Editing Expected utility hypothesis (section)

===Irrational deviations===
[[Behavioral finance]] has produced several [[generalized expected utility]] theories to account for
instances where people's choices deviate from those predicted by expected utility theory. These deviations are described as "[[Rational choice theory|irrational]]" because they can depend on the way the problem is presented, not on the actual costs, rewards, or probabilities involved. Particular theories, including [[prospect theory]], [[rank-dependent expected utility]], and [[cumulative prospect theory]], are considered insufficient to predict preferences and the expected utility.<ref>{{cite journal | vauthors = Baratgin J | title = Rationality, the Bayesian standpoint, and the Monty-Hall problem | journal = Frontiers in Psychology | volume = 6 | pages = 1168 | date = 2015-08-11 | pmid = 26321986 | pmc = 4531217 | doi = 10.3389/fpsyg.2015.01168 | doi-access = free }}</ref>  Additionally, experiments have shown systematic violations and generalizations based on the results of Savage and von Neumann–Morgenstern. This is because preferences and utility functions constructed under different contexts differ significantly. This is demonstrated in the contrast of individual preferences under the insurance and lottery context, which shows the degree of indeterminacy of the expected utility theory. Additionally, experiments have shown systematic violations and generalizations based on the results of Savage and von Neumann–Morgenstern.

In practice, there will be many situations where the probabilities are unknown, and one operates under [[uncertainty]]. In economics, [[Knightian uncertainty]] or [[ambiguity aversion|ambiguity]] may occur. Thus, one must make assumptions about the probabilities, but the expected values of various decisions can be very [[sensitivity analysis|sensitive]] to the assumptions. This is particularly problematic when the expectation is dominated by rare extreme events, as in a [[long-tailed distribution]]. Alternative decision techniques are [[Robust decision|robust]] to the uncertainty of probability of outcomes, either not depending on probabilities of outcomes and only requiring [[scenario analysis]] (as in [[minimax]] or [[minimax regret]]), or being less sensitive to assumptions.

[[Bayesian probability|Bayesian]] approaches to probability treat it as a degree of belief. Thus, they do not distinguish between risk and a wider concept of uncertainty: they deny the existence of Knightian uncertainty. They would model uncertain probabilities with [[multilevel model|hierarchical model]]s, i.e., as distributions whose parameters are drawn from a higher-level distribution ([[hyperprior]]s).