I have expressed my strong and long-held criticisms of classical decision theory – that based on maximum expected utility (MEU) –  before and again before that.  I want to expand here on one of my criticisms.
One feature of MEU theory is that the preferences of a decision-maker are decoupled from the decision-making process itself.  The MEU process works independently of the preferences of the decision-maker, which are assumed to be independent inputs to the decision-making process.    This may be fine for some decisions, and for some decision-makers, but there are many, many real-world decisions where this decoupling is infeasible or undesirable, or both.
For example, I have talked before about network goods, goods for which the utility received by one consumer depends on the utility received by other consumers.   A fax machine, in the paradigm example, provides no benefits at all to someone whose network of contacts or colleagues includes no one else with a fax machine.   A rational consumer (rational in the narrow sense of MEU theory, as well as rational in the prior sense of being reason-based) would wait to see whether other consumers  in her network decide to purchase such a good (or are likely to decide to purchase it) before deciding to do so herself.   In this case, her preferences are endogeneous to the decision-process, and it makes no sense to model preferences as logically or chronologically prior to the process.   Like most people  in marketing, I have yet to encounter a good or service which is not a network good:  even so-called commodities, like coal, are subject to fashion, to peer-group pressures, and to imitative purchase behaviors.  (In so far as something looks like a commodity in the real world, some marketing manager is not doing his or her job.)
A second class of decisions also require us to consider preferences and decision-processes as strongly coupled.  These are situations where there are multiple decision-makers or stakeholders.     A truly self-interested agent (such as those assumed by mainstream micro-economics) cares not a jot for the interests of other stakeholders, but for those of us out here in the real world, this is almost never the case.  In any multiple-stakeholder decision – ie, any decision where the consequences accrue to more than one party – a non-selfish decision-maker would first seek to learn of the consequences of the different decision-options to other stakeholders as well as to herself, and of the preferences of those other stakeholders over these consequences.  Thus, any sensible decision-making process needs to allow for the elicitation and sharing of consequences and preferences between stakeholders.  In any reasonably complex decision – such as deciding whether to restrict use of some chemical on public health grounds, or deciding on a new distribution strategy for a commercial product  – these consequences will be dispersed and non-uniform in their effects.   This is why democratic government regulatory agencies, such as environmental agencies, conduct public hearings, enquiries and consultations exercises prior to making determinations.  And this is why even the most self-interested of corporate decision-makers invariably consider the views of shareholders, of regulators, of funders, of customers, of supply chain partners (both upstream and downstream), or of those internal staff who will be carrying out the decision, when they want the selected decision-option to be executed successfully.    No CEO is an island.
The fact that the consequences of major regulatory and corporate decisions are usually non-uniform in their impacts on stakeholders  – each decision-option advantaging some people or groups, while disadvantaging others – makes the application of any standard, context-independent decision-rule nonsensical.   Applying standard statistical tests as decision rules falls into this nonsensical category, something statisticians have known all along, but others seem not to. (See the references below for more on this.)
Any rational, feasible decision-process intended for the sorts of decisions we citizens, consumers and businesses face every day needs to allow preferences to emerge as part of the decision-making process, with preferences and the decision-process strongly coupled together.  Once again, as on so many other aspects, MEU theory fails.   Remind me again why it stays in Economics text books and MBA curricula.
References:
L. Atkins and D. Jarrett [1979]:  The significance of “significance tests”.  In:  J. Irvine, I. Miles and J. Evans (Editors): Demystifying Social Statistics. London, UK: Pluto Press.
D. J. Fiorino [1989]:  Environmental risk and democratic process:  a critical review.  Columbia Journal of Environmental Law,  14: 501-547.  (This paper presents reasons why deliberative democratic processes are necessary in environmental regulation.)
T. Page [1978]:  A generic view of toxic chemicals and similar risks.  Ecology Law Quarterly.  7 (2): 207-244.