  We study the assignment problem in situations where, in addition to having
ordinal preferences, agents also have *ordinal intensities*: they can make
simple and internally consistent 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 social-choice environment we first introduce a
rank-based criterion that enables interpersonal comparability of such ordinal
intensities. Building on this criterion, we define 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. We present some first results
on the (non-)existence of such allocations without imposing restrictions on
preferences or intensities other than strictness.
