Using Models for Rational Choice : Motivation

The decision of whether to be or not to be is very complex. We will try to simplify and explain this complexity, by using models. A model can be defined as follows [1] : A model is a representation containing the essential structure of some object or event in the real world.

The representation of a model may take two major forms. It can take a physical form, as in a model airplane, or it can take a symbolic form, using natural language, a computer program, or a set of mathematical equations.

To be useful, a model must be easier to change and manipulate than the real world. This allows us, for example, to change the model, test it and check the results of the model. Such operations may be impossible in the real world, so frequently, models are an important tool for analyzing a problem.

In order to create a model, we must first make some assumptions about the essential structure and relationships of objects and/or events in the real world. These assumptions are about what is necessary or important to explain in the problem at hand.

Balancing Accuracy and Simplicity

There are many possible models for decision making. Essentially, the models vary in the balancing of two contradicting desirable properties: accuracy and simplicity.

Intuitively, a model is accurate, if when a decision is correct according to the model, then it is indeed correct in reality. However, if the model is not simple then it is not very useful. As an extreme example, assuming that the world is deterministic, we could have a computer to which we feed the location of every atom in the universe. Then we could perform a simulation for each option which we can choose, and see the outcome. After performing all the simulations, we can choose the option for which the outcome was best. Such a model is perfectly accurate, however, it is not possible to build such a computer program in reality, because it is too complicated.

In this example, a perfectly accurate model is not simple enough to be implemented by a computer. However, we want a simple model not so much for implementation by computers. Simplicity is desirable because a simple model is easier for humans to understand and analyze. Simple models allow us to gain insight into the the complex reality which is to be modeled. Using such insight people may devise heuristics, or "rules of thumb". These are simple guidelines which people use in order to make judgments and decisions.

In general, the greater the number of simplifying assumptions made about the essential structure of the real world, the simpler the model. Our goal is to create simple models that are also accurate. In most cases, however, such models are not available. Typically, people start with simple models, and add complexity in order to obtain more accurate models. It is up to us to decide at what point the gain in accuracy no longer warrants the additional complexity of the model.

There has been a lot of research on models for decision making. Much of it is quite complex mathematically. In these web pages only relatively basic models will be presented. For additional simplification the models are not displayed in their general form, rather, they are modified and adapted to use concrete terms which ashers may apply more easily , and get some intuitive insights about the decision of whether to exit.

Mathematical Models

We are going to used models which are stated using mathematical equations. This approach may seem cumbersome especially for those not adept in math, however, it has significant benefits.

Mathematics has been used extensively in the past, and there are already many models which can describe a large number of real world situations. In particular, there has been much research on models for decision making.

In addition, many transformations and manipulations are available in the language of mathematics. Once a mathematical model is developed, then such transformations can be used. An example of one such transformation is maximization. This is especially useful for decision making since if we can construct a model which assigns numerical values to outcomes in the real world, then we can define a good decision as one that maximizes the value of the outcome.

Finally, mathematics makes it easier to succinctly express some thoughts which not easily expressed in other languages.

Probability

In principle, all factual beliefs are a matter of probabilities. Factual knowledge is certainty. If you see it is raining outside then you know it is raining. However, you probably don't know whether it is raining now in the Sahara desert, although you probably believe it is not. There is a small probability that it is raining in the desert as well.

It is more difficult to see events in our own life as being affected by probability. People often prefer to explain events in terms of cause and effect. For example, Israeli pilot trainers in the Israeli air force praised trainees after successful flights, and scorned them after unsuccessful ones. The trainers noted that right after being praised, the next flight was worse, but after being scorned, the next flight was better. Their conclusion was that praise was ineffective, probably because it causes the trainees to become careless, whereas scorning was an effective way to improve the performance of pilots. However, there is a much easier explanation in terms of probability. Most flights are average, only a small part of them are either very bad or very good. Therefore, there is always a greater probability for a flight to be average. Thus the next flight after a good one is more likely to be worse, and the next flight after a bad one is likely to be better. This has nothing to do with the trainers remarks. There is much research in cognitive psychology about the inability of people to reason with probability.

For the decision of whether to be or not to be, there are many things which are uncertain. If we decide to exit, it is uncertain whether we will in fact succeed. If we continue to live, it is uncertain whether our future life will improve or worsen. Probability is the way mathematicians model uncertainty, therefore, in our models, we are going to use probability extensively. This will allow us to use more rigorous reasoning of uncertainty, reasoning which humans find very difficult.

REFERENCES

[1] David W. Stockburger Introductory Statistics: Concepts, Models, and Applications, 1996. Models