Silverlining

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Jarnebrant, Toubia & Johnson: The Silver Lining Effect Article submitted to Management Science

The Silver Lining Effect: Formal Analysis and Experiment

Peter Jarnebrant

Department of Marketing, Columbia Business School, Columbia University, New York, NY 10027, poj2101@columbia.edu

Olivier Toubia

Department of Marketing, Columbia Business School, Columbia University, New York, NY 10027, ot2107@ columbia.edu

Eric Johnson

Department of Marketing, Columbia Business School, Columbia University, New York, NY 10027, ejj3@columbia.edu

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.

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1. Introduction

Decision-makers are often faced with mixed outcomes, as captured in the saying “I have good news and I have bad news.” In this paper we look at the case where the bad news is larger in magnitude than the good, and ask: Does the decision maker want these events combined or presented separately? Thaler, in his seminal paper (Thaler 1985), showed that a decision maker faced with such a mixed outcome...