Harmful Random Utility Models

In many choice settings self-punishment affects individual taste, by inducing the decision maker (DM) to disregard some of the best options. In these circumstances the DM may not maximize her true preference, but some harmful distortion of it, in which the first i alternatives are shifted, in reverse order, to the bottom. Harmful Random Utility Models (harmful RUMs), which are RUMs whose support is limited to the harmful distortions of some preference, offer a natural representation of the consequences of self-punishment on choices. Harmful RUMs are characterized by the existence of a linear order that allows to recover choice probabilities from selections over the ground set. An algorithm detects self-punishment, and elicits the DM's unobservable tastes that explain the observed choice. Necessary and sufficient conditions for a full identification of the DM's preference and randomization over its harmful distortions are singled out. In all but two cases, there is a unique justification by self-punishment of data. Finally, a degree of self-punishment, which measures the extent of the denial of pleasure adopted by the DM in her decision, is characterized.