ON MAY 30th Michael Bloomberg, New York's mayor, proposed a ban on the sale of sugary drinks in sizes larger than 16 ounces (roughly half a litre) at stadiums, restaurants, cinemas and food carts. The ban is meant to reduce obesity. In an interview with the New York Times Mr Bloomberg, channelling his inner action hero, said: “New York is not about wringing your hands; it's about doing something. I think that's what the public wants the mayor to do.”

Precisely what the ban would do, however, is not at all clear. Grocery stores will not be affected; they can still sell two-litre bottles of grape soda for 99 cents. Dairy and alcoholic drinks are exempt. You can still get a 24-ounce beer at Yankee Stadium, and a 1,600-calorie chocolate-chip cookie-dough milkshake at any of New York's dozens of Baskin-Robbins ice-cream shops. And as Mr Bloomberg himself noted, the ban does not limit the amount of soda one person can buy at one time; it just increases the number of containers in which it can be sold.

Frank Bruni, a columnist and former restaurant critic for the New York Times, called Mr Bloomberg's ban “an absurd and random gesture”, but ultimately approved. Alex Koppelman struck a similar tone in the New Yorker: “Even if the ban does nothing but shift the discussion of what the government can do to protect the health of its citizens in his favour, Nanny Bloomberg will have won, and we'll be better off for it.”

Those defences, like Mr Bloomberg's, express a familiar syllogism. Something must be done about X (in this case, obesity). Y (in this case, an admittedly ineffectual ban) is something. Therefore Y must be done. This syllogism gave America Prohibition, mandatory-minimum sentences, the sentencing disparity between convictions for crack and powder cocaine, and that great guarantee of everyone's security, shoe removal at airports.

Still, Mr Bloomberg is not wrong to worry about New Yorkers' waistlines. Around two-thirds of Americans, including almost one-third of children, are overweight or obese. Obese people are at greater risk of heart attacks, diabetes, strokes and a host of other ailments that not merely hurt them, but stretch America's already overtaxed health-care system. The Centres for Disease Control put the cost of obesity in America at $147 billion in 2008.

Despite all this, obesity has proved a thorny policy problem. It is trickier than smoking, which Mr Bloomberg managed to ban successfully. People need not smoke, but they must eat. Smoking harms non-smokers directly and measurably, through second-hand smoke; the social harms of obesity are more diffuse. Tell a smoker at a restaurant that the smell of his cigarette is bothering you and he may put it out; tell an overweight person eating a doughnut that he is putting an undue strain on your health-care system and he will give you a blank stare.

Banning smoking and ratcheting up taxes on tobacco are easy. In the case of obesity, what do you ban or tax? Most foods are not harmful in moderation. Taxing cheap calories—processed and fast foods, sugary drinks—would hit the poor hardest. Should the government give tax credits for gym memberships? For miles walked or stairs climbed? Anti-obesity crusaders worry about food deserts—inner-city areas that lack fruit and vegetables—though some studies doubt any link between poor access to healthy food and obesity. And in the end, people will still choose to buy what they like. Small wonder politicians despair.

If Mr Bloomberg is the stick, Michelle Obama is the carrot—the organic, lightly poached, tarragon-dressed carrot. First Ladies tend to pick an issue on which to focus during their husbands' tenure. Laura Bush chose literacy; Hillary Clinton orchestrated a public-policy disaster; Michelle Obama has picked on obesity, especially among children. In early 2010 she launched Let's Move!, an initiative to encourage children to eat more healthily and exercise more. The previous year, she broke ground on an ambitious White House garden. Previous White House chefs had grown the odd tomato here and herb there, but, as Mrs Obama writes in her new book, “American Grown”, not since Eleanor Roosevelt's victory garden during the second world war had anyone grown food on the White House lawn.

And what a garden it is. Pak choi in springtime! Tomatillos in the summer! Seventy thousand bees producing hundreds of pounds of honey to donate to local homeless shelters and give to “visiting dignitaries and heads of state”!

The glow of togetherness

In short, those inclined to mock the Obamas will find much to enjoy. But Mrs Obama's book is intelligent, and displays a far more nuanced understanding of the many causes of obesity than Nanny Bloomberg does. Early on, Mrs Obama discusses the vanished Chicago of her childhood. Her grandmother grew vegetables in a vacant neighbourhood lot; that garden has gone. Her father worked on fruit and vegetable trucks that sold produce to urban areas without grocers' shops; those too have gone. Her mother and father ate dinner with their children every night. She and her brothers often played outside, whereas children “these days are probably a lot more likely to huddle around a video-game console than join in a game of Double Dutch.”

Mrs Obama, in other words, suggests battling obesity on multiple fronts: exercise, healthy eating, teaching city children to garden, family dinners. Not incidentally, “American Grown” is a remarkably happy book, full of photogenic vegetables, delicious recipes (the one for spring-pea salad is a winner) and people who enjoy farming and gardening. Contrast this with Mr Bloomberg's strictures. There are plenty of issues where New York's mayor has better instincts than the First Lady. But in this case, bottom-up happiness looks a better bet than top-down prohibition.

Economist.com/blogs/lexington