We study information elicitation mechanisms in which a principal agent attempts to elicit the private information of other agents using a carefully selected payment scheme based on proper scoring rules. Scoring rules, like many other mechanisms set in a probabilistic environment, assume that all participating agents share some common belief about the underlying probability of events. In real-life situations however, the underlying distributions are not known precisely, and small differences in beliefs of agents about these distributions may alter their behavior under the prescribed mechanism. We propose designing elicitation mechanisms that will be robust to small changes in belief. We show how to algorithmically design such mechanisms in polynomial time using tools of stochastic programming and convex programming, and discuss implementation issues for multiagent scenarios.