The Silver Lining Effect: Formal Analysis and Experiments

The silver lining effect predicts that segregating a small gain from a larger loss results in greater psychological value than does integrating them into a smaller loss. Using a generic prospect theory value function, we formalize this effect and derive conditions under which it should occur. We show analytically that there exists a threshold such that segregation is optimal for gains smaller than this threshold. The threshold is increasing in the size of the loss and decreasing in the degree of loss aversion of the decision maker. Our formal analysis results in a set of hypotheses suggesting that the silver lining effect is more likely to occur when: (i) the gain is smaller (for a given loss), (ii) the loss is larger (for a given gain), (iii) the decision maker is less loss averse. We test and confirm these predictions in a study of preferences for gambles, which we analyze in a hierarchical Bayesian framework.