Question

Should one always select the decision path that has the highest expectation value? Why/Why not? Give an example where one might not.

Answer 1

No, one should not

There are 4 basic elements in decision theory: acts, events, outcomes, and payoffs.  Acts are the actions being considered by the agent -in the example elow, taking the raincoat or not; events are occurrences taking place outside the control of the agent (rain or lack thereof); outcomes are the result of the occurrence (or lack of it) of acts and events (staying dry or not; being burdened by the raincoat or not); payoffs are the values the decision maker is placing on the occurrences (for example, how much being free of the nuisance of carrying an raincoat is worth to one).  Payoffs can be positive (staying dry) or negative (the raincoat nuisance).  It is often useful to represent a decision problem by a tree.

Here a square indicates a node in the tree where a decision is made and a circle where events take place.  The tree does not contain payoffs yet, but they can easily be placed by the outcomes.

In general, we can note two things.  First, the nature of the payoffs depends on one’s objectives.  If one is interested only in making money, then payoffs are best accounted for in terms of money.  However, if one is interested in, say, safety, then the payoffs are best accounted for in terms of risk of accident, for example.