The second way today’s plutocrats flex their political muscle is more novel. Matthew Bishop and Michael Green, a pair of business writers, have called this approach “philanthrocapitalism” — activist engagement with public policy and social problems. This isn’t the traditional charity of supporting hospitals and museums, uncontroversial good causes in which sitting on the board can offer the additional perk of status in the social elite. Philanthrocapitalism is a more self-consciously innovative and entrepreneurial effort to tackle the world’s most urgent social problems; philanthrocapitalists deploy not merely the fortunes they accumulated, but also the skills, energy and ambition they used to amass those fortunes in the first place.

Bill Gates is the leading philanthrocapitalist, and he has many emulators — nowadays, having your own policy-oriented think tank is a far more effective status symbol among the super-rich than the mere conspicuous consumption of yachts or private jets. Philanthrocapitalism can be partisan — George Soros, one of the pioneers of this new approach, backed a big effort to try to prevent the re-election of George W. Bush — but it is most often about finding technocratic, evidence-based solutions to social problems and then advocating their wider adoption.

Philanthrocapitalism, particularly when you agree with the basic values of the capitalist in charge, can achieve remarkable things. Consider the work the Bill and Melinda Gates Foundation has done on malaria, or the transformative impact of Mr. Soros’s Open Society Foundations in Eastern Europe.

Mr. Bloomberg took philanthrocapitalism one step further — he used his résumé and his wealth to win elected political office. In City Hall, Mr. Bloomberg’s greatest achievements were technocratic triumphs — restricting smoking in public places, posting calorie counts and championing biking. As he prepares for life after political office, he is already honing the more typical plutocratic skill of using his money to shape public policy by energetically engaging in national battles over issues like gun control and immigration reform.

At its best, this form of plutocratic political power offers the tantalizing possibility of policy practiced at the highest professional level with none of the messiness and deal making and venality of traditional politics. You might call it the Silicon Valley school of politics — a technocratic, data-based, objective search for solutions to our problems, uncorrupted by vested interests or, when it comes to issues like smoking or soft drinks, our own self-indulgence.

But the same economic forces that have made this technocratic version of plutocratic politics possible — particularly the winner-take-all spiral that has increased inequality — have also helped define its limits. Surging income inequality doesn’t create just an economic divide. The gap is cultural and social, too. Plutocrats inhabit a different world from everyone else, with different schools, different means of travel, different food, even different life expectancies. The technocratic solutions to public-policy problems they deliver from those Olympian heights arrive in a wrapper of remote benevolence. Plutocrats are no more likely to send their own children to the charter schools they champion than they are to need the malaria cures they support.