Note that you can still get EUM-like properties without completeness: you just can’t use a single fully-fleshed-out utility function. You need either several utility functions (that is, your system is made of subagents) or, equivalently, a utility function that is not completely defined (that is, your system has Knightian uncertainty over its utility function).
A person is defined to be rational, I believe, if he does the best he can,
using reason and all available information, to further his own interests and
values. I argue that Knightian behavior is rational in this sense. However,
rationality is often used loosely in another sense, which is that all behavior
is rationalizable as serving to maximize some preference. The two senses
of rational are in a way converse. The first says that when preference ex-
ists, behavior serves it. The second says that all behavior is generated by
preferences. The second sense seems to be very unlikely to be true, except
by definition. It does not even seem to be useful as a definition. If choice
is made the definition of preference, then one is led, like a true sophist,
to the conclusion that people always do what they want to do, even when
compelled to do things by threats of violence. The first sense of rationality
is the one which is important for economic theory, at least as it is presently
formulated. One would like to believe that people usually act so as to serve
their own economic interests, at least when these interests are clear and do
not conflict with other interests. If one identifies the two converse senses of
rationality, one needlessly jeopardizes the first sense, since the second sense
is probably more likely to be rejected than the first.
This has been discussed here before, but it’s a nice succinct description.
Immediately following and relevant to this discussion:
Associated with each definition of rationality is a different point of view
toward incomplete preference. The view associated with the first definition
of rationality is that the preference ordering is a constituent of a model which
explains some but not all behavior. Behavior never contradicts the ordering,
but not all choices are explained by it, nor are all stated or felt preferences.
The model is not contradicted if an individual expresses strong preferences
between alternatives which he finds incomparable according to the model.
Knightian decision theory. Part I 83
Such unexplained preferences or choices may be erratic and intransitive, but
this is no cause for concern. Such behavior does not make the individual
irrational, since the intransitive choices are not assumed to be in pursuit of
some goal. The individual becomes irrational only if one tries to infer some
unchanging goals from his choices or statements. It is because I adopt the
point of view just stated that I said earlier that the Knightian theory is not
contradicted if an individual shows a preference for one undominated choice
over another.
Note that you can still get EUM-like properties without completeness: you just can’t use a single fully-fleshed-out utility function. You need either several utility functions (that is, your system is made of subagents) or, equivalently, a utility function that is not completely defined (that is, your system has Knightian uncertainty over its utility function).
See Knightian Decision Theory. Part I
Arguably humans ourselves are better modeled as agents with incomplete preferences. See also Why Subagents?
from Knightian Decision Theory:
This has been discussed here before, but it’s a nice succinct description.
Immediately following and relevant to this discussion: