Undescribable Contingencies *

We develop a model of complex undescribable contingencies. These are contingencies that are understood by economic agents — their consequences and probabilities are known — but are such that every description of such events necessarily leaves out relevant features that have a non-negligible impact on the parties’ expected utilities. Using a simple co-insurance problem as backdrop, we introduce a model where states are described in terms of objective features, and the description of an event specifies a finite number of such features. In this setting, undescribable contingencies are present when the first-best risk-sharing contract varies with the states of nature in a complex way that makes it highly sensitive to the component features of the states. We also show that two key ingredients of our model — probabilities that are finitely additive but fail countable additivity, and a state space that is small (discrete in our model) in a measure-theoretic sense — are necessary ingredients of any model of undescribable contingencies that delivers our results. JEL Classification: C69, D81, D89.