In the problem of aggregating experts' probabilistic predictions or opinions over an ordered set of outcomes, we introduce the axiom of level-strategyproofness (level-SP) and argue that it is natural in several real-life applications and robust as a notion. It implies truthfulness in a rich domain of single-peaked preferences over the space of cumulative distributions. This contrasts with the existing literature, where we usually assume single-peaked preferences over the space of probability distributions instead. Our main results are (1) explicit characterizations of all level-SP methods with and without the addition of other axioms (certainty preservation, plausibility preservation, proportionality); (2) comparisons and axiomatic characterizations of two new and practical level-SP methods: the proportional-cumulative and the middlemost-cumulative; (3) an application of the proportional-cumulative to construct a new voting method that extends majority judgment and where voters can express their uncertainties/doubts about the merits/qualities of the candidates/alternatives to be ranked.