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This paper studies social welfare and allocation efficiency in situations where, in addition to having ordinal preferences, agents also have *ordinal intensities*: they can make comparisons such as "I prefer a to b more than I prefer c to d" without necessarily being able to quantify them. In this new informational environment for social choice, the paper first introduces a rank-based criterion for interpersonal comparisons of such ordinal intensities. Building on it, the "intensinist" social welfare function is introduced. This maps profiles of ordinal intensities to weak orders over social alternatives using a scoring method which generalizes that of the classic Borda count in a way that allows for differences in agents' intensities to be reflected in preference aggregation more accurately and in a much richer class of situations. Building on the same comparability criterion, the paper also studies the classic assignment problem by defining an allocation to be "intensity-efficient" if it is Pareto efficient with respect to the preferences induced by the agents' intensities and also such that, when another allocation assigns the same pairs of items to the same pairs of agents but in a "flipped" way, the former allocation assigns the commonly preferred item in every such pair to the agent who prefers it more. Some first results on the (non-)existence of such allocations are presented without imposing restrictions on preferences or intensities other than strictness, and the relation -- or lack thereof -- is studied between intensity-efficient and classical utilitarian allocations.