Introducing the new Principle of Exhaustivity for solving real life problems

Applying Principle of Exhaustivity to solve real life problems

 

Hope you have already gone through our first two posts. We were not very specific there—it was just background building.

In this session we will tell you about one of the most important principles we found effective from our problem solving experiences.

We call this as “Principle of Exhaustivity”.

Let us take a simple problem structure. When we are faced with a problem, we have:

·         One or more than one goal or objective that we have to somehow reach. A solution to the problem is supposed to meet the goal. Usually, problems are of single goal kind.

·         Choices or options one of which we have to choose for satisfying the objective. Choosing the right option is the solution to the problem.

·         Criteria on the basis of which we will choose the right option.

Take for example the problem of purchasing a new mobile phone for yourself. At the very outset, suppose you have decided a range of prices within which you will make the purchase. Your objective is to get a phone that would give you maximum satisfaction or utility of use within the given budget.

Applying principle of exhaustivity at the level of options or choices

Now is the time to evaluate the various models of various brands that you can buy within your budget. These will be your options or choices.

How would you finally choose one phone out of possible many? In your mind you must have had some idea about that. The phone OS may be Android, iOS, Blackberry, Symbian, Windows, Ubuntu or some other. It may have larger or smaller screen size. Its battery may last long or not so long. These are a few amongst all the criteria based on which you will evaluate available choices.  

If the principle of exhaustivity is ingrained deeply in your mindset, you will exhaustively evaluate all available phones, and not just a few that are shown in a shop or a website. This situation is:

·         Application of the principle of exhaustivity at the level of identifying options or choices. It is very important to identify possible choices exhaustively as, many times the right choice remains unseen or hidden.

Sometimes hidden choices are to be unearthed or a new option needs to be created.

Applying principle of exhaustivity at the level of criteria for evaluation of choices

Similarly, after exhaustively identifying possible choices, you will sit down and carefully list out exhaustively all the important criteria on the basis of which you will evaluate the shortlisted choices. This situation is:

·         Application of the principle of exhaustivity at the level of identifying the most important evaluation criteria. At this stage if you leave out some important criteria you may finally end up in choosing a phone set you won’t like.

Here, we would like to make a strong recommendation:

·         While choosing your set of evaluation criteria, identify the evaluation criteria exhaustively, but please do not choose too many, choose only the most important ones. If you choose too many criteria, your mind and judgment may become confused.

You may wonder - how many is too many? Yes, we also wonder. There is no hard and fast rule here. But still we would generally suggest:

·         Limit the number of primary level criteria to single digit.

Yes, there may be many levels of criteria and sub-criteria for choosing your option in a more complex choice scenario. Later we will discuss this in more details.

We had to raise this issue at this point because exhaustivity was in conflict with the effectiveness of approach.

Be exhaustive, but be exhaustive in identifying only the criteria that are most important in evaluating the available choices.

Applying principle of exhaustivity at the level of goal or objective

Till now, we have seen application of the exhaustivity principle at two levels. There is one more level of application of this principle that is vitally important. That is:

·         Application of the principle of exhaustivity at the level of identifying the goal or objective itself. Though the goal in most cases is only one, sometimes you need to stop and think, carefully analyzing the problem to clearly understand what really the goal is.

It is a fact of life that many times the goal itself is wrongly defined or chosen and accordingly after a lot of effort a wrong solution is reached.

Application of the exhaustivity principle at this level may not mean you identify many goals exhaustively, or identify one goal from many. It means that you need to analyze thoroughly, giving some time in identifying the right goal.

We will take up this principle again in the next session. Interestingly this principle seems either trivial or obvious. One may ask, well we do evaluate exhaustively, is there any need to specify this as a standalone separate important principle at all?

There is no direct answer, as there is no ready-made unique solution to any real world problem. We can only say that we have encountered apparently intractable problems conquered by application of this straightforward principle. We have seen correctness assurance level of a solution (where correctness assurance was the key criteria) that could not be measured at all rise up to more than 99% just by dovetailing this principle with other known techniques being applied.

Surprisingly we have also seen experienced practitioners of problem solving in certain domains missing this key principle occasionally. This happens because of its apparent obvious nature. To get over this taken-for-granted situation, one needs to ingrain this principle deeply in one’s problem solving mindset.

We will now end this session with a cute problem for you. This is a standard problem posed to many audiences many times. We would say, try to solve it in your own way. Either you may be baffled and give up or you may suddenly discover the answer. You may find it very easy or you may not. In all cases, we would ask you to reach the solution by applying the exhaustivity principle carefully.

Problem 1:

A man and his son were involved in a car accident. The father died on the scene, but the child was rushed to the hospital. When he arrived the surgeon said, "I can't operate on this boy, he is my son!” How could this be?

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