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From a reader’s comment and my response: “One of your students mentioned "making decisions in the midst of incomplete information" as one of the most important lessons learned from you. May I ask you to write an article on this topic? It is one of the constant challenges faced by every scientist trying to push the boundary of human knowledge. I'd love to hear your thoughts/experiences in this regard. Thx”.  博主回复(2011-5-7 21:30)：Thank you. Let me think about this

This is a very good question and a vexing problem faced by all of us. Let me first give some background.

1.     Students of Operations Research (OR) all know the existence of a topic within OR called “Decision Analysis (DA) ”. I have also touched on the subject in one of my blog articles http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=16273 which incidentally is well worth re-reading (re-reading it myself three years later, I’d not change a word nor think I can do better).

2.     “Decision Analysis (DA)”, however, suffers several drawbacks when applying to real world problems.

a.     Most real problems are so computationally intensive that render the methodology of  DA impractical or infeasible.

b.     DA only deals with “one shot” decision making, i.e., you decide once and there are no recourse or second chances

c.      DA requires the decision maker to amalgamate all consequences of the decision into one measurement in the units of “utility” (e.g., money). Utility Theory can be questioned theoretically regarding its assumption (see next point), and practically in terms our ability to assess utility.

d.     If one believes in Utility theory, then, it requires the decision maker to choose the decision that maximize the expected utility. But we know human beings do not always derive comfort from expected (or average) basis. Recall my frequent analogy of immersing one foot in boiling water and the other in ice in previous blog articles.

3.     Regarding criticism point 2b above, there is actually a sub-branch of DA called “Sequential Decision Analysis”. This endeavor expands the decision possibilities from “yes”, “no” to include “wait and see or no decision”. The point here is that by waiting for more information, it may make the correct decision easier to ascertain. The “Sequential Probability Ratio Test (SPRT)” in statistics is one specific example. However, this extension only takes care of acquiring possible new information. Other issues such as feedback, second chance, and changing environment are not addressed.

4.     Consequently, when it comes to making decisions in complex real world problems, decision theory at best is only of qualitative use in help us avoiding emotion or rash actions.

Under this background, what did I tell my student and myself about practical decision making under incomplete or uncertain information? Here knowledge of control theory comes in. In my article on optimal control  http://bbs.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=209522

Four prominent features of control theory were pointed out, namely, FEEDBACK, DYNAMICS, UNCERTAINTY, and EXTENSION to LEARNING and ADAPTATION. For practical decision making, each of these comes into play.

By “feedback” we learn from mistakes. In life, second chances are plentiful and there are always a series of related decisions in which midcourse corrections are possible.

By “dynamics” we mean things and environment including goals do change. These will induce changes in decisions that we subsequently make. Very seldom it is a “one shot” affair

Finally “uncertainty, learning and adaptation” are generalizations of the sequential decision analysis approach mentioned in point 3 above. My other articles about  "recipe for life" http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=8186   in general terms, and http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=276944 in a specific but important situation illustrated how they are relevant in my own decision making in life.

Of course, a precise formula for practical decision making under uncertainty for real world problems does not exist. The above are still guidelines and are what makes life interesting and let me earn a living among other things.

Lastly, consulting my series of articles on "How to do Research" and "On Research and Education" will also be helpful.