Corruption and rocket science

Non-linear dynamics is rocket science, in every sense of the word. An interesting book Optimal Control of Non-linear Process, with applications in drugs, corruption and terror by Grass et.al, published by Springer , explores the link between two seemingly unrelated disciplines — non-linear dynamics and corruption. The result is interesting, to say the least. This article summarises the findings of the study reported in the book.

A dynamic model is a mathematical abstraction of a real life situation. It is extensively used in engineering, sciences, economics and business. The model uses a quantity, many times physical, called a variable and studies its status with time. The book uses two models — a simple model to understand the corrupt population and a more complicated one to bring out the dynamics of political corruption.

Punishment and graft

The first model of interest to us is a one-dimensional model, involving one variable, the proportion of corrupt population. The model is built on the premise that people flit between being corrupt and honest depending on the difference between the utility of being corrupt, in terms of wealth, power etc., and the punishment or the deterrent. Further, honest people become corrupt by their contact with the corrupt.

The important question is whether there can be an equilibrium. Equilibrium is a state when disturbed, will not be pulled away but return to its original state, like a marble sitting in a trough. In simple words, will the ratio of honest to corrupt population reach a constant? The model shows that this will never happen! In the language of mathematics, it is an unstable equilibrium. With time, a country can only be totally honest or corrupt, a zero or one situation. Ironically, that is what we are witnessing now, an exponential progress towards total corruption. Assume, for a moment that there exists a nation which is totally honest and no laws for anti-corruption.

In this country, the model predicts that even one black sheep can pull the nation towards disaster at an exponential rate. Applying this to our country, where the corruption percentage is high, if the deterrent is lukewarm, the nation would race to total corruption.

The model gives a ray of hope. If the punishment is severe, and the population has a small percentage of honest people, the nation will become corruption free with time. The time depends on the two factors, benefit due to corruption and the severity of law against it.

Three factors at play

In order to analyse the corruption in politics, the authors graduate to a higher dimension. We now have three factors which are intertwined. The popularity of the politician, public awareness of corruption brought out by popular movements, press and judiciary and the extent of corruption. The resulting mathematical model is formidable. The politicians optimise the popularity and corruption. Though the results can be expressed quantitatively, let us understand it qualitatively.

The model assumes that the politicians are not corrupt, simply because it hurts their popularity. That popularity is affected by campaigns. When popularity increases, corruption increases, a scene we have seen time and again in Indian politics! There is a time lag between the corruption and the campaigns. It takes time to realise the extent of corruption.

This is again a scenario we have seen in many scams in recent times. The politicians sense the growing criticism and loss of popularity and the rate of corruption takes a southward march. Because of the time lag, corruption reaches its nadir even when the popular uprising is high. Since the driving force for the anti-corruption lobby is corruption itself, the campaign loses steam and comes down. The popularity of politicians is at a low and the campaign is low.

Interestingly, corruption starts to rise again at this point and the people do not realise it. The time lag works in the favour of politicians. The model shows that there can never be an equilibrium. Corruption is a cycle. It keeps oscillating around a mean. The peak and the trough above and below the mean need to be worked out. Nevertheless, the only way to keep it in check is a powerful campaign.

So what do we learn from this model? This country requires severe anti-corruption laws. A mild protracted action may do more harm. And Anna Hazare and his group cannot rest. Fighting corruption is a never-ending exercise.

(The author is Professor, Department of Engineering Design, IIT, Madras.)

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