On the tony Belle Haven peninsula in Greenwich, Conn., overlooking Long Island Sound, sits a massive neoclassical house that looks as if it could have been transplanted from the University of Virginia campus, the alma mater of the property’s owner: hedge fund billionaire Paul Tudor Jones II. A mansion on Greenwich’s gold coast might not be the most obvious place to go looking for solutions to America’s growing wealth gap. Yet it was there two years ago that Jones began hatching a plan to shrink the widening chasm between rich and poor.

Jones, 60, who has an estimated net worth of $4.5 billion, was having coffee one day with Deepak Chopra, the holistic medicine advocate and bestselling author, who knows the Wall Street titan through Jones’s wife, Sonia, an Australian by birth who runs a yoga and wellness business. Chopra had grown deeply concerned about income inequality. “I had been going to Occupy Wall Street meetings and saw the rage but didn’t see the solutions,” he says.

During a spirited discussion with Jones about America’s disappearing middle class, Chopra, who teaches a course at Columbia Business School called Just Capital & Cause-Driven Marketing, brought up an idea one of his students had suggested in class: create a stock market index that would drive capital to companies that treated their employees and communities well. The concept of a market-driven approach appealed to Jones, the onetime cotton trader who founded Tudor Investment Corp. in 1980, became famous by predicting the crash of ’87, and today manages $13.8 billion. “I thought, Wouldn’t this be a great thing to do?” says Jones.

Jones did some quick research—and was both surprised and more than a little embarrassed to discover that taking a values-based approach to the stock market was hardly an original thought. So-called socially responsible investing, he soon learned, was a $6.6 trillion industry that had existed for decades. And yet it had never popped up on the radar of the hedge fund titan—or, Jones concluded, succeeded in putting much pressure on Fortune 500 companies to share more of their wealth with workers. That, he quips, is “a sad commentary both on the space and the space between my ears.”

Then Jones had a different idea: competition. Why not rank America’s top 1,000 companies based not on what Wall Street values—profits—but rather on what Main Street wants? If the list caught on, he reasoned, companies might someday vie to be ranked higher than their rivals. And to do so they would have to pay workers more fairly, make products more sustainably, and give more back to the community.

To put his plan into action, Jones earlier this year created a nonprofit called Just Capital—inspired by the title of Chopra’s Columbia course. The mission is to research what makes people like or dislike corporations and then to create an annual list—which will debut in the fall of 2016—tentatively called the Just 1000. “We want to give the American public a voice where it’s never had a voice,” says Jones. “It’s going to be crystal clear and unbiased and without prejudice. And it’s going to drive corporate behavior.”

Skeptics might wonder what kind of difference a simple list can make. But Jones believes that harnessing public opinion can prove powerful—and that changing the behavior of big companies could have a cascading effect. “When we talk about moving the needle on corporate America, we’re talking about a scale that’s unrivaled anywhere else on the globe,” he says. “I actually think this has the potential to be the most impactful nonprofit that I’ve ever been involved with.” (To read about 51 companies already having a positive impact, see our Change the World list.)

In the beginning Jones will personally provide most of the funding for Just Capital, which he estimates will need about $5 million to $6 million a year to operate. But he hopes the nonprofit will eventually become self sustaining by, for instance, selling companies tools to analyze their rankings on the Just 1000 list and through licensing deals. (Think we’re a just 1000 company! decals.) To avoid conflicts of interest, Just Capital will accept no corporate donations.

Jones has assembled a diverse collection of members for the Just board, which besides Deepak Chopra includes Huffington Post founder Arianna Huffington; Ray Chambers, the former head of the private equity firm Wesray Capital; former Shell executive John Hofmeister; Blake Mycoskie, the founder of Toms shoes, which gives away one pair to developing countries for each that it sells; and Jochen Zeitz, the former CEO of Puma who created PumaVision, an ethical framework defined by being fair, honest, positive, and creative. What do they have in common? “They all have big hearts,” says Jones, half-jokingly. He says he is actively recruiting more former CEOs to make sure corporate America’s point of view is represented.

But different perspectives won’t alter his adamant belief that the system has gotten out of balance. “There’s such an emphasis on making money that we’ve really taken the humanity out of business,” he says. “And part of the reason is that we’re not having the right value debate both in society and in our corporate boardrooms.”

Jones is well aware that many will question why a billionaire investor is suddenly so concerned about working-class families. Is it genuine? But he counters that caring about others has always been in his DNA. Jones grew up in Memphis and says his parents stressed Christian values and imbued him with a lifelong desire to give back. Jones recalls that his father, who ran a business newspaper, provided his workers with generous pensions even though his company was small. “He wanted to make sure that workers who gave their lives to his business were well taken care of,” says Jones. In 1988, Jones founded New York City’s Robin Hood Foundation, which now raises roughly $200 million a year, much of it from Jones’s hedge fund peers, to fight poverty in New York City.

Last spring Jones shared his views about the need for a fairer society in a TED talk that so far has garnered more than 1.3 million online views. What attracted so many viewers was the sight of one of the richest men in the country coming right out and saying that the wealth gap is threatening America. One sound bite in particular generated a lot of buzz: “This kind of gap between the wealthiest and the poorest will get closed. History shows it usually ends in one of three ways—either higher taxes, revolution, or war. None of those are on my bucket list.”

Is the situation really that dire? Just Capital board member Huffington thinks it might be. “If you look at the gun violence in Chicago, certain neighborhoods are becoming like a Third World city,” she says. “We’re seeing riots in inner-city Baltimore. What’s that about? And the fact that everything is so segregated. We don’t want to live in a country where we have to live behind gates with our children protected by guards.” Huffington worries as well that wealth inequality can lead to extreme politics. “Change will not come the same way as the French Revolution, just as I’m sure the next terrorist attack will not be like the last,” she says. “But what we’re doing is not sustainable.”

Another cause for concern is America’s disappearing middle-class lifestyle. As Jones pointed out in his TED talk, when it comes to quality of life—wealth, life expectancy, literacy, social mobility, etc.—the U.S. comes in last, by a large margin, compared with 21 other developed nations. Real wages for the working class have flatlined over the past four decades, while those for the top 1% have soared. Even more troublesome: Over that period productivity has increased by 80%, which means that most gains from productivity have gone to shareholders, not employees. The Federal Reserve conducted a study that nicely sums it up: Some 47% of Americans would be incapable of paying an unexpected $400 bill without selling something or going deeper into debt. In other words, one leaky roof and you’re broke.

To reverse that trend, Jones believes that companies simply must pay their employees better—which he views as a far superior way to address income inequality than raising taxes. “Look, I frankly don’t care about the level of my taxes that much,” he says. “The reason I’m generally against higher taxes is because I think our government spending is commensurately as inefficient as the tax itself. If we can redistribute through the private sector, we can have a fivefold impact compared to redistributing wealth through fiscal means.” Otherwise, some fear, we could be headed for an extreme tax hike, such as a jump to the 80% rate on income over $500,000 suggested by Thomas Piketty, the French economist and author of the recent bestselling book Capital in the Twenty-First Century.

With U.S. corporate profit margins now at 11.5%, near a 40-year high, Jones believes companies can afford to share more with their employees without hurting the bottom line. As many have pointed out, companies seem to have no trouble coming up with ever-expanding compensation packages for their top executives. The AFL-CIO reported that in 2014 the average pay of a CEO was 373 times that of the average employee—multiples of what it was a few decades ago. A new rule approved by the Securities and Exchange Commission in early August will require public companies to show the total annual compensation of the CEO as a ratio compared with the average worker.

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But what about a CEO’s duty to his shareholders? Jones argues that companies that treat their employees well will see better financial results over the long term. The poster child for that thinking is Starbucks SBUX , which provides its workers with generous health benefits and recently began offering to cover the cost of an online college education. Over the past three years Starbucks’ stock has generated a total return of 156.5%, vs. 58.7% for the S&P 500.

The idea that workers should receive a bigger slice of earnings has been gaining traction of late. Companies including Walmart WMT , Target TGT , TJX TJX , and McDonald’s MCD have recently announced plans to pay their employees more. At the same time cities from L.A. to Seattle to New York are planning to institute a $15 minimum wage, more than double the federal rate of $7.25 an hour. It’s a good start but not enough. Jones hopes his list will tilt the balance.

Rating companies on an abstract notion like how “just” they are isn’t simple. “Coming up with a fair ranking system is what keeps me up at night,” says Jones. The list will examine criteria such as environmental sustainability, ethics of top management, and the quality and price of a company’s products.

It’s likely that the results of Just Capital’s survey will show that the top concern of Americans is to be paid a living wage—no surprise there. People also care strongly about having access to quality products at an affordable price, however. That will present a challenge when issuing grades. “You’re going to have a variety of contradictions,” says Jones. “But what we’re going to do in a fastidious, detailed, and meticulous fashion is to drill down on Americans’ preferences and provide an overall ranking.”

Fast-Food Workers To Rally In 230 U.S. Cities Seeking Higher Pay Protesters rally for higher minimum wages for fast-food workers in New York City on April 15, 2015.Photograph by Victor J. Blue—Bloomberg via Getty Images

Martin Whittaker, Just Capital’s CEO, emphasizes that the nonprofit is neutral on the issues. It is merely channeling the 40,000 U.S. citizens polled in its survey, the results of which will be released in late September. “We’re not trying to advance the corporate social-responsibility agenda,” he says. “If we can simply improve transparency and information flow, companies will be motivated to be more just.”

Gary Pinkus, the head of McKinsey’s North American consulting practice, which is not affiliated with the Just Capital project, believes that the Just 1000 list could have an impact if the methodology is sound. And he says the subject is front-of-mind for executives today. “Prompting this discussion would certainly help,” he says. “Our largest and most global companies are hyper-aware of what it means to operate in a way that is just and that operating only by quarterly profits will get them in trouble.” Pinkus also points out, however, that the root causes of income inequality are more complex than what corporations pay people. It also has to do with whether people have adequate education, and how fast the economy is growing.

Before he wrote The Wealth of Nations, Adam Smith, the father of modern capitalism, penned The Theory of Moral Sentiments. In the book he stressed that capitalism had to have a moral foundation to be sustainable. Otherwise the rift between the rich and the poor would lead to “the highest degree of disorder.” In a way, Jones is trying to get America back to the roots of capitalism. “Our society,” he says, “is not where we want it to be in terms of how we think of ourselves as Americans. By attacking wealth inequality we can have a more stable, stronger society.” And, he hopes, we can avoid what he fears deeply: war, revolution, and higher taxes.

To see the full Change the World list, visit fortune.com/change-the-world.

A version of this article appears in the September 1, 2015 issue of Fortune magazine.