# 7 Completeness

Another key assumption in a rational choice model is that decision makers are opinionated about *all* the objects of choice. That is, there are no objects \(x\) and \(y\) such that \(x\) and \(y\) are incomparable for the decision maker.

- Completeness
- For all \(x, y\in X\), exactly one of \(x \mathrel{P} y\), \(y\mathrel{P} x\) or \(x \mathrel{I} y\) is true. I.e., for all \(x, y\in X\), not-\(x\mathrel{N} y\).

Completeness is a common simplifying assumption in many rational choice models. However, assuming completeness does not have the same type of justification as transitivity:

[O]f all the axioms of utility theory, the completeness axiom is perhaps the most questionable. Like others, it is inaccurate as a description of real life; but unlike them we find it hard to accept even from the normative viewpoint. (Aumann 1962, 446)