Obvious Strategy-proofness with Respect to a Partition

We define and study obvious strategy-proofness with respect to a partition of the set of agents. It encompasses strategy-proofness as a special case when the partition is the coarsest one and obvious strategy-proofness when the partition is the finest. For any partition, it falls between these two extremes. We establish two general properties of this new notion and apply it to the simple anonymous voting problem with two alternatives and strict preferences.