increase in the stochastic reference point. This means that individuals may prefer stochastically dominated lotteries. In this sense, hope, understood as a small probability of a better outcome, can be a curse. While Kőszegi and Rabin focus on a linear specification of the utility function, we show that this effect occurs more broadly. Using fairly plausible assumptions and parameter values, we specify the conditions under which it occurs, as well as the type of lotteries in which this should be expected. We then show that while a simple subjective transformation of probability into weights of the reference point may in some cases mitigate the issue, in others, it can intensify it or even generate new ones. Finally, we extend the model by adding the individual's current reference point (status quo) to the stochastic reference point. We show that this modification can reconcile Kőszegi and Rabin's model with the apparent empirical infrequency of stochastically dominated choices while maintaining its main qualitative results.