Criminals too are rational individuals who think and undertake a cost-benefit analysis before committing a crime. Like any decision that involves risk, criminals too consider the expected returns based on the rewards on the upside and the penalties on the downside. In their case, what matters is the probability of being caught

Why do people commit crimes? Don’t they fear being caught? Where are the police officers? What is the government doing? Well, the government is there, the policemen are there, and so is the fear. Everyone is well aware of the legal, financial, physical and mental costs. Yet we have criminals – the murderers, cheats and thieves. So why do they commit such crimes if they know the costs? It is because they also know the gains (whether financial or emotional), and they rationally compare these two to make their decision.

Yes, criminals too are rational individuals who think and undertake a cost-benefit analysis before committing a crime.

Like any decision that involves a risk, criminals too consider the expected returns based on the rewards on the upside and the penalties on the downside. In their case, what matters is the probability of being caught.

Based on these parameters, we can build a simple framework that should help us look at the reasons behind a crime, and the options that the government has to prevent that crime.

Like most cases, the criminal wants to maximise his expected return, which is the sum of the probability of being caught times the penalty and the probability of escape times the reward.

To make our model quantifiable and easy to understand, we will define all our parameters in numerical terms. This is only to ensure that the results are easy to comprehend.

The protagonist in our model is an ordinary rational thief, contemplating whether or not to loot his neighbour’s shop. The contents of the shop would fetch him 1,000 in cash.

That’s the reward. We assume that the penalty does not involve jail, but a hefty fine of 9,000.

The probability of being caught would depend on the number of police personnel and also the number of criminals present in the city. Higher the number of police, higher the probability of being caught.

Higher the number of criminals, lower the probability, as the limited police personnel would be chasing too many criminals.

In simple terms, we can define the probability of being caught as the number of policemen divided by the number of criminals.

Assume that the actual figures for number of policemen and criminals are 50 and 500. So the probability of being caught is 0.1 and probability of escape is 0.9.

With this, the expected return is 0.1 times -9000 plus 0.9 times 1000, which adds up to 0. Given these values for our parameters [reward, penalty and prob (caught)], the criminal has zero expected gains.

Hence, he is indifferent to committing the crime.

Now let’s make changes to our parameters, one at a time, and see how the expected return, and thereby the rational criminal’s action would change.

Reward: An increase in the reward, let’s say, from 1000 to 2000 would increase the expected return to 900, thereby making the looting decision lucrative.

On the other hand, a fall in reward would drag the expected return below zero.

Therefore, assuming other parameters remain constant, we can say that higher rewards lead to higher crimes.

Penalty: A penalty has the exact opposite effect on the crime rate. In our example, if the penalty is raised to 10,000, then the expected return falls to -100. A higher penalty reduces the incentive to commit a crime.

Probability of being caught: This parameter depends on both the count of policemen and the count of criminals. If the number of criminals rises from 500 to 1,000 for the same number of policemen (50), then the probability falls from 0.1 to 0.05, and the expected return rises to 500.

In our base case (where expected return is 0), if even one more person decides to commit a crime, then the probability of being caught would tilt in favour of the criminals. This would lead to a positive expected return, thus pulling in more people to commit similar crimes.

There are two possible solutions to this problem.

Either increase the count of policemen to keep the probability intact, or raise the penalty. Increasing the number of policemen involves a cost. The government needs to pay for their wages, uniform, transport, office and other requirements.

As fiscal constraints tighten, such expenditures become even more difficult.

The second alternative of imposing a higher penalty looks more appealing to the government. Instead of incurring a cost, the penalty helps raise revenue. Even in reality, you would see that in countries with a low police to population ratio, the government levies heavy penalties and fines on illegal activities. This is observed more in the developing world where issues of overpopulation and economic backwardness prevail.

A higher penalty, however, is less effective as a deterring tool than increasing police personnel. There are different types of crimes with different rewards, and these rewards keep changing (mostly increasing) with time. Penalties though are not updated regularly, as it requires regular monitoring, which itself requires more personnel. The expected return is more likely to become positive with time, leading to more crime and more criminals.

Raising the penalty might increase the collection from the offenders who are caught, but it would not be a deterrent enough to put a lid on the increasing number of criminals.

Also, the aim of the government is to reduce the number of criminals, rather than increase their revenue from fines/penalties.

An increase in the number of policemen has a direct positive impact on the number of criminals paying the penalty, whatever may be the amount of that penalty. This has a longterm effect of cutting down the number of criminals in the city.

Governments across the world have tried both the alternatives based on their own cost benefit analysis.

Since criminals (or potential criminals) too act rationally, the government would be in a better position to deal with them if they treat them as rational individuals.