There's a fun "what if" game that people like to play with politics — particularly at the presidential level. You've probably seen some examples. For example, a "what if only white men voted in 2012" map that shows nearly every locale in dark red, with a few pockets of blue on the coasts. It's an interesting thought experiment that says more about the demographic than anything, but of course, doesn't tell us much about who is going to win elections.

A variant of the "what if" idea was articulated by Fox Business's Stuart Varney on Thursday. Talking about food stamps on Fox News, he said: "This is redistribution. This is the administration taking from this group, giving to that group — essentially buying votes." What if, in other words, Democrats didn't "buy votes" from the poor by supplementing their incomes with food assistance?

We've heard this argument before, many times, including most famously from candidate Mitt Romney on discreetly recorded videotape in 2012. Romney's argument was a little different — about how 47 percent of Americans don't pay taxes and were in the tank for President Obama for economic reasons — but the idea is largely the same: Economics drives election results.

Here's the thing, though. There's literally no link between the population of people on food stamps in a state and how that state votes. We pulled House data in every state for 2010, 2012 and 2014, averaged the margin of victory for each state and compared it to the percentage of the population on food stamps.

Here's 2010 (colored red because it was a strong House election cycle for Republicans).

If Varney were right, you'd expect to see a more obvious line headed from the lower left portion of the graph (low use of the Supplemental Nutrition Assistance Program -- a.k.a. food stamps -- and more Republican votes) to the upper right (more SNAP, more Democratic votes). But you don't. It's a broad cloud of points, all over the map. Mathematically, there's no correlation -- and in part, that's due to high rates of food stamp use in the South.

If we look at 2012, shortly after food stamp use surged (thanks almost entirely to the recession), it looks like this:

That's more like what Varney imagines. More SNAP use (note how much further to the right the dots go), and a more Democratic-leaning vote.

But any assumption that there's a causal link between the two should be undermined by a look at 2014.

In 2014, SNAP use (using data from the Department of Agriculture) hadn't changed much, but votes shifted more Republican.

Why? Because of the electorate, of course. The Democrats got more votes in 2012 because more Democrats voted. They got fewer in 2014 because turnout among Democrats was lower (among other things, of course).

Did welfare recipients make the difference in 2012? It's very hard to make that case. If you look at exit poll data for those in the lowest income bracket in the survey — people making $30,000 a year or less — eliminating them from voting entirely would have swung the 2012 results in a few states, including prizes like Florida and Ohio. But there are many caveats involved (the first being that you can't just eliminate an entire demographic group). Exit poll data is an approximation that gets less specific as it gets more granular. And besides, not everyone who earns below $30,000 a year is on SNAP, so excluding that group across the board — the best estimate we can get! — doesn't really tell us anything concrete.

And then there's the fact that this group routinely votes heavily for Democrats anyways. The 63 percent of the vote Obama took in this demographic was down five points from his showing in 2008 — before the alleged "vote-buying" began — and on par with John Kerry's 62 percent in 2004.

In addition, earlier this year, Pew Research Center unveiled a study showing that poorer Americans are much less likely to vote than wealthier ones. There are lots of reasons for this, too, including having less disposable time and generally less-stable living conditions.

If the Democrats' strategy is to ply those people with food stamps to get them to the polls, there's very little sign that it is working. At all.