Everybody knows that money buys elections. That's what opponents of the Citizens United decision have been ominously warning us for six years, and their message resonates. A CNN poll found that 67 percent of Americans think that "elections are generally for sale to the candidate who can raise the most money."

The trouble is that there is very little evidence for this. Even though the candidate with the most money usually wins, the general rule is that money chases winners rather than creates winners. People give to candidates they think are likely to win, and incumbents (who almost always win) and candidates in safe districts still raise money, even if they're not challenged. On the flip side, donors and parties don't waste support on long-shot races.

More importantly, money never guarantees any election. For instance, billionaire Meg Whitman spent $144 million of her own money on the California governor's race; Jerry Brown spent just $36 million but crushed Whitman, 53 percent to 40 percent.

Mitt Romney, the GOP, and their PACs outspent Barack Obama and friends by over $120 million, and we know what came of that. Anthony Brown (D) outspent Larry Hogan (R) almost five to one in the 2014 Maryland governor's race and lost, in a state that is two to one Democrat.

We can likely add Jeb Bush's candidacy to this list. The Jeb! campaign and pro-Jeb groups have collectively raised $155 million. Only Hillary Clinton has raised more. According to the New York Times, he's dominating "the money race" among Republicans.

But in the actual race, he got a dismal sixth place in Iowa, with 2.8 percent of the vote. Polls put Jeb fifth in New Hampshire and fifth nationally. Currently, Betfair places his odds of winning the nomination at 5.2 percent.

In fact, the whole Republican race shows that money can't simply buy votes. Scott Walker raised $34 million in three months, spent all of it — and then dropped out, five months before Iowa. Meanwhile, Donald Trump has dominated news coverage and polls for months with only $19 million.

When you plot money vs. poll numbers, what jumps out is how little correlation there is:

... And money vs. Iowa caucus votes:

... And money vs. odds of winning the nomination:

Jeb and Jeb-PACs have spent $89.1 million so far and received 5,238 votes — over $17,000 per vote received. Trump has spent just $300 per vote.

This is not to say that money doesn't matter — you can't run a campaign without it, and campaign finance laws are designed to make it difficult for upstart challengers to become competitive. But after a certain amount (about $500,000 for a typical congressional race), there are rapidly diminishing returns, and dumping more money on a failing campaign will not save it.

There's a lot of baseless fears about free speech, but the idea that the people with the most expensive microphone will always get their way is one of the easiest to disprove. More speech, more discussion, and more competition in the field of ideas is not what's wrong with American politics — but they might be part of the solution to it.