# Mathematical Model of Syubhat and Syahwat and Policy Implications

It has been quite some time since the last time Islam has any full-fledged state that run on Islamic principle. Even the latter era of Ottoman Caliphate is not so Islamic compared to its earlier era, which means Islam’s experience on running a modern state has been dated since 1924.

Our contemporary experience regarding Islam in public space is just reactionary utopian hope caused by our post-colonial inferiority complex. As a result, the direction of Islamic reform falls short of its grand ambition. It’s just a mass of confused reactionary movements without a single unitary goal. We need a clear principle on how to exercise Islam in the modern world.

However, I believe that the rules of Islam is pretty clear. Some ijtihad might be needed to give rulings on fundamentally modern issues, but the core principle are already final. However, implementation details to effectively enforce those rulings to citizen might need innovations. The innovation is plainly operational and is not meant as a substitute of Islamic law. We need to model how to control citizen behavior.

What makes (or prevents) people to do (or from doing) something? My initial guess, and also taking hints from contemporary developments in behavioral sciences, is cost-benefit analysis. People will do certain actions if the benefits outweigh the cost, and will refrain from doing so if the cost outweigh the benefit.

Let Xn be benefit or a set of benefits where n=1, 2, 3, … and Yn be cost or a set of costs where n= 1, 2, 3, …

For now let’s just explore the case where the largest n is 3. Therefore we have a set of benefit {X1, X2, X3} and a set of cost {Y1,Y2, Y3}. For action P, if X1+X2+X3 > Y1+Y2+Y3, then action P will be done. Conversely, if X1+X2+X3 < Y1+Y2+Y3, then action P will not be done.

Let’s give a concrete manifestation to that abstract equation. Suppose that action P is Qiyamul Lail. This action has various reward mentioned in Quran and Hadits, while also have some associated costs, such as the discomfort of waking up at inconvenient time (e.g. 3AM). Because the rewards are massive and obviously dwarfs the cost of temporary discomfort, doing Qiyamul Lail is the rational thing to do. The model can also apply to prohibition too. The equation is just the opposite. Harmful deeds are effectively prevented if and only if the cost is greater than the associated benefit. Pork *might* be “tasty”, but the threat of hellfire prevents people from consuming it. Temporary pleasure is just not worth near-eternal damnation.

Using the concept outlined above, we modeled human as a rational decision maker with pleasure-seeking and pain-avoidance tendencies. However, the rationality model that is used is bounded-rationality model instead of the full-rationality model. Furthermore, different people have different sensitivity coefficient regarding their pleasure-pain receptor. Not to mention that even the knowledge that is already within the boundary of rationality are sometimes forgotten, so effectively people decide using whatever that is available in their working memory at any given time, which is a partial extent of their bounded-rationality. The imperfection of the model can be attributed into one of two things: syubhat and syahwat.

Syubhat
Formal definitions of what syubhat is should have been already written in classical Islamic texts, so I will spare the reader from rehashing it. What I will do here instead is to tie its effect on the model.

Syubhat is the obscurement of existing variable or introduction of new, invalid variable to the cost-benefit equation.

For example, simple ideal cost-benefit model for riba practice is as follows:

[Benefit of additional money from interest] < [Cost of going to hell] + [Cost of borrowers defaulting]

As a result, individuals will refrain from doing riba because going to hell gives infinite disutility while interest profit only provide a finite benefit or finite utility. Now consider an individual exposed with a syubhat that declares interest are not prohibited in Islam. The cost-benefit model is now not ideal, which is:

[Benefit of additional money from interest] > [Cost of borrowers defaulting]

Suddenly the cost of going to hell is nonexistent. Now the only thing that prevents riba practice is the perceived risk of borrowers. We have a finite benefit of interest profit versus finite cost of borrowers defaulting. Sometimes the economy is growing and we have abundant credit in the market. Other times, economy tanks and credit tightens. That is the resulting dynamics from the modified cost-benefit model. Action or inaction is only determined by the magnitude of each side of the equation. Sometimes the decision shifts to the left-hand side, sometimes to the right hand side.

Policy to reduce/eliminate syubhat: educating individuals to correct their cost-benefit analysis. This will eliminate the new and invalid variables and reintroduce the discarded, but valid, variables.

Concrete policy examples might be formal education teaching these basic knowledge. But unless we are the government with the mandate to do so, bypassing the formal education system is hard. So we have to think of other methods that is practically feasible, cost-efficient, covered a lot of the population, and sustainable. Dakwah movement? It has been done but still no significant result.

Syahwat
Syahwat is the variations of sensitivity coefficient. Different variable have different weights on the cost-benefit model. This is the model without sensitivity coefficient.

X1 + X2 + X3 < Y1 + Y2 + Y3

This is the model with sensitivity coefficient

aX1 + bX2 + cX3 < dY1 + eY2 + fY3, with X being benefit, Y being cost, and a,b,c,d,e, and f being the sensitivity or weigh coefficient for each variables

Let’s look at the previous example again. The cost-benefit model of riba practice became like this:

a x [Benefit of additional money from interest] < b x [Cost of going to hell] + c x [Cost of borrowers defaulting]

with a, b, c are weight coefficients. What happen if an individual knows that riba is prohibited, but keeps doing it anyway? It means coefficient b is too little so it undermines the magnitude of the cost of going to hell.

There are two solution for the problem of syahwat:

• Increase the coefficient value so it will bring the true value of the associated variables. For examples, the individual constantly reminded about the cost. However, its effectiveness might vary from person to person, so it’s not a great solution.
• Introduce another benefit or cost that will tilt the equation. For example, a government enact a rule to imprison individuals who practice riba to jail. Hence, even if an individual belittles the threats in the afterlife, he might have different weight coefficient regarding the possibility of living in jail.