If there's anything that progressives believe without question, it's that money badly corrupts American politics. Most also think the problem has become exponentially worse since the Supreme Court's Citizens United decision opened the door to a flood of additional money by unregulated (and often anonymous) individual and institutional donors. The result is rank corruption, as the super-rich mold our politics to benefit themselves and screw everyone else.

What we thus need is a constitutional amendment to overturn Citizens United and institute the public financing of political campaigns so that politicians can be freed up to do what's best for the public and not what's best for those holding the cash.

It's a powerful story, and one that has always seemed right to me.

But is it true?

At the congressional level, it might well be. Running for the House and Senate is expensive, and so politicians need to fundraise constantly. And that opens the door to various forms of influence-peddling among legislators. As Nicholas Kristof notes, at least one academic study has documented evidence that the preferences of ordinary citizens matter much less in policymaking than the desires of wealthy individuals and business groups.

But on the presidential level? There the evidence is far less conclusive, with recent history seeming to demonstrate that money accomplishes far less than one might assume. It's not that wealthy, lavishly spending donors don't influence what presidential candidates say and do. It's that they appear not to exercise much influence on how citizens vote.

Take the money spent by Republican candidates so far in this election cycle. NBC News tells us that Jeb Bush and Marco Rubio together have so far spent, via their campaigns and outside groups, an astonishing $91 million on ads. The result? They're languishing at a combined 16.4 percent in the polls nationally, 15.7 percent in Iowa, and 19.1 percent in New Hampshire.

Donald Trump and Ted Cruz, meanwhile, are polling at a combined 53.6 percent nationally, 54.3 percent in Iowa, and 43.7 percent in New Hampshire. Their total expenditures on ads? Just $8 million.

A political scientist would say that this makes money a variable that lacks much explanatory power at all.

Lest you think this is just a function of the unusually intense anti-establishment fervor of the 2016 election, consider the fact that the notorious Koch brothers spent over $400 million in 2011 and 2012 trying to defeat Barack Obama and help Republicans take control of Congress. The result? An Obama victory and gains for Democrats in both the House and Senate.

More recently, the Kochs put their thumbs on the scale in the GOP presidential primaries by throwing money at Scott Walker — a man who, after some high-profile gaffes and a string of mediocre debate performances, became the first major candidate to drop out of the race.

What explains the inability of money to decisively shape public opinion? For one thing, social media has empowered candidates to communicate with voters, both directly and by way of the more traditional media, which eagerly follows an online buzz once it starts and grows to a critical mass. Just ask Donald Trump — a candidate who had more of his own money to spend than anyone else and who, thanks to a six-month barrage of tweets and outrageous comments to media outlets, managed to buy himself the equivalent of a billion-dollar's worth of free advertising.

But that isn't a sufficient explanation. For that we need to remember the old adage immortalized by the Beatles: Money (and attention) can't buy you love. Trump might have tweeted up a storm and been ignored, or been treated by likely voters as the sideshow that so many commentators originally took his campaign to be. Instead, they liked what they heard from him and rallied to his side.

All the money and tweets in the world won't matter if the people don't like the message and the messenger. (I'm looking at you, Jeb and Marco.)

This is a crucially important point for progressives — because they need to get this right. The case for regulating and limiting money in politics needs to be based on facts. It might seem wrong in some abstract sense for a small group of people or families to be permitted to spend their fortunes on funding their preferred presidential contenders. But if that money is largely ineffective, reform efforts should be directed elsewhere.

Like, for instance, at the role that money plays in influencing the voting patterns of individual legislators. Tracing that influence, demonstrating it to the public, and then devising laws (and perhaps a constitutional amendment) that could prevent it isn't as sexy as writing splashy exposes about eccentric billionaires lobbing money at a handful of presidential candidates.

But it just might stand a better chance of making a positive difference.