The left wing of the Democratic Party is excited — and newly emboldened.

You can see it in the gleeful aftermath of last week's surprise primary victory of self-proclaimed democratic socialist Alexandria Ocasio-Cortez against the fourth-ranking Democrat in the House. Finally the left has a young, passionate, politically formidable tribune to help champion its agenda and show the rest of the party how it might triumph over a thoroughly Trumpified Republican Party — by confidently and unapologetically pushing a left-wing economic-populist message. That's the kind of message that will galvanize the Democratic base and motivate throngs of disaffected young and working-class voters, who are far more open to sweeping critiques of capitalism than those who run the institutional party, to show up at the polls on Election Day.

Or so Ocasio-Cortez's victory appears to the party's left-wing activists. But is it true? Does the future of the Democratic Party run through socialism?

We have ample reason to doubt it.

Don't get me wrong: There is undeniably something compelling about the idea of the Democrats throwing off the constraints of neoliberal centrism that hemmed in Bill Clinton, Barack Obama, and Hillary Clinton's losing presidential campaign, and which have been so thoroughly internalized by the Democratic leadership that they shape everything from the party's small-ball political messaging to its decisions about which local candidates will be offered institutional backing and support.

The centrist sensibility leads Democratic leadership to believe that, while a candidate like Ocasio-Cortez might sometimes prevail in a diverse, urban, deep blue district like NY-14 (which is roughly 50 percent Hispanic, just 18 percent white, and which went for Clinton over President Trump by a margin of 77-20 percent), she would suffer a different fate elsewhere. In more racially homogeneous suburban or rural districts, especially in the Midwest, the party therefore needs to run moderate candidates who will soft-pedal items on the democratic-socialist wish list.

The left, by contrast, wants to free up candidates across the country to push a message of working-class solidarity combined with a sweeping critique of the Republican Party that goes far beyond the personal corruption of Trump and his administration's assault on "norms." The democratic socialists aim to challenge the pro-business outlook that has controlled the GOP since Ronald Reagan, reached a kind of apotheosis with the Trump administration, and even infected leading Democrats, who are all too eager to do the bidding of bankers and hedge fund managers.

But the left's plan won't work. There simply aren't enough left-wing voters in this country — with its two-party, winner-take-all electoral system — for democratic socialists to prevail in a big way at the national level.

Now, the left vociferously disagrees with the median voter theorem, which holds that in electoral systems like ours the winner will be the candidate who comes closest to the center of the ideological spectrum. Against this assumption, the left points to the remarkable success of the Republican Party in winning elections by running base-mobilization campaigns that explicitly flee from the center. George W. Bush tried this in 2004, and the strategy worked. And of course, Trump prevailed in 2016 after a much more extreme version of the same approach. The left insists that the Democrats will enjoy the same kind of success if they abandon their centrist caution and embrace a full-throated democratic socialist agenda.

Yet as a recent comprehensive Economist/YouGov poll makes clear, the numbers just aren't there. When nearly 1,500 respondents of various partisan commitments were asked about Democratic ideology, a plurality of them (40 percent) pronounced it too liberal with only 11 percent declaring it not liberal enough. (Twenty-six percent consider the ideological positioning of the party to be about right.) When respondents were asked a parallel question about Republicans, a slightly smaller share (35 percent) declared the party too conservative, while 19 percent asserted that it wasn't conservative enough. (Twenty percent consider the GOP's degree of conservatism to be about right.)

When the results are broken down by party, the result are similarly unbalanced. Whereas only 19 percent of self-described Democrats consider their party to be not liberal enough (with 13 percent calling it too liberal and 53 pleased with where it is), a grand total of 37 percent of Republicans think of their party as not conservative enough (with just 10 percent calling it too conservative and 45 percent content with its ideological placement). As for independents, twice as many judge the Republicans insufficiently conservative (16 percent) as judge Democrats insufficiently liberal (8 percent), with slightly more (36 percent) deeming Democrats to be too liberal than Republicans too conservative (29 percent).

The overall impression given by the poll results is of a Republican Party being pulled by the voters ever-further to the right and a Democratic Party either fairly close to an ideal ideological position or already too far to the left.

Skeptics can surely raise objections. Maybe, for example, the term "liberal" is tripping up respondents, since it can be and is often used in the United States both to name a center-left ideology and to describe a politician's relative leftwardness. (So Bernie Sanders was supposedly "more liberal" than Hillary Clinton because he was further left, even though she was the liberal in the race and he was more of a democratic socialist.) Maybe if the poll had used other terms the results would have been more favorable to the left.

But I doubt it. There's a reason why (unlike in Europe and Latin America) socialist politicians have enjoyed so little electoral success in this country — namely because there's a widespread aversion to the big-government policies they tend to favor.

Of course it's possible that there's a large reservoir of untapped left-wing voters in the country. Maybe the millions of people who normally refrain from voting would come out of the woodwork on Election Day if they heard a full-throated case for socialism coming from Democrat candidates. Maybe some of these voters aren't even aware that this is what they're longing to hear and would simply respond once the message got out.

Some on the left will say that this is exactly what will happen — that left-wing intellectuals, activists, and politicians are capable of "creating a public" where one doesn't yet exist. These inveterate optimists will have to forgive the rest of us for calling this wishful thinking — an electoral program founded on a leap of faith.

Of course, stranger things have happened. Just ask the legion of pundits, political strategists, and number crunchers who assured us that Trump could never win the Republican nomination and then was almost certain to lose the general election.

But a gamble is still a gamble. Trump was an extreme long shot who happened to pay off for the GOP. Perhaps something similar will happen on the left and an army of socialist candidates will transform the Democratic Party's electoral prospects beginning this November and culminating in the 2020 showdown over the presidency.

Perhaps. But we shouldn't lose sight of how little we have to go on in judging its prospects. With the stakes enormously high, the left is proposing that Democrats embrace a politics of the hunch and the fervent hope.