# Mistaking the Solution for the Problem

How do you solve a problem? How do you decide what to do? What new computer should you buy? What new smartphone? Should you buy anything? Is it better to simply do something — anything — rather than dither about?

In reviewing my decision theory posts for 2011 that could address some of those questions, I realized that an important distinction had been overlooked. I had talked about the nuances of making decisions, but had not made sufficient distinction between the steps necessary to make the decision. That distinction is there implicitly, but just as I wrote about the difference between game theory and decision theory, we should also keep in mind another important, and essential distinction.

That crucial distinction has three parts: (1) analyzing the problem, (2) formulating the conditions of decision theory, and (3) deciding on an action. The last distinction is important because the result of a decision theoretical calculation is a probability and that is only as good as the inputs. Often, the proper choice is not the one with the highest payoff given the various assumptions. Sometimes the computation of a best decision overlooks the higher probability of making a decision that results in a “good enough” result. And there is always the example of a person who wins millions on the lottery even though any reasonable calculation shows that an expected return is negative. It would be difficult to argue with the winner that gambling is a bad bet. It all depends on how we define the problem.

It is a standard truism that if you cannot articulate the problem, you do not understand it. Too often people jump into action based on an initial assumption and miss solving the real problem. Doing a proper problem analysis is usually not difficult, and that is how people get into trouble. It seems so simple that they jump over it and end up making mistakes.

No matter how informal, a problem analysis should precede setting up the parameters for a decision calculation. This means describing the situation and exactly what makes it a problem. Then evaluate all the conditions that can influence the problem. Since everything in the universe is connected to every other thing, that can be a challenge and lead to unnecessary computations unless the relevant parameters are organized according to their likely influence on the problem. The gravity of Saturn and Jupiter affect my actions very slightly. In deciding which smartphone to buy, changes in the positions of Saturn and Jupiter are not important.

I got this far in writing and suddenly realized that I should consider the font of all wisdom, Wikipedia. after a little nosing around, I found an entry on decision making that pretty much mirrors what I just said, but with bullets instead of prose. The article introduces several topics which might be the subject of future posts, but one section, “Optimizing vs. Satisficing [a combination of satisfy and suffice]” is close to my third distinction above. After we have described the problem, and after we have set up the computations for decision theory, do we go with the computed optimum or for something that is “good enough” with a higher probability of getting it? A sub-optimal solution is easier to compute and often is good enough. If I need a mobile phone now, then any major brand name phone is probably good enough. If I only want a new phone and time is not critical, then I might get more enjoyment out of studying the market and eventually purchasing a phone that might be slightly better than what I would have bought after simply looking at the alternatives in a single store.

Example: A baseball player has a feeling for the probability of hitting against a given pitcher. He also knows that swinging for a line drive and relatively sure base hit is more probable to succeed than hitting a home run, but the score is tied and it is the bottom of the ninth; which is the better strategy? Assume the next batter is good. Assume the next batter is bad. And yes, there are two outs. And as always, there is the personal aspect running through the baseball player’s head: “What will be the effect on my salary next year is I hit the winning home run or if I strike out?”

The point is that the eventual decision made will depend on how the problem is defined as much as how the solution is analyzed.

This is extremely important because, in the heat of the moment, we often mistake the solution for the problem. How can that be? Suppose a client asks me to help select a new computer because his old one is getting slow. Has the client appropriately identified his problem as knowing which computer to buy?

Assuming one wishes to define a problem with choices carefully, making a decision matrix is a good tool. This can be done on any spreadsheet easily enough, and in a later post, I will work some examples of how to set up problem and make a decision using a spreadsheet. Since I would rather not write one myself, I am sorting through the thousands of online ready-made Excel templates to find a few that have been set up to make a decision matrix so that I can recommend them and use one as an example. The closest I have come so far is one on the Microsoft site which, unfortunately, had an awkward bug in the computations that should have been caught before posting it. That lowers my confidence in its vetting process. We all hope my vetting will be better.

A person familiar with Excel and decision theory could probably set up a whole new template with little difficulty, but I am a novice at Excel, so I will continue to comb through the available freebies. If anyone is impatient to obtain a sophisticated software aid in making decisions, try Treeage. I had its pricey pro version for a year (it is a renewable thing, not a purchase — hey, it is the company’s business model. I do not defend it.), and it was very good — but, like I said, pricey.

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