 Start with the Completeness axiom, which says that an agent can compare, in terms of the weak preference relation, all pairs of options in \(S\). Whether or not Completeness is a plausible rationality constraint depends both on what sort of options are under consideration, and how we interpret preferences over these options. If the option set includes all kinds of states of affairs, then Completeness is not immediately compelling. For instance, it is questionable whether an agent should be able to compare the option whereby two additional people in the world are made literate with the option whereby two additional people reach the age of sixty. If, on the other hand, all options in the set are quite similar to each other, say, all options are investment portfolios, then Completeness is more compelling. But even if we do not restrict the kinds of options under consideration, the question of whether or not Completeness should be satisfied turns on the meaning of preference. For instance, if preferences merely represent choice behaviour or choice dispositions, as they do according to the “revealed preference theory” popular amongst economists (see Sen 1973), then Completeness is automatically satisfied, on the assumption that a choice must inevitably be made. By contrast, if preferences are understood rather as mental attitudes, typically considered judgments about whether an option is better or more desirable than another, then the doubts about Completeness alluded to above are pertinent (for further discussion, see Mandler 2001).