And the winner is? No one.

The hospital has to pay. The workers get a check — and not much more. The union can still argue for an card-check election, but its legal route is more unclear than ever.

If anyone — or anything — wins out, in fact, it is the doctrine of federal labor law and a ubiquitous New Deal relic: the National Labor Relations Board.

“We don’t have the power to supersede the NLRB,” Board of Aldermen President Carl Goldfield said in an interview Tuesday. “If somebody wants to resort to it, we don’t have any control over that.”

Also on Tuesday, Margaret Kern — the independent arbitrator hired by the hospital and union to adjudicate disputes arising under a March 2006 fair elections agreement — did just that.

Although her order that the hospital pay $4.5 million was an undeniable break from previously discussed remedies, the short-term sting of the fine is outweighed in the long run by the decision’s grounding in federal labor law.

In her ruling, Kern declined to force Yale-New Haven Hospital to recognize a union on the grounds that she had minimal authority under the law to issue a bargaining order.

Prior to Kern’s ruling, union leaders and hospital officials had long treated her adjudication and the NLRB settlement as two different events with two different potential outcomes — the union hoping for a bargaining order or a card-check election, and the hospital declining to pledge that it would ultimately support her jurisdiction should she rule against them.

But in the wake of Kern’s fundamental deference to the NLRB settlement, Hospital Spokesman Vin Petrini said he found the ruling to be “consistent with the findings of the NLRB, which require that a bargaining order is not required under these circumstances.”

For SEIU 1199 spokesman Bill Meyerson, meanwhile, yesterday’s remedy was another indication of the NLRB’s failure to effectively protect workers’ rights. Pointing to the hospital’s recent NLRB settlement, which did not force it to acknowledge its illegal labor practices, he said the settlement’s punishment — forcing the hospital to post flyers notifying employees of the hospital’s transgressions for 60 days — was largely inadequate.

“Going through the NLRB is also not an option because that has never been, and continues not to be, a vehicle for a free and fair process for workers to choose without fear of intimidation,” Meyerson said. “For instance, the NLRB remedy is that [the hospital] post a notice that they didn’t do anything wrong and won’t do anything again. That is not satisfactory. No one would think that would be an adequate remedy to the misconduct that the hospital engaged in.”

Still, the money matters. Meyerson called the $4.5 million compensation to the union and hospital employees “unprecedented.” Former NLRB member John Raudabaugh said in a Tuesday interview that the NLRB would never hand down such a settlement.

“The board would not have a remedy of this kind — the statute wouldn’t permit this,” he said. “I know of no case out there or guidance on this subject matter … if the consultants and the hospital together conducted themselves in a way that was overreaching and intimidating. But the [National Labor Relations Act] has no discussion about a remedy of that kind.”

Then again, with a near-$800 million annual operating budget, does $4.5 million mean more than a drop in the bucket? If not, then labor law precedent still trumps in the end.

After all, an NLRB-sponsored secret-ballot election is a likely next step in the dispute.

Both Meyerson and Goldfield acknowledged that the March 2006 agreement between the hospital and the union stipulated that the independent arbitrator would default to NLRB policies unless otherwise indicated in the operating provisions, which protected hospital workers from intimidation.

But Raudabaugh said as long as Congress makes no changes to the law, it would be foolish to think an independent arbitrator could issue a bargaining order.

“It’s fair to say that remedies under the National Labor Relations Act are in need of study and debate and possible revision,” Raudabaugh said. “But that’s the job of Congress to do. Not for some private sector arbitrator.”