Кризис 2008 года и выборы в Индии: как математика хвостовых рисков объясняет провалы партий

While others were getting worked up over a former finance secretary’s mischievous pronouncement on the latest GDP figures, I was reading a post by someone altogether more responsible: the Nobel winner Paul Krugman on the US bond market. He was discussing it with another professor from the Massachusetts Institute of Technology. At one point they discussed what happened with, and to, the highly risky, subprime loans. Krugman mentioned something called copulas, a term I had not heard of. So I googled it and was told that “a copula describes the dependence structure between variables, rather than just the probability of independent events” and further that it “connects individual (marginal) probabilities into a combined picture.” What does this mean? According to Abe Sklar’s Theorem, which I had not heard of either, “any joint distribution splits into two pieces: the individual behaviors (marginals) and the dependence between them (the copula).” Further googling, which is the current term for research, showed that copulas were massively used in the programmes used in the financial markets in the West in the period leading up to the crisis of 2008 to model joint risks and extreme events. They might have caused it eventually. To simplify hugely, for which my apologies, that’s basically what bundling of risky assets was all about. You combined various probabilities and got a single risk probability for the entire package. The method used was something called a ‘Gaussian copula’. Google told me it “combines different probability distributions into a single joint distribution by capturing the correlation between variables.” But there was a problem which was ignored: what if there were a few probabilities that were way off the mean? And that’s exactly what happened by September 2008. The whole thing collapsed and we got the Atlantic Financial Crisis whose effects are still being felt. Politics and copulas I will not stretch the analogy too far because that would be ridiculous. But it occurred to me that the question of joint probabilities could be important in the context of politics also because political parties combine the risks in individual candidates and come up with consolidated assessments of their chances of winning X or Y or Z number of seats, a kind of Gaussian copula, if you like. The BJP for example believes that, as a party, it can definitely win between 220-240 seats. That’s like a normal distribution with most of its candidates falling under the bell. But what of the tails of this distribution? This can become of critical importance if there are too many candidates with extreme risks. They would lie at the tails of the distribution. It is easy to get an idea of their riskiness by looking at the winning and losing margins. So consider: of the 543 candidates chosen to contest an election, even if 20 per cent fall in this category, where the margins are small, the BJP could lose nearly 108 seats. Something like that may well have happened in 2024 when it lost 63 seats, of which 33 were in UP. Poor candidate selection, rather than any lofty reason like the rumoured abolition of reservations, could have been the reason. The same thing applies to all political parties. They all can, and do, choose candidates with high risks of losing for whatever local reason. Candidate risk The Congress is a case in point and it should look into this if it wants to increase its Lok Sabha strength. Is it choosing its candidates badly? In Gaussian terms, is the tail demolishing the dog? Back in 2014, Rahul Gandhi tried to reform the ticket distribution method by choosing candidates via the American primaries process, which is basically “may the most popular person get the ticket”. It was a great initiative because it sought to minimise tail risk. But it failed spectacularly. The Congress went from 207 seats in 2009 to just 44 in 2014. There are many theories about why this happened but no one questions either the need or the method used to minimise candidate risk. Rahul then gave up the reform. A very popular party leader like Indira Gandhi or Narendra Modi can be used to mitigate some of the high risk. People then vote for that leader rather than the candidate. The problem lies, however, in (a) the popular leader no longer being able to mitigate the risk sufficiently and (b) in choosing too many high-risk candidates, hoping for the best. This is why at least a quarter or more of all contestants always lose. So the real task is to identify and accept high tail risk. This becomes hard when there is competition within a party to distribute patronage because tail risks get underestimated and are reported wrongly to the party high commands. Published on September 7, 2026