A new study shows just how weird our American system of government turns out to be.

Republicans dominate America’s state governments — even in some of the country’s most liberal states.

Wisconsin, Florida, Ohio, and Michigan have all voted Democratic in the past two presidential elections. But Republicans have complete control over their state legislatures and governorships, paving the way for them to enact far-reaching conservative policy agendas.

A new study takes a closer look at why. Professor Steven Rogers of Saint Louis University found that voters don’t make decisions about whether to reelect their state lawmakers because of their specific policies, campaign promises, voting records, or any of the other things you’d normally expect to be relevant to their position as local lawmakers.

Republican dominance in the Wisconsin statehouse probably has more to do with President Obama than with Gov. Scott Walker’s budget plan.

That’s because the politics of statehouses turn out not to be local at all. Instead, Rogers finds there’s one major factor in deciding who controls the statehouse: the popularity of the American president.

Want to know why the past few years have been such a spectacular failure for Democrats in state politics? Look to President Obama’s approval ratings.

Voters don’t know or care about their state lawmakers

We have an idea of American democracy that goes something like this: The Constitution gives different politicians oversight over different governmental bodies, which in turn affect citizens at the national, state, and local levels.

The politicians who control these different governmental bodies are, naturally, different people. So if a state lawmaker is doing a crummy job or passing unpopular legislation, her constituents can punish her individually at the ballot box.

There’s just one problem: This seems to be not at all what really happens.

In his new study, Rogers writes that the public often has no idea what’s going on in their state legislatures, or what their state representatives are arguing about or why. They don’t even know who their representatives are.

"I mean, ask yourself, do you know who your state legislator is? Do you know what they do in their day-to-day job?" Rogers says in an interview. (I didn’t, but I also live in Washington, DC, which doesn’t have a state legislature, so at least I have an excuse.) "The answer for most people is ‘no’ and ‘no,’ so they then have to make an evaluation based on something — even if that something has little to nothing to do with what the state legislator does herself."

He notes that just 1 percent of local news is about statehouse news. The vast majority of local coverage — more than 60 percent — is instead about the presidential election, one study found.

Fewer than 20 percent of voters can identify their state legislator, according to a Vanderbilt study published in 2013. An even higher number have no opinion about whether said legislator is doing a good job.

Not knowing who your lawmaker is will make it pretty difficult to evaluate his or her work. So how are voters making up their minds?

A sad reality: presidential approval ratings drive state legislature elections

It is in this void that voters tend to focus on something else altogether: what they think of the president.

It’s not that voters’ perceptions of the state legislatures themselves are completely irrelevant. Voters are about 6 percent more likely to vote against their state lawmaker if they disapprove of their state legislature, and they’re about 9 percent more likely to do so if they disapprove of their governor.

But the president’s popularity was way, way more important in shaping outcomes for state lawmakers.

Democrats have gotten creamed in statehouses during Obama’s tenure.

Rogers looked at a big data set of online polling from the 2008, 2010, and 2012 elections. He found that voters were more than 40 percent more likely to vote against their state lawmaker if they disapproved of the president. (That controlled for the pull of partisanship, or voting against a lawmaker because he or she is a member of the opposition party, according to Rogers.) Overall, attitudes toward the presidency were more than three times more important for a legislator’s reelection bid than attitudes toward the state legislature itself.

Now, there’s no point at which the unpopularity of a president automatically dooms his party’s state legislators to defeat. But Rogers’s data makes clear that voters are reacting to the presidency when they cast their ballot for these positions, even though they don’t have any bearing on what happens inside the White House.

A chart from Rogers’s study shows that voters don’t distinguish much between US House and US statehouse elections.

A state lawmaker’s fate is basically out of his or her hands

And it’s not just about who the public decides to support once in the voting booth. Even earlier in the process, it turns out that state legislators are much more likely to face a challenge at all if they belong to the party of an unpopular president. (This turns out to be a big deal because only 33 percent of them get challenged at all.)

This is somehow still true even when the president is not on the ballot. Presidential approval ratings are about as crucial for state lawmakers even in midterm elections, according to Rogers. And it’s not just the Obama administration — Rogers looked at data going back decades.

"This happens across every president," he says. "The relationship between presidential approval and seat change emerges for pretty much any set of elections since we have been measuring presidential approval."

Simply being a member of the president’s party increases the odds that state legislators will get a challenger by about 4 percent. By comparison, overseeing 4 percent growth in your state’s economy — a feat in only a tiny handful of states — increases your chances of avoiding a challenger by just 4 percent.

So if a state lawmaker helps unleash massive economic growth at home, that’s about as useful as simply not being a member of the president’s party — at least in terms of his or her reelection prospects.

This all makes for a rather grim conclusion. As Rogers notes: "State legislators have relatively little control over their own elections."

Why this matters: Statehouse policy is incredibly important

As Vox’s Matt Yglesias has written, Democrats have been getting clobbered across statehouses in the Obama era. A full 70 percent of state legislatures are currently in Republican hands.

In his story, Yglesias ran down some of the ways Republicans' grip on the statehouse has enabled them to enact key parts of their policy agenda:

Republicans have unified control of 25 states. Along with the usual set of tax cuts for high-income individuals and business-friendly regulations, the result has been: — An unprecedented wave of restrictions on abortion rights. — The spread of union-hostile "right to work" laws into the Great Lakes states. — New curbs on voting rights, to further tilt the electorate in a richer, whiter, older direction. — Large-scale layoffs of teachers and other public sector workers who are likely to support Democrats.

So the stakes are enormous. Most stories explain Republicans’ advantage by pointing to things like conservatives’ outsize funding edge, helped by groups like the Koch network, and a lack of down-ballot Democratic talent. Yglesias identified a few more reasons for the disparity, including Republicans’ ideological flexibility and Democratic complacency and overconfidence in their president.

But Rogers’s new data points to the president’s popularity as the single crucial factor. This is where Rogers’s research is really breaking new ground: The key for Democrats to regain the state legislatures may rest on President Obama’s popularity.

That may be dispiriting news for a state senator who is eagerly looking at the best yard signs to get out ahead of Election Day. But with Obama’s approval ratings finally beginning to tick up, maybe it’s not such bad news for Democratic lawmakers after all.

The bad map we see every presidential election