An approximate dual-self model and paradoxes of choice under risk

We derive a simplified version of the model of Fudenberg and Levine, 2006 and Fudenberg and Levine, 2011 and show how this approximate model is useful in explaining choice under risk. We show that in the simple case of three outcomes, the model can generate indifference curves that “fan out” in the Marschak–Machina triangle, and thus can explain the well-known Allais and common ratio paradoxes that models such as prospect theory and regret theory are designed to capture. At the same time, our model is consistent with modern macroeconomic theory and evidence and generates predictions across a much wider set of domains than these models.

► We simplify the model of Fudenberg and Levine (2011).
► We derive several properties of the model.
► We use it to explain choice among lotteries.
► The model respects stochastic dominance and corresponds to expected utility in a special case.
► The model can explain the well-known Allais and common ratio paradoxes.