At the same time, some of America’s wealthiest are responding with an unprecedented flood of money into politics, largely supporting Republican candidates who have pledged to cut taxes. A New York Times investigation documented in October how 158 families were responsible for almost half the money raised in the current presidential race. People from the finance industry lead the list.

This year Mr. Jones said in a TED talk that traditionally there are three ways to change income inequality: “By revolution, higher taxes or wars.” His alternative is Just Capital.

Mr. Jones argues that income inequality is being driven by what he calls “shareholder hegemony,” the principle that companies first and foremost should satisfy investors. The solution is for companies to make social responsibility as important as profits and share price.

Mr. Jones, who declined to be interviewed, has a net worth Forbes estimates at $4.7 billion and was one of the few hedge-fund managers who foresaw the 1987 market crash. He is known for founding the Robin Hood Foundation, a charitable organization started in 1988 that raised $101 million last year for anti-poverty programs in New York.

Just Capital’s mission fits into an existing trend. Socially responsible investing, the favoring of companies that demonstrate environmental and social awareness, is a growing movement, driven in large part by the economic ascendance of millennials and women. As of this month, Morningstar said about 2 percent of the mutual funds it tracked were tagged “socially conscious.” Such funds “typically perform on par or a little better than conventional funds,” said Jon Hale, director of manager research at Morningstar.

Not all economists agree with Mr. Jones’s notion that monitoring corporate behavior would narrow the distance between the very rich and the rest. Mr. Wilkin, the economist, argued that inequity was driven not just by bloated executive compensation or the single-minded pursuit of profit, but also by what he called a two-tier economy in which some industries, like technology, finance and health care, soared ahead and left the rest behind. Just Capital, he said, was “wishful thinking that there is a market solution to income inequality that doesn’t involve increasing taxes.”

Image Paul Tudor Jones II’s Just Capital asked what Americans valued most in a company. The top answer was pay and benefits. Credit... Eduardo Munoz/Reuters

There are many nonprofits that seek to address income inequality. Mr. Jones and Mr. Chopra bring a waft of New Age spirituality to theirs. The Just Capital board includes Arianna Huffington, a founder of The Huffington Post, and several wealthy business leaders who also are directors of the Chopra Foundation.