In SLAM (Simultaneous localization and mapping) problems, Pose Graph Optimization (PGO) is a technique to refine an initial estimate of a set of poses (positions and orientations) from a set of pairwise relative measurements. The optimization procedure can be negatively affected even by a single outlier measurement, with possible catastrophic and meaningless results. Although recent works on robust optimization aim to mitigate the presence of outlier measurements, robust solutions capable of handling large numbers of outliers are yet to come. This paper presents IPC, acronym for Incremental Probabilistic Consensus, a method that approximates the solution to the combinatorial problem of finding the maximally consistent set of measurements in an incremental fashion. It evaluates the consistency of each loop closure measurement through a consensus-based procedure, possibly applied to a subset of the global problem, where all previously integrated inlier measurements have veto power. We evaluated IPC on standard benchmarks against several state-of-the-art methods. Although it is simple and relatively easy to implement, IPC competes with or outperforms the other tested methods in handling outliers while providing online performances. We release with this paper an open-source implementation of the proposed method.