THE EVIDENCE continues to mount about the implausibility — make that the irresponsibility — of Mitt Romney’s pick-a-number-any-number tax plan. In his latest non-answer to how he would make up the $5 trillion budgetary hole he proposes to dig by lowering marginal income tax rates 20 percent and cutting other taxes, Mr. Romney has said he might not press to eliminate or curtail specific deductions or credits. Instead, he has suggested, taxpayers might be given a maximum amount to use for deductions as they saw fit.

“One way of doing that would be, say everybody gets — I’ll pick a number — $25,000 of deductions and credits, and you can decide which ones to use,” Mr. Romney said in the second debate. “Your home mortgage interest deduction, charity, child tax credit and so forth, you can use those as part of filling that bucket, if you will, of deductions.” At other times, Mr. Romney has thrown out other possible bucket sizes — $17,000, perhaps, or $50,000. There’s one big flaw in Mr. Romney’s bucket, however: it would not bail enough money into the tax system.

On the plus side, the notion of what would essentially be a new, super-sized deduction to take the place of itemization is appealing to economists. As Roberton Williams of the Tax Policy Center points out, “it would raise revenue in a highly progressive way,” because the wealthiest taxpayers would experience the biggest hit. Wealthier taxpayers are more likely to itemize deductions, claim far more in itemized deductions and, because of the progressive rate structure, obtain more benefit from each individual dollar of deductions. If itemized deductions were capped at $25,000, 90 percent of the revenue raised would come from those in the top 20 percent. Half would come from the top 1 percent.

Here’s the problem, though: The revenue raised even from the stingiest of Mr. Romney’s proposed caps, $17,000, would not come close to replacing the money lost from lowering rates 20 percent and making the other tax changes he proposes. Indeed, according to the tax center, eliminating all itemized deductions would raise $2 trillion of revenue over 10 years — leaving roughly a $3 trillion shortfall. Capping deductions at $17,000 would raise $1.7 trillion; at $25,000, $1.3 trillion, at $50,000, $760 billion. Of course the flip side of the lower cap is that, while raising more revenue, it would pinch more of the middle-class families Mr. Romney has pledged to shield. For example, the tax center analysis shows, even with his proposed reduction in marginal rates, 61 percent of households earning between $100,000 and $200,000 annually would see their overall tax bills rise with a $17,000 cap on deductions. The average increase would be $2,205.

And remember: That cap would still not raise enough revenue to fill the hole Mr. Romney proposes to dig. The Romney campaign responded to the Tax Policy Center analysis not by disputing the figures but by criticizing the center for having the cheek to analyze Mr. Romney’s ideas.

Mr. Romney “has only suggested that capping itemized deductions is one option that could be explored, and there are others,” economic policy director Pierce Scranton said in a statement posted on the campaign Web site. “TPC has erroneously taken these illustrations and presented them as the Governor’s actual plan.”

Well, if he’s got another plan — one that does add up — we’d love to see it.