Approximations of Coherent Lower Probabilities by 2-monotone Capacities

We investigate the problem of approximating a coherent lower probability on a finite space by a 2-monotone capacity that is at the same time as close as possible while not including additional information. We show that this can be tackled by means of a linear programming problem, and investigate the features of the set of undominated solutions. While our approach is based on a distance proposed by Baroni and Vicig, we also discuss a number of alternatives. Finally, we show that our work applies to the more general problem of approximating coherent lower previsions.