It’s the rare idea that Jon Stewart and John Boehner can agree on: New York Mayor Mike Bloomberg’s proposed ban on large soda is wrong. “Are you kidding me?” the House Minority leader quipped, when asked about outlawing sodas larger than 16 ounces.

Some have suggested less invasive ways to limit the consumption of sugary drinks, largely looking to a soda tax as better solution. “A per-ounce tax on sweetened beverages would equally deter all different means of consumption,” writes Slate’s Matt Yglesias, adding that it would have the added benefit of raising revenue to pursue other welfare enhancing programs.

A soda tax no doubt would bring in some cash for the state. Would it equally deter consumption of sodas in the same way as a portion-size ban? That’s a bit difficult to know, largely because we’ve never seen any state or city ban large sodas (more general research on portion size suggests that it is an effective way to reduce consumption of food).

We have, however, had a lot of experience taxing soda as 33 states currently do so. What we’ve learned there is this: Soda taxes would, if enacted at high levels, have the potential to significantly reduce Body Mass Index. States, however, have so far only introduced modest taxes that have brought about modest results.

Yale University’s Jason Fletcher has spent a lot of time studying soda taxes and their impact on consumption. In 2010 he published research in Contemporary Economic Policy looking at how soda consumption changed between 1990 and 2006, after states enacted taxes. The average tax hovered around 3 percent, although did vary by state.

Each 1 percent increase in the soda tax rate correlated with a 0.003 point drop in Body Mass Index. To put that in context, “the .003 points is less than one thousandth of what a borderline obese person would need to lose to become borderline normal weight.” Fletcher describes this as a “modest” change in BMI.

“Typically imposed beverage taxes are neither large enough nor transparent enough to lead to meaningful behavioral change,” Fletcher concluded in a separate paper for the journal Health Affairs.

That doesn’t mean soda taxes couldn’t work: Kelly Brownell, who directs Yale’s University Rudd Center on Obesity, has published research suggesting that a really big tax on soda — about 15 to 20 percent — would reduce soda consumption by 8 percent. Such a tax level would certainly be high, but not unprecedented: Cigarettes, for example, are currently taxed at an average rate of 58 percent.

A big tax on sodas, however, turn out to be just as unpopular as Bloomberg’s proposed ban: In Maine, a 20 percent tax on sodas was quickly overturned by referendum. Former New York governor David Patterson proposed an 18 percent tax rate in 2008 that fizzled in the state legislature.

Soda taxes, in short, work in theory. In practice though, they don’t have a great track record, implemented at levels low enough to prove politically palatable — but also have little impact on public health.