Is it reasonable for life insurance companies to demand that their customers try to get fit? Reasonable or not, it is already happening. John Hancock, one of the oldest life insurance companies in the US, announced last week that it would in future only write policies that offer rewards for customers who use various forms of fitness trackers or join gyms. Similar offers are available in Britain, where 1.1 million people have signed up to such schemes. It is entirely sensible that people who take out health insurance should also try to become healthier. But if the process is carried to extremes, it could undermine one of the fundamental principles of any insurance market.

Insurance works because we are ignorant of our individual fates. It is the fact that any of us might turn out to be a bad risk that makes it sensible for everyone to insure against that remote chance. The pooling of individual risks that can only be known in aggregate underlies the whole system. But there is a subtle mismatch of aims between insurers and their customers. The customers want to avoid the consequences of misfortune; the insurers want customers who avoid misfortune. The two aims are reconciled because both sides are operating behind a veil of ignorance.

Insurers have an interest in knowing as much as possible about their customers. Customers have an interest in insurers underestimating their real risk. But there is a further complication. Each individual customer also has an interest in the insurers pricing all the others accurately, with the help of as much information as possible. And both sides will benefit if ways are found to reduce the risk of the misfortune insured against. Fireproofing houses is good for both sides of the home insurance business. Giving up smoking is good for both sides of the life insurance business. The balance between knowledge and ignorance of risk has traditionally been struck at the level of statistical knowledge about large groups. Take motor insurance: women used to get cheaper car insurance because they crash less and drive better than men. Young drivers pay far more than old ones, for the same kind of reasons.

But statistically significant groups are getting smaller in the age of big data. In the US, one data company uses 442 non-medical attributes to predict medical costs and so which clients are profitable to insure. In the light of the health disparities between the rich and poor areas of Britain, private insurers could do the same here with no more information than a postcode. This is why the NHS has to cover everyone, if it is to work as it should. The risks must be shared between healthy and unhealthy, rich and poor. No one must be left out of the pool. Offering rewards for healthy behaviour benefits all of society. But penalising unhealthy behaviour with worse or less insurance injures those who really need protection. Given the correlation between unhealthy lifestyles and lower incomes, the risks are only too clear.