The findings have been uninspiring so far. In a study he did in 2008 in New York City, only slightly more than half of consumers even saw the posted calories, and of those, a little over a quarter (around 15 percent of the total) said the information changed what they ordered. He conducted a larger study in 2010 in Philadelphia after that city started requiring chain restaurants to post calories, and the results were similar.

When he delved deeper, he found that those who changed their ordering behavior tended to be the more educated consumers — in other words, not the target population. Americans with more education tend to be less likely to be obese than those with less, though there are exceptions.

The researchers could not tell whether this subgroup ordered less because of the calorie posting, or because they would have behaved differently anyway. Either way, their change was not enough to make the average number of calories everybody was buying go down.

“It doesn’t appear to be changing what people order for fast food at a population level,” Mr. Elbel said.