In 2014, a slew of headlines seemed to confirm what many had long suspected — that the rich were actually the ones in control and the rest of us chumps were just along for the ride:

"Study: US is an oligarchy, not a democracy"; "Princeton Study: US No Longer An Actual Democracy"; "Study: You Have 'Near-Zero' Impact on US Policy"; "Study: Politicians listen to rich people, not you"; "Rich people rule!"

All of these stories were about a study by political scientists Martin Gilens of Princeton and Benjamin Page of Northwestern, modestly titled, "Testing Theories of American Politics: Elites, Interest Groups, and Average Citizens."

Their conclusion was explosive: "Economic elites and organized groups representing business interests have substantial independent impacts on U.S. government policy, while average citizens and mass-based interest groups have little or no independent influence."

The paper soon went viral as proof that America is an "oligarchy" (the press's term, not theirs) where the views of the rich control what happens and the views of the middle class are ignored. The authors were even on The Daily Show — not bad for academics without so much as a book to promote:

There's only one problem: Research published since then has raised serious questions about this paper, both its finding and its analysis. This is, of course, how normal science works; some academics put a finding out there, and their peers pick it apart.

But the study has become a frequently invoked piece of evidence in debates about money in politics, and the public and political debate has not kept up with the scholarly one. And the latest scholarly critiques suggest that while the rich certainly have more political influence than the middle class, ordinary Americans still win a substantial share of the time, even when the affluent oppose them.

America is an imperfect democracy, in other words — but it's hardly an oligarchy.

When the rich and middle class disagree, each wins about half the time

Since its initial release, the Gilens/Page paper's findings have been targeted in three separate debunkings. Cornell professor Peter Enns, recent Princeton PhD graduate Omar Bashir, and a team of three researchers — UT Austin grad student J. Alexander Branham, University of Michigan professor Stuart Soroka, and UT professor Christopher Wlezien — have all taken a look at Gilens and Page's underlying data and found that their analysis doesn't hold up.

Gilens and Page used a database of 1,779 policy issues — which included data on the opinions of median-income Americans, the rich, business interests, and non-business interest groups like unions or the National Rifle Association — to determine whose opinions correlated most closely with actual government policy.

But the researchers critiquing the paper found that middle-income Americans and rich Americans actually agree on an overwhelming majority of topics. Out of the 1,779 bills in the Gilens/Page data set, majorities of the rich and middle class agree on 1,594; there are 616 bills both groups oppose and 978 bills both groups favor. That means the groups agree on 89.6 percent of bills.

That leaves only 185 bills on which the rich and the middle class disagree, and even there the disagreements are small. On average, the groups' opinion gaps on the 185 bills is 10.9 percentage points; so, say, 45 percent of the middle class might support a bill while 55.9 percent of the rich support it.

Bashir and Branham/Soroka/Wlezien find that on these 185 bills, the rich got their preferred outcome 53 percent of the time and the middle class got what they wanted 47 percent of the time. The difference between the two is not statistically significant. And there are some funny examples in the list of middle-class victories. For instance, the middle class got what they wanted on public financing of elections: in all three 1990s surveys included in the Gilens data, they opposed it, while the rich favor it. That matches up with more recent research showing that wealthy people are more supportive of public election funding.

So it's hard to say definitively, based on this data, that the rich are getting what they want more than the middle class. And it's hard to claim, as Gilens and Page do, that "ordinary citizens get what they want from government only when they happen to agree with elites or interest groups that are really calling the shots." Even when they disagree with elites, ordinary citizens get what they want about half the time.

Branham, Soroka, and Wlezien also look at which specific issues spur disagreement: Do they fall down on ideological lines? Sort of, but not dramatically so. The authors find that the middle class got 26 liberal policy wins (either a bill they supported passing or one they opposed getting blocked), 20 conservative wins, and 29 ideologically neutral wins. The rich got 28 liberal wins, 26 conservative wins, and 37 neutral wins. The rich's wins are slightly more conservative on average, but not hugely so.

Okay, but maybe those conservative wins for the rich were all on issues that mattered most to the rich. Maybe the middle class wins occasionally on social issues, but the rich succeed in preventing redistribution and other economic policies they don't like.

Again, not really. The researchers found the rich’s win rate for economic issues where there's disagreement is 57.1 percent, compared with 51.1 percent for social issues. There's a difference, but not a robust one. "The win rates for the two issue types are not statistically different from one another," Branham, Soroka, and Wlezien conclude.

They also looked at the views of the poor — those at the 10th percentile of the income scale. Here, too, there's lots of agreement. The poor, middle class, and rich agree on 80.2 percent of policies. But here they find more evidence for differences in income-based representation. Bills supported just by the rich but not the poor or middle class passed 38.5 percent of the time, and those supported by just the middle class passed 37.5 percent. But policies supported by the poor and no one else passed a mere 18.6 percent of the time. "These results suggest that the rich and middle are effective at blocking policies that the poor want," the authors conclude.

"Policy ends up about where it would have been"

Bashir's paper prods at the Gilens data even more and finds a number of holes. Bashir concludes that strong support from the middle class is about as good a predictor of a policy being adopted as strong support from the rich. "In the original data set, change is enacted 47 percent of the time that median-income Americans favor it at a rate of 80 percent or more," Bashir writes. "Yet change is enacted 52 percent of the time that elites favor it at that rate."

And the two groups fare roughly as poorly when interest groups are pitted against them: "The rich get their favored outcome despite the combined opposition of [interest groups and the middle] at a rate of 32 percent; meanwhile, average Americans’ favored outcome occurs 30 percent of the time that they face combined opposition from interest groups and the wealthy. "

Bashir also notes that the Gilens and Page model explains very little. Its R-squared value is a measly 0.074. That is, 7.4 percent of variation in policy outcomes is determined by the measured views of the rich, the poor, and interest groups put together. So even if the rich control the bulk of that (and Bashir argues they do not), the absolute amount of sway over policy that represents is quite limited indeed.

Peter Enns's paper takes another approach to analyzing cases of rich versus middle-class disagreement. He notes that it's not just that the rich and middle class agree a lot; their levels of support for various policies also move in tandem. If policy A is more popular among the rich than policy B, then it's probably more popular than policy B among the middle class as well. This means the policies you'd most expect to pass, based on rich people's opinions, are also the policies you'd most expect to pass based on middle-class people's opinions. So the actual policy outcomes you'd predict based on a model where only the rich matter aren't very different from the ones you'd predict based on a model where only the middle class matters.

"Even when policy preferences differ across groups … policy ends up about where it would have been if those in the middle received the exact same representation as the wealthy," Enns concludes. "These conclusions hold when we only consider economic and social welfare policies and when we include the preferences of organized interest groups in the statistical model."

Gilens and Page's defense doesn't really rescue the argument

I reached out to Gilens and Page to see what they made of the emerging critique of their work, and in particular the one included in the Bashir and Branham/Soroka/Wlezien papers.

Gilens made four main points. First, the definition of "rich" here is "at the 90th percentile of the income distribution." Households at the 90th percentile currently make $160,000 a year. They're rich, for sure, but not superrich. It's impractical to use surveys to measure the opinions of the ultra rich (millionaires, billionaires), but Gilens argues that their opinions would diverge from the middle class more dramatically. That might be, but it's somewhat orthogonal to the claims about the influence of the 90th percentile made in the original Gilens/Page paper.

Second, he insists that the issues where the rich win despite middle-class opposition are important ones relating to redistribution and economic policy. But Branham, Soroka, and Wlezien found that win rates for the rich weren't significantly different between economic and social issues.

Third, he writes that even though the middle class and rich agree on most things, "a political system that responds to the preferences of average citizens is profoundly different from one in which average citizens get their way only when they happen to agree with the preferences of the well to-do." This is a fair point, but again, the average citizen does not only win when they agree with the well-to-do. When they disagree, they win about half the time anyway.

Finally, Gilens argues that the use of "win rates" by Branham, Soroka, and Wlezien is misleading. By focusing on whether majorities of each group support a policy, they ignore gradations in the level of support. He also takes issue with them lumping in wins that consisted of a policy not passing — pretty common in a system with strong status quo bias, like American politics — with ones that consisted of a policy passing, a much rarer event:

When the rich (but not the middle-class) favor a policy, the policy is adopted 37 percent of the time; when the middle-class (but not the rich) favor a policy, the policy is adopted 26 percent of the time. Conversely, when the rich (but not the middle-class) oppose a policy, the policy fails 74 percent of the time and when the middle-class (but not the rich) oppose a policy, the policy fails 63 percent of the time."

In other words, the tiny gap in win rates gets somewhat wider when you break it down a little. Branham, Soroka, and Wlezien say this criticism misses the point. "While the rich do slightly better when explicitly taking into account the status quo, the rich still do not dominate the middle," they note. The middle class still gets its preferred policies enacted 26 percent of the time even when the rich are opposed. The picture Gilens and Page painted of a world where the opinions of the middle class literally count for nothing doesn't hold up.

"Our argument is not that American democracy is perfect," they say in a prepared response to Gilens. "Our paper responds to a specific claim made by Gilens and Page, namely, that when a majority of citizens disagrees with economic elites or with organized interests, they generally lose." That contention, they argue, is vastly overstated.

How much does representation really matter?

The implicit argument behind the Gilens/Page paper, and of Gilens's book Affluence and Influence, is that in a democracy, there should be strong congruence between policy outcomes and the opinions of the American middle class — or, at the very least, between policy outcomes and the views of the American public as a whole.

This might seem intuitive. In a democracy, if 80 percent of people want universal health care, shouldn't there be universal health care? But this contention relies on a rather literal, and implausible, definition of democracy. As Vox's Matt Yglesias once put it, "The idea that the point of democracy is to implement legislative outcomes that are supported by broad-based surveys seems almost like a straw man dreamed up by an eighteenth-century monarchist."

Think about it. Most Americans aren't very politically engaged — and most don't want to be politically engaged, preferring that professional policymakers make decisions for them, so long as the economy stays on track. What are the odds that they've formed stable, durable opinions on dozens of highly specific policy issues?

For example, the Gilens data set includes a 1986 poll about the creation of an investment tax credit for corporations, a 2002 poll asking if the federal government spends enough on HIV/AIDS research and treatment, a 1997 poll asking whether trade agreements should be subject to a simple up-or-down vote, and a 1991 poll on whether non-bank corporations like GE should be allowed to own banks.

These are all fairly technical points that require a decent amount of background knowledge to understand, let alone develop a coherent opinion about. I write about economic policy for a living and you'd have to give me a couple of days before I had a real, informed opinion about investment tax credits. What are the odds that people whose jobs don't mandate they follow policy debates would have that kind of background knowledge? What are the odds that the 2002 respondents even knew how much the US was spending on HIV/AIDS, let alone whether that was too high or too low?

This is known in public opinion research as the problem of "non-attitudes," and while Gilens and Page do what they can to address it, it's hard to eliminate entirely.

And if you look at the times in history when government was most responsive to public opinion, it doesn't appear that responsiveness is super well-correlated with good governance. For example, Affluence and Influence finds that the nadir of representativeness was the mid-1960s, when Medicare, the war on poverty, and the Voting Rights Act were enacted; and the peak was George W. Bush's first term. Does that mean LBJ's administration was a democratic failure and Bush's was a democratic success? Or does it just suggest that the Bush administration was effective at getting highly persuadable voters to back big tax cuts and the Iraq War, rather than reflecting their wishes?

It's for reasons like this that most political theorists don't use pure representation as their test of whether a democracy is functioning well. Political theorist Andrew Sabl writes that while empirical political scientists like Gilens "assume that the normative standard for a well-functioning democracy is whether policy outcomes track public preferences," political theorists argue that the standard should be "something — as it might seem, almost anything — else."

There are "deliberative democrats," who think democracies should strive to enact the policies the people would support after calm, careful deliberation; there are small-r republicans, who measure democracies' success by the civic virtue of their residents; but you won't find basically any support for the idea that democracies should enact the people's opinions exactly as currently stated.

It's entirely possible, of course, to think the political theorists are wrong and that responsiveness really is the most important thing. These are matters of values, not of empirical truth or falsity. But strict responsiveness is not obviously the most important feature of a democracy.

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