In standard revealed preference, we don't assume that the agent has rational preferences over a choice set $X$, and we can then ask: under what conditions can $X$ be rationalized by a rational preference relation?
One answer turns out to be: if the choice set $\mathcal C$ contains all subsets $C\subset X$ of 3 elements or less, and the weak axiom of revealed preference is satisfied.
But now, what if we already know from the outset that the preference relation of the decisionmaker is rational, and we just want to pinpoint uniquely which preference relation this is? Then at the very least, we only need every 2-element subset of $X$, but it seems that this can be imporved. Is there work on this?
EDIT: Let me state the question more clearly: What are minimal conditions on a choice collection $\mathcal C\subseteq \mathcal P(X)$ such that for any preference relation that generates choices $c(C)$, that preference relation is the unique rationalization of those choices?