The “out of sight, out of mind” effect suggests that policies to lower salience taxes might reduce consumption distortions. I find it liberating to buy goods in foreign currency when I have difficulty converting the price into dollars. So to begin with, sales tax rates that are nice round numbers, like 10 percent, are likely to be more distortionary (than rates with many decimals) because it is so easy calculate the tax burden.
Ayres cites a study by Amy Finkelstein, which demonstrates that E-Z Pass tollways charge significantly higher tolls than tollways where drivers can only pay cash. Finkelstein interprets these higher toll rates as the effect of lower salience of costs.
In my reading of the paper, Finkelstein shows how hidden (or low-salience) taxes can give governments an incentive to raise rates significantly, but this is not the main idea that Ayres takes away from reading the paper. Ayres' takeaway point is: At a given tax rate, lower salience means less distortionary effect of the tax rate. That's probably true, but a key point of Finkelstein's analysis is that the tax rate isn't given.
The analysis of the distortionary effects of tax salience on tollways also teaches us about other types of taxes. For example, sales taxes are annoyingly salient because they force math on people every time they make a transaction, but a value added tax (essentially a consumption tax that requires no math at transaction time) is less salient.
Taking Finkelstein's tax salience lessons to the sales tax versus VAT debate, Ayres would say that a VAT is less distortionary because on account of being less salient. But, that's only true for a given tax rate. Finkelstein's findings suggest that the VAT rate would be higher than a comparable sales-tax rate, and higher tax rates generate bigger distortions.
In short, irrational taxation (taxing by increments of Euler's number) is a cute idea, but we cannot forget that tax rate decisions are a political process. I am not sure we should give our government officials another incentive to raise taxes.