Systems modelling

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# 3.2 Why quantitative models

The stage of choosing a model could include consideration of diagrams or conceptual models as well as quantitative models. So when should you consider a quantitative model as the appropriate next step? There are four main conditions that are necessary for a quantitative model to be an appropriate choice.

1. At the chosen level of aggregation, all the significant features or behaviours of the system must be adequately quantified, i.e. measured. If this condition is not satisfied then any model will have to impute numerical values for the unqualified features or behaviours, which can lead to distortions in any conclusions derived from the model. Even where all the important issues are quantified, there are other issues associated with data that may preclude the use of a quantitative model. In particular, if the data are unreliable, or are extremely expensive in time or money to collect, then quantitative modelling may not be feasible.

2. The purpose should involve a level of discrimination or differentiation that can only be achieved by quantitative comparisons. There are many of these, for example:

• Which is the most effective intervention?

• When will this behaviour become manifest?

• How many cases of each illness should we expect next month?

If the main purpose can be accomplished without a quantitative model then seek the answer non-quantitatively. The reason for this is that the sheer complexity and data gathering required for most quantitative models can only be justified if it is essential. Also the process of converting the problem into mathematical form and then interpreting the answers back from a numerical output may obscure the core systems issues.

3. Where the system of interest involves a significant number of interacting feedback loops at the level of aggregation required. That is, a situation where the behaviour of X affects the behaviour of Y, and the behaviour of Y also affects the behaviour of X. Almost by definition all systems involve interacting feedback loops, but in most cases they do not need to be explicitly modelled if they are not essential in determining the behaviour of interest. However if the behaviour of interest is directly governed by the interaction of more than three feedback loops you are likely to be forced to use a quantitative model to understand what is going on.

4. Where the behaviour or features of the system of interest are governed by stochastic processes. Stochastic, or random processes are those like the toss of a coin or selection of a card from a pack. Here a range of results is possible, but you cannot know in advance exactly which result will occur although you may know the chance (formally, the probability) of a particular result occurring. In such a situation you will usually need a model to arrive at a thorough understanding, since it is only by using a model that you can explore the behaviour over and over again with randomly chosen sets of values. Human beings are notoriously bad at predicting the outcomes of systems governed by such stochastic processes. The popularity of gambling, and the interpretations placed on predictions of the weather are examples of this.

## SAQ 6

In which of the following situations do you think it would be appropriate to use a quantitative model, and why?

1. Devising a policy to conserve stocks of fish in the North Sea.

2. Determining the best approach to negotiating a merger between two competing companies, from the point of view of one of the companies.

3. Choosing between two different routes for a new road development.

1. The size of fish stocks is governed by a complex series of feedback loops, including the relationship between fishing activities and fish stock. It would be essential to carry out sufficient quantitative modelling to establish the range of activity that could be sustained, given the available information on the fish and the sea. However this is usually the easiest part of devising a policy that will work!

2. Here quantitative modelling cannot assist in devising the approach to negotiations. There may need to be some calculation of the potential savings and benefits associated with the merger, but these will not be reliable because of the lack of data on the competitor company or on the merged company.

3. This is an area where quantitative modelling, known as cost-benefit analysis, has been widely used to try to establish the relative merits of alternatives. However many of the sensitive factors, such as conserving wildlife, avoiding traffic congestion, reducing accidents and noise, reducing amenity of countryside and so on are not readily quantified in financial terms. The use of cost-benefit models therefore reduces to interminable arguments regarding the imputation of values to these factors. So this is a case where quantitative modelling is used, but probably should not be.

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