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Sunday, 27 January 2013

Rape in India.A mathematical angle.

In the recent past there has been focus on rape in India due to a gory and heinous rape committed against a young woman in Delhi by a few men. There has been general uproar that the rape rate is going up and strict laws and quick implementation of such laws is of paramount importance. There have been suggestions from committees what steps to be taken to bring about necessary changes.                                                                                   
                                                                                   
All this is good and necessary. There should be very strict laws against rape and such laws have to be implemented quickly and efficiently and all the necessary measures that have to be taken should be taken at the earliest.                                                                                 
However I would like to point out a few things which may throw a new light on this subject.                                                                               

I was thinking about the increased number of rape in India (it has doubled within a decade or so).However what we have to consider that population of India has grown also by a substantial number during that period. Also there is the fact that the life expectancy of India has grown by almost 9 (or slightly higher) years from 1990 to 2010-11.                                                                              
Therefore the percentage of adult population (above 18) who are more prone to this crime has increased.                                                                         

Let us take this factor one by one.                                                                             
The population in India was 1241491960 (on July 2011 as per World Bank data.)                         
No of rape cases reported in 2011 in India=  23582  (Data supplied by Indian home ministry).                

There are always large no of unreported cases of rape due to various reasons. The experts differ in their opinion about how much is the percentage of unreported cases. But we may take any arbitrary value and I have chosen to be quite liberal about it and taken this as 15 times the reported cases.
                                                                       
Then the percentage of rape as a percentage of total population comes to= (15×23582) ÷ (1241491960×100) =0.028
This is an arbitrary number and varies according to how many times the unreported against the reported cases you have assumed.                                                                                                                                    
We must remember that most of the rape cases are committed by the adult population, that is people aged above 18.                                                                                                                                               
The percentage of people above 18 is about   60% in 2011.                                                                                                                          
So if we take account of the this factor then the percentage of rape cases in ratio of adult population in India in 2011 is = (15×23582)/ (0.6×1241491960×100) = 0.047        %
This is also an arbitrary number because I have taken an arbitrary value of unreported cases to be 15 times the reported cases.                                                                                                                                   
Now let us have a look at the figure of year 1990.                                                                                                                                        
(All data are supplied by the same sources)                                                                                                                                       
The population in India in 1990 =873785400                                                                                                           
No of rape cases reported in 1990 in India=  9200                                                                                       
We can very safely and legitimately assume that the unreported cases were far higher 20 years back because of different sociological issues like the stigma attached to the rape and lack of media coverage.                                                                                                                                            
If we  assume the arbitrary number of times of unreported cases against reported cases to be 1.6 times than 20 year later which seems very sensible, then the percentage of rape as a percentage of total population is = (1.6×15×9200)/( 873785400×100) = 0.025                                                                                         
We see an increase in ratio of percentage of rape cases against of total population =0.028/0.025 =1.13 times, that is a 13 percent increase
                                   
However the as the life expectancy was lower in 1990 compared to 2011 the percentage of adult population was also considerably lower.                                                                                                                                                                
As I said the life expectancy has increased by almost 9 years or more during this period we may assume that the adult population of age above is was around 53.5% of total population.                 

Therefore the percentage of rape cases as against the adult population in 1990= (1.6×15×9200)/ (0.535×873785400×100) = 0.047%                                                   
Although this is also an arbitrary number but it is a significant one.                                                                                                                                                             
Because the ratio of rape cases as percentage of adult population in 2011 and 1990 is = 0.047/0.047 = 1 that is same and a constant number.                                                         
Therefore rape cases have not increased perhaps not at all if we look at proper perspective.                                                             

You can juggle around with the times of unreported cases to the reported cases any way you like. But if you accept the fact that unreported cases  were 60%  higher 20 years back then there is no change in percentage of rape as regards to the adult population of India which is the most significant number.

You go on interpolating these data as long as you can but this constant number will not change significantly with change of time.                                                                                                                                                                      
So the basic nature of man kind perhaps does not change whatever laws and regulations and mechanisms are there.                                                                                                                                                             
There is also another interesting comparison to make.                                                           
The population of United States 2011 was 304094000 (Supplied by US CENSUS BUREAU)
No of rape cases in United States in that year 90000.

We must take account that in US rape cases are far more reported including minor offences.                                                        
Also the efficiency of law making, implementation of laws and finding out crimes are far more accurate in US than in India.                                                          
So if we take the unreported cases in US 3 times less than India the percentage of rape cases as against total population of that country becomes=(15/3)× 90000/(304094000×100) = 0.148                                                      
Then the rate of rape compared to India is 0.148/0.028 = 5.28 times.

The adult population of US higher than India due to higher life expectancy in that country .So the percentage of rape in comparison to the adult population will be higher.                            
One can take different data at different years and make that comparison between India and US, but my hunch is that these factors will not change significantly.                                                  
The data and factors for European countries vary slightly from US but do not change significantly.
                                   
This leads us to another conclusion that whatever laws you make and irrespective of efficiency of law making and implementing those does not affect that much upon the rapes committed.

There must be many reasons and external and internal factors why percentage of rape is higher in western countries than in India, since I do not believe the innate nature of the people vary from country to country.


However it may be concluded that the basic nature of man does not change regardless of laws and implementations. 

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