Dealing with unknowns and uncertainty

More pertinent though is where a question is posed (in order to eliminate options) that has a degree of uncertainty attached to it. This can be represented in the "Twenty Questions" model by the person answering the questions being unable to answer a straightforward 'Yes' or 'No' to a question. The answer might be "I think it is yes, but, I'm not sure".

In the game of "Twenty Questions" the answer to a question answered in this way might be ignored, but, what if every question was answered this way? Then, to have any chance of arriving at a solution, a probability has to be assigned to each answer.

This may seem to negate the strategy, or, at the best give it a very dubious conclusion. But, this isn't necessarily true. This is best explained by a game that was very popular in the 1970's called, amongst other names, "Mastermind".

This game consists of a peg board with six rows of holes with a dozen holes in each row. There is also a number of pegs of six different colours. The idea is that one player writes down a combination of six colours (some of which could be the same) in a particular order and then for the other player to work out what this combination is by making guesses through placing six coloured pegs at a time into the holes in the peg board. As there were twelve columns (of six rows) the player could have a maximum of twelve guesses in which to discover the code.

The first try would have to be a complete guess of six pegs chosen at random. These will be placed into the first column. Then the person who has set the code tells the guesser how many of the pegs are of the right colour and how many are in the right position . There is no indication given though, as to which of the pegs are correct and which were incorrect: the guesser is simply given the two numbers.

When I was working away in Copenhagen one time , my fourteen year old daughter came to visit me. To keep ourselves amused one rainy afternoon, we decided to play this game of "Mastermind". It wasn't long before both of us got the hang of it - which was to use the information given in an accumulative way to progress towards the solution.

Soon, we were both able to guess each others code within no more than six guesses; at which time the game began to get boring. Then we decided to make it more difficult by making a rule that each of us could tell one lie when providing the information as to how many of the pegs were of the right colour and in the right position.

This made the game considerably more difficult because there were many possible alternative solutions, the correct solution having to be found by a process of elimination. Despite this handicap though, we were eventually able to guess each others code within eight or nine guesses.

At this point the game became boring again, so, we decided to let each other tell two lies when declaring the numbers of right colours and right positions. This more than doubled the complexity of the elimination process, but, eventually we reached a stage of being able to consistently guess each other's code within the allowable maximum of twelve guesses.

This game proves quite elegantly that uncertainty can be overcome if a suitable strategy is employed. The trick was to give each peg position a probability of being right, then testing the most likely solution to see if the uncertainty could be eliminated. The net result was that solutions could be found just as surely as when the information was accurate - it just took a few more guesses.

This is the way Game Theory is used to eliminate uncertainty. It doesn't trust answers to questions, but, counters this problem by asking additional questions to cover the possibility that some answers may be wrong.

This can be modelled by imagining the game of "Twenty Questions" being played where you can ask several different people about the same unknown object. Then, when a person answers a question with "I'm not sure whether the answer is a 'Yes' or a 'No' there will be other people to ask and perhaps one of them might be able to answer with more certainty.

Where there might be conflicting answers, with some answering 'Yes' and some answering 'No' the ratio of 'Yeses' and 'Noes' could be used to give the answer 'Yes' or 'No' a probability of being the correct answer.

Staying with this same model, it would only be common sense to assign some sort of weightings to the answers given. For example, if the question involves the person having to have a certain amount of technical knowledge to answer correctly, an answer from a person who is known to have such technical knowledge would carry far more weight than a person who is known not to have any such knowledge.

Taking all this reasoning into consideration, the idea that you can make an optimum choice from amongst a limitless number of choices does not seem such a hopeless task as it would first appear. It simply involves devising a suitable strategy where uncertainties can be eliminated by:

Asking appropriate questions

Asking several people the same question

Giving weightings to the answers

A Game Theory strategy might then be summed up as:

Finding suitable questions to ask

Finding suitable people to provide answers

Making sure that the questions can be posed to a number of different people

Such a strategy is ideal for highly technical environments where there is so much to know that everyone can be expected to have substantial gaps in their knowledge.

One final point of note. The game of "Twenty Questions" does not rely on being able to ask exactly the right questions. Different combinations of quite different questions can be posed, which might still lead to a correct solution. In this way, lack of knowledge can be bypassed. It is not necessary to have to know all the questions that could be asked, as long as a suitable strategy is employed to eliminate the uncertainties.

Now take a quick glance back to the introduction, at the list of the twenty four initial assumptions that have to be made before embarking upon an e-commerce venture. Do they seem quite as formidable as when you first looked at them?