The Food and Drug Administration recently announced it would extend the menu-labeling compliance date for covered establishments to May 7, 2018. Part of the 2010 Patient Protection and Affordable Care Act, restaurants with 20 or more locations that serve essentially the same menu are required to post energy content for standard menu items on menus and menu boards.

I hope the recent extension of the compliance date to next year fosters a massive re-think of a law that is based more on hype than evidence.

The basic framework for nudging health gains through mandatory nutritional labels is deceptively simple. Advocates presume a simple linear relationship between availability of nutritional information and behavioral changes in dietary choices that improve public health.

But, the fanciful nature of this law becomes apparent with simple application of probability theory. The extent to which labeling changes health outcomes is proportional to the occurrence of each of the following four steps:

Step 2: Consumers understand the labels.

Step 3: Consumers, as a result, make improvements in their food choices.

Step 4: Consumers, as a further result, experience improved health.

Let us first consider an optimistic simulation that assumes that each of the above four steps is associated with a 50-percent probability. That is, the joint probability of all four steps occurring is 50 percent × 50 percent × 50 percent × 50 percent = 6.25 percent. That would mean only one in 20 people would experience improved health.

Now, consider a less optimistic simulation that assumes each step is associated with a 25-percent probability. That is, the joint probability of all four steps occurring is 25 percent × 25 percent × 25 percent × 25 percent = 0.39 percent. In other words, only about one in 250 people would benefit from the labeling nudge.

A pessimistic simulation assumes each step is associated with a 10-percent probability. Under this pessimistic scenario, only one in 10,000 people would benefit.

Evidence leans heavily toward the pessimistic simulation. Studies clearly point to taste, not nutritional information, as the most important attribute of purchase decisions. That is, consumers are not so enthusiastic about reading food labels.

Consumers also struggle to interpret labels, as echoed by former First Lady in a 2010 speech when she described her own food-shopping experiences: “The last thing I had time to do was to stand in a grocery store aisle squinting at ingredients that I couldn’t pronounce to figure out whether something was healthy or not.”

There is also scant support for the prediction that mandatory labeling nudges consumers toward healthier diets. Studies show that local jurisdiction labeling laws do little more than help consumers estimate calories associated with various foods rather than steer them toward healthier eating. This is like a law that gives everyone their own scale — the law improves estimates by citizens of their weight, but does not motivate them to lose weight.

In sum, little evidence supports the prediction that, if labels are read, understood and cause diets to change, personal health improves. So far, the connection between nutritional label nudges and improved health is more of a hope than a well-examined theory.

I am not optimistic that “heroic policymakers” will be able to resist “ramping-up” pressure on citizens that resist their good-intentioned, but fanciful policies. Rather than conclude that the laws have insufficient theoretical and empirical backing, policymakers are likely to expand their nutritional labeling mandates or conclude that tax hikes and bans on various foods are essential.

A lot of work remains for advocates of nutritional labeling laws. Mandated labels reflect ongoing “heroic policymaking” characterized by policymakers experimenting on citizens. Simple application of basic probability theory offers a more scientific framework for modeling the effects of informational nudges that can foster a less heroic but more realistic set of policies aimed at improving public health.

Michael L. Marlow is Professor of Economics at Cal Poly, San Luis Obispo and author of “Label Nudges? A connection between nutritional labeling and improved health is more hope than well-examined theory.”

The views expressed by contributors are their own and not the views of The Hill.