IT HAS become a cliché to call obesity a big problem for a reason: more than 2.1 billion people, or nearly 30% of the global population, are overweight or obese. Excess weight leads to about 5% of worldwide deaths. On current trends, almost half of the world’s adults will be fat by 2030. Over the past three decades, according to a study in the Lancet, a medical journal, no nation has slimmed down.

It’s enough to drive a person to comfort eating. But a new study from the McKinsey Global Institute (MGI), the consultancy’s research arm, offers some hope. It looks at 74 anti-obesity measures around the world, and judges the cost and impact of the 44 for which there were sufficient data. None alone could do much, it concludes, but all 44 together could mean about a fifth of overweight people achieving a reasonable waistline within five to ten years.

The interventions range from nudges (making healthy eating choices easier) to shoves (taking poor eating choices away). The most effective would force food producers and restaurants to make servings smaller and limit fatty ingredients (see chart). Others are less paternalistic, such as having grocery stores promote healthy products instead of sugary ones. But leaving it to individuals to slim down through dieting and exercise without any such help, MGI concludes, consistently fails.

How much governments should do to promote healthier lifestyles sparks vigorous debate, especially among Americans, who prize freedom as much as freedom fries. When Michael Bloomberg, then the mayor of New York, tried to limit the size of sugary drinks in 2012 he faced a backlash, and was stopped by the courts. In Europe a number of countries have all but rid foods of trans fats, which have particularly potent artery-clogging effects. America is heading in that direction, too.

John Stuart Mill, the liberty-loving 19th-century philosopher, saw state action as justifiable to prevent deeds harmful to others. Some regard anti-obesity measures as falling into that category. Rich countries devote 2-7% of their health spending to the problem, and up to 20% if you include treatment of associated diseases, such as diabetes. The economic burden of obesity, MGI estimates, is 2.8% of global GDP, roughly equal to that of smoking or war.

Almost all the measures analysed in the report are cost-effective, offering health-care savings and productivity gains that would outweigh their cost over the lifetime of the target population. If they were all deployed in Britain, which it uses as a worked example, the economic benefit would be around $25 billion a year. Yet Britain currently spends less than $1 billion a year on weight-management programmes, public-health campaigns and the like.

The MGI report is but a partial picture. It cannot vouch for all of the third-party research it cites. And it focuses on behaviour, rather than clinical questions such as the role of specific nutrients or genetics in obesity. It thus glosses over disagreement about what makes people fat. More study is promised. Consider this an appetiser.