Reported rapes are one measure of how unsafe our women are. But what do we do with those reports?

A file photo of people protesting outside court in New Delhi demanding death sentence for the convicts of the Delhi bus gang rape case. Photo: PTI
Here’s a dilemma: I write this regular mathematics column, and sometimes there is so much non-mathematical news…well, that’s always true. Never mind. Sometimes the non-mathematical news so captures public attention that it’s hard to believe anyone will read this column.
Like this week, dominated by news of violence in Uttar Pradesh and the Delhi gang rape trial verdict. That infamous rape trial verdict, of course.
Yet it’s possible to tease out mathematical strands from even news like this. For example: A New York Times report about the rape verdict carried this line: “nine months later reports of rape still saturate the country’s newspapers—whether because of increased attacks or increased reporting is not clear.” Which is an old dilemma: if there’s a rise in news about a phenomenon, is it happening more often? Or is it being reported more often?
With rape, there’s no easy way to answer those questions. Still, there are plenty of figures available for easy public consumption and it’s instructive to put them together to see what questions they raise.
What kinds of questions? Well, another report (Verdict tomorrow, tells us there were 1,036 cases of rape in Delhi in 2013 till 15 August. This compares to 433 cases in the same 7.5 months last year, and 706 in all of 2012. That itself is a rise from 2011, which saw 572 cases reported through the whole year. So, is the incidence of rape increasing every year in Delhi? Or is it that more rape survivors are finding the courage every year to report the horror?
Then try this: Yes, Delhi saw 572 rapes reported in 2011. But that year, UP had nearly four times that number, 2,042. Madhya Pradesh was higher still at 3,406. Tiny Tripura? 205. (Rape Conviction Rates Across IndiaThe Wall Street Journal). Going just by these numbers, should we conclude that MP is a terrible place for women and Tripura a relative haven?
You know the answer. No. The way to compare, of course, is to first match these numbers to the populations of each state. Do that and you find UP had 2.1 reported cases per 100,000 women; Delhi, 7.4; MP, 9.7; Tripura, 11.4.
Yes, MP is a worse place for women than Delhi and UP. But Tripura is even worse. In fact, by this metric, even tinier Mizoram is hands down the worst Indian state to be a woman, with 14.3 reported rapes for every 100,000 women.
We don’t know if reported rapes accurately reflect the actual occurrence, but it’s probably the closest we can get.
There’s also the way these figures are, well, reported to the world. In a news report I found (Crime against women in, a table tells us that reported rapes in India rose from 16,075 in 2001 to 24,923 in 2012, a more than 50% increase. That’s a growth rate over twice as high as our population’s growth, and deserves investigation on that count alone. But the news report also plots this on a graph, and so cleverly that it looks almost flat. If you took a quick look—as most of us would, for who’d pore over a table rather than glance at a graph?—you’d conclude that there was little or no increase in reported rapes in those years. Not at all true, and a telling example of how statistics can hide things.
So reported rapes are one measure of how unsafe our women are. But what do we do with those reports? Are the rapists punished?
There are figures about that too. Not very encouraging ones. In February this year, junior home minister R.P.N. Singh told Parliament that conviction rates in Indian rape cases had declined from 44.3% in 1973 to 26.4% in 2011. (Decline in rape conviction cases, Indian Express).
Which begs the question that if ever more rape cases are being reported, but an ever lower fraction of accused rapists are being punished, what are we really doing? Running in place, at best?
And there’s something about these conviction rates that you should be aware of. Singh’s figures were not the fractions of reported rape cases, but fractions of rape trials completed that have resulted in convictions. There’s a difference. In general, the number of completed trials is less than the number of rapes reported. But more important, completed trials in a given year don’t necessarily have any relation to the rapes reported that year, because it might be cases filed in earlier years whose trials are finished.
And even this is deceptive, because we’re talking about individual convictions. A given case might have more than one accused—like this week’s four convictions. Thus, when Delhi saw 368 rape convictions in 2012, for example, it’s likely that less than that number of rapes found a measure of justice that year.
So, in general, a depressingly low fraction of rape accused are actually punished. Perhaps that’s the best measure of how safe our women are. Or unsafe.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers will explore the joy of mathematics, with occasional forays into other sciences.
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