IT HAS become an unchecked assumption about the Democratic presidential race: The candidates are fighting an ideological war between “left” and “center.” This narrative is false, and it is hardly benign. It minimizes the bold policy ambitions of those in the mislabeled “centrist” lane and falsely characterizes those on the left flank as braver or more committed to reform.

Yes, some candidates in the race are to the left of others. Sens. Bernie Sanders (I-Vt.) and Elizabeth Warren (Mass.) not only want to make sure that all Americans have access to health care, as do all the Democrats, but they want maximum government control in achieving that goal. Their proposals would cost more and would require more regulation than other candidates’ plans. Mr. Sanders’s program, which includes the Medicare-for-all plan that Ms. Warren has endorsed, would cost some $60 trillion to $90 trillion over 10 years, an astonishing number that would imply doubling the size of the federal government.

Mr. Sanders acknowledges that his ambitions are unlikely to be achieved without a “political revolution,” which is fanciful even if it were desirable. His competitors think more realistically about how change is accomplished in a diverse democracy.

But the fact that Mr. Sanders’s and Ms. Warren’s positioning puts them decidedly to the left of others in the race does not make their competitors “centrist.” All, in fact, have put forward ambitious, progressive platforms for reducing inequality and promoting access to health and education.

Former South Bend, Ind., mayor Pete Buttigieg wants to make college free for pretty much everyone — just not for the wealthiest families. He does not favor Medicare-for-all — but he does propose a generous public health-care option that, he predicts, would eventually drive private insurance companies out of business. He just would not force people to move off private plans, as Mr. Sanders and Ms. Warren would.

Former vice president Joe Biden may not favor the precise Green New Deal that some activists desire, but he wants to spend a whopping $1.7 trillion to enable the country to eliminate net carbon emissions by 2050, a massive undertaking. Sen. Amy Klobuchar (Minn.) was the first candidate to roll out a hefty infrastructure plan, proposing $650 billion in federal spending, and she favors legalizing marijuana. Former New York mayor Mike Bloomberg would add a 5 percent surtax to income over $5 million per year, raise the corporate tax rate from 21 percent to 28 percent and tax investment income of high earners at the same rate as ordinary income.

Then there are the policy moves that practically all Democrats agree on: giving legal safe harbor to the young immigrants known as “dreamers”; reviving and expanding President Barack Obama's climate regulations; reengaging with Iran; raising the minimum wage; keeping abortion legal; cracking down on guns.

In fact, every major Democratic candidate is running on an agenda to the left of Mr. Obama’s.

Campaigning in Iowa, Mr. Buttigieg expressed sympathy for Mr. Sanders’s “goals.” But, he added, Mr. Sanders “makes it feel like you're either for a revolution or you’ve got to be for the status quo, and there’s nothing in between.” The Democratic race does not present such a choice, and observers should stop advancing the myth that it does.

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