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It has been a frustrating week for well-intentioned and interventionist political leaders. Michael Bloomberg and David Cameron have been roundly defeated in their efforts to prod citizens into health.

Both the mayor of New York, who wants to limit the size of sugary drink cups in restaurants and cinemas, and the UK prime minister, who sought a minimum unit price for alcohol, lost the argument. They were portrayed as social nannies pushing policies that discriminated against the poor and minorities, who deserve some pleasures.

They were still right. Societies should try to limit alcoholism and obesity, as they have cracked down on tobacco use. Freedom matters and the ideal policy is both effective and unobtrusive, but they both managed to tread the line between illiberalism and irresponsibility. As with tobacco proscriptions, they will probably be accepted in the end.

John Stuart Mill defined it nicely in On Liberty: “The only purpose for which power can be rightfully exercised over any member of a civilised community, against his will, is to prevent harm to others. His own good, either physical or moral, is not a sufficient warrant.”

Targeting non-communicable health conditions such as obesity, diabetes, high blood pressure and alcoholism is an especially sensitive issue since – to put it bluntly – rich people tend to live more healthily than poor people. Any tax or regulation that penalises the latter must have demonstrable benefits for society as a whole.

After his regulation was overturned by the New York Supreme Court, Mr Bloomberg published research on how obesity correlates with consumption of sugary drinks, and where they are concentrated. Both are low in elite districts of New York City such as the Upper East Side and Greenwich Village, and high in poorer areas such as the Bronx and Bedford-Stuyvesant.

There is thus a clear link between social status and health. Call it the Lloyd Blankfein principle. The chairman and chief executive of Goldman Sachs grew up on a public-housing project in East New York – close to Bedford Stuyvesant – but now lives by Central Park. He was once overweight but he dieted and exercised to get in shape as his fortunes rose.

Societies would be healthier if everyone followed his path but it isn’t possible. In practice, people enjoy – or find comfort in – sugary drinks and fatty foods or cheap alcohol. The Institute for Fiscal Studies in the UK estimates that a “fat tax” would cost the poor seven times as much as a proportion of income as the wealthy.

Mill’s principle and the social effects make blunt intervention to force people to eat and drink more healthily hard to justify. In November, Denmark dropped a “fat tax” that it imposed in 2011 on foods with a high fat content. Shoppers had evaded the tax by driving over the border to shop in Sweden, and it had other unintended effects.

But the New York ban on serving soda in paper cups larger than 16 ounces – three times the old standard size – would hardly be a draconian clampdown. It would not prevent anyone slurping their way through 24 ounces of Coca-Cola while watching a film or having a meal. They would merely face the inconvenience of buying two cups.

Mr Bloomberg’s plan is thus a “nudge” proposal of the kind now favoured by psychologists and behavioural economists. It does not impose a ban on an activity – it simply adjusts the environment to give people incentives to make better and healthier choices.

Little measures such as changing a cup size sound absurd, but they can be very effective. “We are exquisitely sensitive to environment,” says Theresa Marteau, head of the Behaviour and Health Research Unit at Cambridge university. “We are just like rats – energy misers and cognitive misers. If there is a shortcut, we will take it.”

Nudges are less blunt than laws, since they still permit people some discretion – they merely try to guide them. Mr Cameron’s coalition is keen on the approach, declaring in 2010: “Our government will be a much smarter one, shunning bureaucratic levers …and finding intelligent ways to encourage, support and enable people to make better choices for themselves.”

The minimum price per unit for alcohol was more of a lever than a nudge. The idea was to curb the UK tendency toward binge drinking by barring supermarkets from heavily discounting alcohol. It would not have encouraged people to stop buying booze cheaply – it would have prevented them.

You need a very good reason to intervene so forcefully in people’s choices, especially when it amounts to a regressive income tax. It puts alcohol firmly in the same category as cigarettes, a pernicious form of good that a government will tax not only to raise revenues, but actively to curb its consumption.

I still think the idea was justified. Even a law-abiding drunk drowning his sorrows at home imposes health costs on others – as does the person who contracts type 2 diabetes by ingesting too much sugar. New York City incurs an estimated $4.7bn in annual costs due to obesity, much of it paid by public programmes such as Medicare and Medicaid.

With obesity, the social cost more or less stops there, apart from bad parental influence on children. With drunkenness, it often goes further – alcoholism triggers crime, and turns accident and emergency departments in UK hospitals into bedlams.

Liberty and social equality mean that governments should adopt the lightest methods possible to address such social ills – they should label and advertise before nudging and banning. But both Mr Bloomberg and Mr Cameron struck a fair balance – or they at least tried.

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