Harmful choices

We investigate the choice behavior of a decision maker (DM) who harms herself, by maximizing some distortion of her true preference, in which the first $i$ alternatives are moved to the bottom, in a reversed order. The deterministic declination of our pattern has no empirical power, but it allows to define a degree of self-punishment, which measures the extent of the denial of pleasure adopted by the DM in her decision. We analyze irrational choices that display the lowest degree of self-punishment, and a characterization of them is provided. Moreover, we characterize the choice behavior that exhibits the highest degree of self-punishment, and we show that it comprises almost all choices. We also characterize stochastic self-punishment, which collects all the Random Utility Models (RUMs) whose support is restricted to the harmful distortions of some preference. Full identification of the DM's preference and randomization over its harmful distortions is allowed if each alternative is selected from the ground set with probability greater than zero. Finally, the degree of self-punishment of harmful stochastic choices is characterized.