The success of extended warranties and buyer protection plans suggests that insurance against a small loss has high decision utility. We explore whether the behavioral insight that people are highly averse to small chances of loss can be used to create a powerful incentive that has very low expected value. We compare decisions of individuals offered fixed payments for healthy choices to those offered insurance in exchange for healthy choices. We test the prediction that aversion to small losses will result in very high rates of health behavior uptake in exchange for insurance. Three hundred participants endowed with a $2 bonus randomly received one of two incentives for completing a scheduled health risk assessment: (1) an insurance guarantee against the 1% risk of losing the $2 bonus or (2) a fixed payment at the expected value of the insurance. Relative to the fixed payment condition, participants in the insurance intervention were 70% more likely to meet their health risk assessment appointment ( 0.01). Fixed payments of $2.59 were needed for every $1 spent on insurance to achieve the same behavioral effect. Loss aversion, probability weighting, and the certainty effect may account for this result. Incentive design may benefit from utilizing an insurance paradigm.

Mammography is the most effective screening tool for early diagnosis of breast cancer. Based on the mammography findings, radiologists need to choose from one of the following three alternatives: 1) take immediate diagnostic actions including prompt biopsy to confirm breast cancer; 2) recommend a follow-up mammogram; 3) recommend routine annual mammography. There are no validated structured guidelines based on a decision-analytical framework to aid radiologists in making such patient management decisions. Surprisingly, only 15-45% of the breast biopsies and less than 1% of short-interval follow-up recommendations are found to be malignant, resulting in unnecessary tests and patient-anxiety. We develop a finite-horizon discrete-time Markov decision process (MDP) model that may help radiologists make patient-management decisions to maximize a patient's total expected quality-adjusted life years. We use clinical data to find the policies recommended by the MDP model and also compare them to decisions made by radiologists at a large mammography practice. We also derive the structural properties of the MDP model, including sufficiency conditions that ensure the existence of a double control-limit type policy.

Based on subjective survival probability questions in the Health and Retirement Study (HRS), we use an econometric model to estimate the determinants of individual-level uncertainty about personal longevity. This model is built around the modal response hypothesis (MRH), a mathematical expression of the idea that survey responses of 0%, 50%, or 100% to probability questions indicate a high level of uncertainty about the relevant probability. We show that subjective survival expectations in 2002 line up very well with realized mortality of the HRS respondents between 2002 and 2010. We show that the MRH model performs better than typically used models in the literature of subjective probabilities. Our model gives more accurate estimates of low probability events and it is able to predict the unusually high fraction of focal 0%, 50%, and 100% answers observed in many data sets on subjective probabilities. We show that subjects place too much weight on parents' age at death when forming expectations about their own longevity, whereas other covariates such as demographics, cognition, personality, subjective health, and health behavior are under weighted. We also find that less educated people, smokers, and women have less certain beliefs, and recent health shocks increase uncertainty about survival, too.