They are a preposterous political pairing: lanky Ralph Nader, the consumer advocate whose name for half a century has been synonymous with liberalism, and diminutive Grover Norquist, the anti-tax crusader who has been a much-feared enforcer of purity among conservatives.

But there the two men were Tuesday afternoon, bantering playfully as the normally dour Nader hosted Norquist at a gathering exploring areas of “convergence” between left and right.

“Contrary to libertarian philosophy, there is such a thing as a free lunch,” Nader teased, inviting Norquist to stay and eat after their joint appearance at the Carnegie Institution.

Norquist accepted. “It’s not free,” he said. “It’s just somebody else paid for it.”

Nader, 80, made some quixotic detours late in his career, most notably his third-party candidacy that very likely cost Al Gore the presidency. But in his latest venture, Nader has regained his mojo. He is seeking — and finding — conservative allies to help him with some of his favorite causes. The left could learn much from the effort, particularly how to borrow the language of the right to advance liberal causes.

Nowhere is this clearer than on the topic of raising the minimum wage. Democrats have made the argument that an increase is morally right and that the only thing standing in the way is corporate greed. That may be so, but it hasn’t won them enough Republican support to get the increase through Congress. But what if Democrats were to make a free-market argument that a higher minimum wage would shrink the federal government and reduce the welfare state?

That’s the argument Ron Unz made to Nader’s gathering. Unz, a wealthy businessman known for his 1994 Republican primary challenge to California Gov. Pete Wilson and his fight against bilingual education, has serious conservative credentials, most recently as publisher of the American Conservative magazine. But now he’s leading a ballot measure in California to raise the minimum wage to $12 an hour.

“The government spends over $250 billion a year in social welfare programs aimed at the working poor,” he said, addressing the group via Skype. “If we simply made the working poor much less poor by raising their wages to a much more reasonable level, a lot of that money would be saved, probably in the range of $40 to $50 billion a year.” The $250 billion spent on welfare for the working poor, Unz said, amounts to a “massive subsidy for businesses” that are paying less than a living wage and “forcing taxpayers to make up the difference.”

But what about the Congressional Budget Office study this year predicting that increasing the minimum wage to $10.10 would cost 500,000 workers their jobs? Actually, Unz argued, the study found that 98 percent of minimum-wage workers would benefit from a wage increase, while only 2 percent would lose their jobs. Further, he said, the higher minimum wage would mean a reduction in Mitt Romney’s “47 percent” — those who, Romney said, won’t consider voting Republican because they don’t pay income taxes — as these new taxpayers become “open to a traditional Republican conservative economic message.”

Unz and Norquist were joined on the program by other conservative figures from the American Enterprise Institute, the Competitive Enterprise Institute, Tea Party Nation, the Cato Institute and the American Conservative — all under the high ceilings of the Carnegie marble temple, built, as one participant pointed out, with robber-baron money. The conservatives’ overlap with the Naderites varied by issue — some on civil liberties, others on trade or military spending — but they generally found common cause with Nader in their suspicion of corporate excess, and their willingness to promote Nader’s latest book, on “left-right convergence.”

The Daily Beast’s Eleanor Clift recently wrote that Nader and Norquist are enjoying a “bromance” of late, two decades after they first teamed up on term limits. The pair continued their partnership with the conservative’s unscheduled appearance at Nader’s event Tuesday.

Nader praised his friend “Grover” as one who “opposes corporatists whether they are Republicans or Democrats” and who “has succeeded like nobody I know” in influencing incumbent lawmakers.

Norquist, in turn, called himself a “big fan of much of Ralph Nader’s work,” and he suggested others should “get over the giggles” about finding agreement with their ideological foes.

One such area of agreement: government transparency. “Ralph is under the impression that if everybody looked at the entire federal budget,” Norquist said, “they would say, ‘Hey, ma, look how they’re spending our money. Let’s send them more.’ I’m willing to bet that they might go the other way — but maybe not, if Ralph makes a good enough argument.”

Nader chuckled at his conservative sidekick.

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