US an Oligarchy?

I saw this article linked on Facebook and decided to give it a read:

A new scientific study from Princeton researcher Martin Gilens and Northwestern researcher Benjamin I. Page has finally put some science behind the recently popular argument that the United States isn't a democracy any more. And they've found that in fact, America is basically an oligarchy.

An oligarchy is a system where power is effectively wielded by a small number of individuals defined by their status called oligarchs. Members of the oligarchy are the rich, the well connected and the politically powerful, as well as particularly well placed individuals in institutions like banking and finance or the military.

Usually when I think of an oligarchy I think of a relatively small group of people, but if the US is one it actually consists of a huge group.  Does that make a difference?  

I was taken aback, though, when I read this:

While there are some limitations to their data set, economists Thomas Piketty and Emmanuel Saez constructed income statistics based on IRS data that go back to 1913. They found that the gap between the ultra-wealthy and the rest of us is much bigger than you would think, as mapped by these graphs from the Center On Budget and Policy Priorities...

Piketty.  Piketty.  I've heard that name before. Ah yes, Thomas Piketty:

Financial Times economics editor Chris Giles says French economist Thomas Piketty's best-selling "Capitalism in the 21st Century," about rising inequality in the West, contains serious errors that undermine his conclusion that wealth distributions are widening.

Giles says there are clear examples of some "fat finger" mistranscriptions and compares the situation to omissions found in Reinhart's and Rogoff's data on debt levels and growth.

But while the two Harvard professors' errors seemed to have been unintended, Giles levels a more serious critique: that Piketty actively manipulated his data.

Read more: http://www.businessinsider.com/the-ft-accusation-against-piketty-2014-5#ixzz3DJOjnNqz

and

Given the excitement that Thomas Piketty’s new book, Capital in the Twenty-First Century, has stirred up within the political left, the French economist probably should have titled it Fifty Shades of Inequality.

In Capital, Piketty presents a painstakingly researched case for doing what progressives ranging from Paul Krugman to Barack Obama want to do anyway, which is to raise taxes and expand the power and reach of government. Unfortunately for liberals, Piketty gets almost everything wrong, starting with the numbers.
http://www.forbes.com/sites/louiswoodhill/2014/05/06/thomas-piketty-gets-the-numbers-wrong/

Any article or study relying on Piketty would thus, in my opinion, be immediately suspect.

The good news, though, is that the authors of the Princeton study didn't mention Piketty's work; it seems that the author of the first linked article tried to buttress his story with other references and opted to choose an extremely bad one.  Also, the word "oligarchy" is mentioned in the Princeton paper only twice.

It makes for an interesting read and one could certainly recoil in horror at the paper's conclusions.  I wonder, though, even if they're right, what an appropriate solution would be to the "problem".

Update:  Perhaps these are some of our oligarchs:

Special interest money and super-wealthy individuals are two of the most prominent features of today’s bourgeois liberalism. The unions, the foundations, the colleges, the liberal-leaning or rent-seeking corporations, the residents of Manhattan and Silicon Valley and Beverly Hills and Ward 3, Warren Buffett, George Soros, Tom Steyer, Marc Lasry, Steve Mostyn, Michael Bloomberg, Jeffrey Katzenberg, Chris Hughes—these groups, these men, they are not misshapen appendages of the Democratic Party. They are its innards. Its guts.