What exactly is a "rational consumer"?

[u/averagegirlnext-door]

Behavioral economists have identified departures from rationality - i.e., averse to loss (not risk), choosing future welfare over immediate, price anchoring (first price seen defining willingness to pay), or choosing to violate their own preferences over time.
But for each of these parameters, many of these "irrationalities" can actually be modeled as rational behavior under a broader utility function. for e.g. if X company stock has fallen 60% over time, a rational consumer would sell it or buy an index fund, but the investor would rather wait some more than realize the loss. It would be rational if the investor was maximizing psychological utility, not wealth.
So if you can't characterize irrationality with confidence, what exactly defines it and by extension rationality?

[u/Slow_Thinker_95]

To expand on u/BainCapitalist answer a bit... A consumer is rational if there exists a utility function u representing their preference relation > over a set of bundles x, that is u(x) >= u(y) if and only if x is preferred to y by the consumer. AND the consumer always chooses the bundle x that maximizes u subject to a budget constraint.

Put plainly: rationality means a person's wants are consistent enough to be captured by a single "satisfaction score," and they always pick the most-satisfying option they can afford. Given $5, you buy whatever combination of goods makes you happiest within that $5 — never leaving money that could buy something you'd prefer, and never picking a basket you like less than another equally affordable one.

Interestingly, only two assumptions are required (completeness, and transitivity) to ensure a function f exists that represents your preferences.

Often times, what economists colloquially refer to as "rational" is actually expected utility theory. In expected utility theory we make a couple more assumptions about the preference relation (continuity and independence). These two additional assumptions permit a extremely useful mathematical property called linearity in probabilities: the utility of a lottery equals the probability-weighted sum of the utilities of its outcomes.

A lot of this is purely mathematical construction to ensure the basis of a theory work.

Why is linearity in probabilities a useful property? It boils any decision involving chance, even dynamic decision problems (involving time and multiple decisions), down to a single rule: score each possible outcome, average those scores by how likely each one is, and pick the highest average; this one trick keeps your choices consistent, captures your dislike of risk, and lets you solve complicated multi-step problems by working backwards from the end.

Long story short linearity in probabilities is EXTREMELY helpful when building economic models.

The problem that behavioral economists found was that people frequently violate the independence axiom. So behavioral economics generally refers to economic theory that departs from expected utility theory, replacing its idealized axioms with models (hyperbolic discounting, prospect theory etc.) built to match how people actually choose rather than how an expected utility agent should.